%%% -*-BibTeX-*- %%% ==================================================================== %%% BibTeX-file{ %%% author = "Nelson H. F. Beebe", %%% version = "3.03", %%% date = "01 April 2003", %%% time = "08:36:27 MST", %%% filename = "toms.bib", %%% address = "Center for Scientific Computing %%% University of Utah %%% Department of Mathematics, 110 LCB %%% 155 S 1400 E RM 233 %%% Salt Lake City, UT 84112-0090 %%% USA", %%% telephone = "+1 801 581 5254", %%% FAX = "+1 801 581 4148", %%% URL = "http://www.math.utah.edu/~beebe", %%% checksum = "15603 28963 125580 1232167", %%% email = "beebe at math.utah.edu, beebe at acm.org, %%% beebe at computer.org, beebe at ieee.org %%% (Internet)", %%% codetable = "ISO/ASCII", %%% keywords = "bibliography, mathematical software, TOMS", %%% supported = "yes", %%% docstring = "This is a BibTeX bibliography for ACM %%% Transactions on Mathematical Software (TOMS) %%% (CODEN ACMSCU, ISSN 0098-3500), completely %%% covering all issues from March 1975 -- date. %%% All papers, including editorials, policy %%% statements, remarks, and corrigenda are %%% included. %%% %%% The ACM maintains World Wide Web pages with %%% journal tables of contents for 1985--date at %%% %%% http://www.acm.org/dl/toc.html %%% http://www.acm.org/toms/ %%% http://www.acm.org/pubs/contents/journals/toms/ %%% %%% Source code for all ACM Algorithms from 1960 %%% to date is available at %%% %%% http://www.acm.org/calgo/contents/ %%% %%% That data has been automatically converted to %%% BibTeX form, corrected for spelling and page %%% number errors, and merged into this file. %%% %%% At version 3.03, the complete year coverage %%% looks like this: %%% %%% 1960 ( 1) 1975 ( 38) 1990 ( 33) %%% 1961 ( 1) 1976 ( 49) 1991 ( 41) %%% 1962 ( 1) 1977 ( 46) 1992 ( 36) %%% 1963 ( 2) 1978 ( 43) 1993 ( 37) %%% 1964 ( 2) 1979 ( 54) 1994 ( 38) %%% 1965 ( 1) 1980 ( 57) 1995 ( 31) %%% 1966 ( 1) 1981 ( 47) 1996 ( 33) %%% 1967 ( 1) 1982 ( 34) 1997 ( 31) %%% 1968 ( 1) 1983 ( 43) 1998 ( 30) %%% 1969 ( 2) 1984 ( 46) 1999 ( 28) %%% 1970 ( 2) 1985 ( 40) 2000 ( 33) %%% 1971 ( 1) 1986 ( 34) 2001 ( 21) %%% 1972 ( 4) 1987 ( 29) 2002 ( 24) %%% 1973 ( 2) 1988 ( 40) 2003 ( 5) %%% 1974 ( 7) 1989 ( 32) %%% %%% Article: 1081 %%% Misc: 1 %%% %%% Total entries: 1082 %%% %%% Abstracts, Keywords, Categories and Subject %%% Descriptors are available for some issues. %%% Eventually, this coverage should be %%% extended to the entire collection, in the %%% interests of enhancing search capabilities. %%% %%% This bibliography includes ACM Algorithms %%% 493 -- 735 (or the latest), including %%% Algorithm 568, published in ACM %%% Transactions on Programming Languages and %%% Systems (TOPLAS). For ACM Algorithms 1 -- %%% 492, see the companion bibliographies, %%% cacm1960.bib and cacm1970.bib. %%% %%% All published Remarks and Corrigenda are %%% cross-referenced in both directions, so %%% that citing a paper will automatically %%% generate citations for those Remarks and %%% Corrigenda. There is one important paper, %%% on multiple-precision integer division, %%% included from the journal Software --- %%% Practice and Experience because it is %%% cross-referenced to a TOMS paper. %%% %%% Algorithms published in Communications of %%% the ACM, prior to the founding of TOMS in %%% 1975, are also included in this %%% bibliography, if a TOMS paper contains %%% Remarks or Corrigenda for them. %%% %%% Source code for ACM Algorithms from 380 %%% onwards, with some omissions, is available %%% via netlib, and via anonymous ftp to %%% %%% ftp://netlib.bell-labs.com/netlib/toms %%% %%% ACM also markets a CD-ROM containing %%% algorithms 495 (March 1975) through 798 %%% (December 1999): the ``CALGO Special Edition %%% CD'', organized as a Web site (see entry %%% ACM:2002:CSE at the end of this file). %%% %%% The initial draft of entries for 1981 -- 1990 %%% was extracted from the ACM Computing Archive %%% CD ROM for the 1980s, with manual corrections %%% and additions from bibliographies in the TeX %%% User Group collection, the author's personal %%% bibliography files, Aake Bjoerck's %%% %%% ftp://math.liu.se/pub/references/habook.bib %%% %%% G. W. Stewart's %%% %%% ftp://thales.cs.umd.edu/pub/references/ref.bib %%% %%% John R. Rice and Richard J. Hanson's %%% Algorithm 620 (available as a BibTeX file via %%% netlib, with additions up to Algorithm 678), %%% and the very large Karlsruhe computer science %%% bibliography collection at %%% %%% ftp://ftp.ira.uka.de/pub/bibliography/ %%% %%% to which many people of have contributed. %%% %%% Math Review MRclass and MRnumber values for %%% 341 entries were supplied from a search of %%% the American Mathematical Society's %%% MathSciNet database for version 2.26 %%% [06-Dec-1996]. That search also turned up %%% a few small errors in author names and %%% title words; they have been corrected to %%% match the original journal articles. %%% %%% Numerous errors in the sources noted above %%% have been corrected. Spelling has been %%% verified with the UNIX spell and GNU ispell %%% programs using the exception dictionary %%% stored in the companion file with extension %%% .sok. %%% %%% Numerous heuristic checks on the validity %%% of the TOMS bibliography files have also %%% been made using software developed by the %%% author for maintenance of the TeX Users %%% Group and BibNet bibliography collections. %%% %%% Every entry from March 1975 -- June 1994 %%% has been compared directly with the article %%% cover pages in the original journal issues %%% to ensure correctness. Several errors were %%% uncovered this way in earlier sources of %%% BibTeX entries and citation data. %%% %%% Considerable effort has been expended to %%% ensure accuracy of this bibliography, %%% because it is expected to be widely used %%% and distributed. Capitalization of %%% original titles, and use of initials or %%% full names in author lists, should match %%% the journal exactly, with two exceptions. %%% (1) Algorithms have been sometimes entitled %%% ``ALGORITHM xyz...'', and sometimes %%% ``Algorithm xyz...''. The latter usage has %%% been adhered to throughout. (2) Remarks %%% and Corrigenda in the journal occasionally %%% fail to cite the full title of the original %%% paper; that has been rectified in the %%% interests of clarity and consistency. %%% %%% ACM copyrights explicitly permit abstracting %%% with credit, so article abstracts, keywords, %%% and subject classifications have been %%% included in this bibliography wherever %%% available. Article reviews have been %%% omitted, until their copyright status has %%% been clarified. %%% %%% bibsource keys in the bibliography entries %%% below indicate the entry originally came %%% from the computer science bibliography %%% archive, even though it has likely since %%% been corrected and updated. %%% %%% URL keys in the bibliography point to %%% World Wide Web locations of additional %%% information about the entry. %%% %%% BibTeX citation tags are uniformly chosen %%% as name:year:abbrev, where name is the %%% family name of the first author or editor, %%% year is a 4-digit number, and abbrev is a %%% 3-letter condensation of important title %%% words. Citation tags were automatically %%% generated by software developed by the %%% author for the BibNet Project. %%% %%% In this bibliography, entries are sorted %%% by journal, and then by publication order, %%% with the help of ``bibsort -byvolume''. The %%% bibsort utility is available from %%% %%% ftp://ftp.math.utah.edu/pub/bibsort %%% %%% The author will be grateful for reports of %%% errors of any kind in this bibliography. %%% %%% The checksum field above contains a CRC-16 %%% checksum as the first value, followed by the %%% equivalent of the standard UNIX wc (word %%% count) utility output of lines, words, and %%% characters. This is produced by Robert %%% Solovay's checksum utility." %%% } %%% ==================================================================== @Preamble{"\input bibnames.sty" # "\hyphenation{ Cher-kas-sky Cue-vas Ka-chit-vich-yan-u-kul Rich-ard Za-bo-row-ski }" } %%% ==================================================================== %%% Acknowledgement abbreviations: @String{ack-nhfb = "Nelson H. F. Beebe, Center for Scientific Computing, University of Utah, Department of Mathematics, 110 LCB, 155 S 1400 E RM 233, Salt Lake City, UT 84112-0090, USA, Tel: +1 801 581 5254, FAX: +1 801 581 4148, e-mail: \path|beebe@math.utah.edu|, \path|beebe@acm.org|, \path|beebe@computer.org|, \path|beebe@ieee.org| (Internet), URL: \path|http://www.math.utah.edu/~beebe/|"} @String{ack-kr = "Karin Remington, Celera Genomics 45 West Gude Drive Rockville, Maryland 20850 Tel: +1 240 453-3038 FAX: +1 240 453-4375 e-mail: \path|remingka@celera.com|"} @String{ack-nj = "Norbert Juffa, 2445 Mission College Blvd. Santa Clara, CA 95054 USA email: \path=norbert@iit.com="} @String{ack-rfb = "Ronald F. Boisvert, Applied and Computational Mathematics Division, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA, Tel: +1 301 975 3812, e-mail: \path=boisvert@cam.nist.gov="} %%% ==================================================================== %%% Journal abbreviations: @String{j-CACM = "Communications of the ACM"} @String{j-SPE = "Soft{\-}ware\emdash Prac{\-}tice and Experience"} @String{j-TOMS = "ACM Transactions on Mathematical Software"} @String{j-TOPLAS = "ACM Transactions on Programming Languages and Systems"} %%% ==================================================================== %%% Bibliography entries from Communications of the ACM. @Article{Ellenberger:1960:NSP, author = "K. W. Ellenberger", title = "{ACM Algorithm 30}: Numerical Solution of the Polynomial Equation", journal = j-CACM, volume = "3", number = "12", pages = "643--643", month = dec, year = "1960", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Fri Feb 07 16:37:16 1997", note = "See also \cite{Novotny:1985:RNS}.", } @Article{Herndon:1961:SNF, author = "J. R. Herndon", title = "{ACM Algorithm 49}: Spherical {Neumann} Function", journal = j-CACM, volume = "4", number = "4", pages = "179--179", month = apr, year = "1961", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Thu Sep 08 09:47:50 1994", note = "See also \cite{Coleman:1978:RSN}.", } @Article{Merner:1962:CEI, author = "J. N. Merner", title = "{ACM Algorithm 149}: Complete Elliptic Integral", journal = j-CACM, volume = "5", number = "12", pages = "605--605", month = dec, year = "1962", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Thu Sep 08 09:47:50 1994", note = "See also \cite{Skovgaard:1978:RCE}.", } @Article{Ludwig:1963:IBR, author = "O. G. Ludwig", title = "{ACM Algorithm 179}: Incomplete Beta Ratio", journal = j-CACM, volume = "6", number = "6", pages = "314--314", month = jun, year = "1963", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Thu Sep 08 09:47:50 1994", note = "See also \cite{Pike:1976:RIB}.", } @Article{Kase:1963:TOP, author = "R. H. Kase", title = "{ACM Algorithm 219}: Topological Ordering for {Pert} Networks", journal = j-CACM, volume = "6", number = "12", pages = "738--739", month = dec, year = "1963", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Thu Sep 08 09:47:51 1994", note = "See also \cite{Tenney:1977:RTO}.", } @Article{Gautschi:1964:BFF, author = "W. Gautschi", title = "{ACM Algorithm 236}: {Bessel} Functions of the First Kind", journal = j-CACM, volume = "7", number = "8", pages = "479--480", month = aug, year = "1964", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Thu Sep 08 09:47:54 1994", note = "See also \cite{Skovgaard:1975:RBF}.", } @Article{Boothroyd:1964:G, author = "J. Boothroyd", title = "{ACM Algorithm 246}: {Graycode}", journal = j-CACM, volume = "7", number = "12", pages = "701--701", month = dec, year = "1964", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Sat Sep 10 09:12:22 1994", note = "See also \cite{Misra:1975:RG,Er:1985:RG}.", } @Article{Gautschi:1965:LFA, author = "W. Gautschi", title = "{ACM Algorithm 259}: {Legendre} Functions for Arguments Larger than One", journal = j-CACM, volume = "8", number = "8", pages = "488--492", month = aug, year = "1965", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Thu Sep 08 09:47:54 1994", note = "See also \cite{Jansen:1977:RLF}.", } @Article{Fletcher:1966:ITB, author = "W. Fletcher", title = "{ACM Algorithm 284}: Interchange of Two Blocks of Data", journal = j-CACM, volume = "9", number = "5", pages = "326--326", month = may, year = "1966", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Thu Sep 08 09:47:54 1994", note = "See also \cite{Ito:1976:RIT}.", } @Article{Hill:1967:CSI, author = "I. D. Hill and M. C. Pike", title = "{ACM Algorithm 299}: Chi-Squared Integral", journal = j-CACM, volume = "10", number = "4", pages = "243--244", month = apr, year = "1967", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Thu Sep 08 09:47:54 1994", note = "See also \cite{elLozy:1976:RAC,Hill:1985:RCS}.", } @Article{Bell:1968:NRD, author = "J. R. Bell", title = "{ACM Algorithm 334}: Normal Random Deviates", journal = j-CACM, volume = "11", number = "7", pages = "498--498", month = jul, year = "1968", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Thu Sep 08 09:47:54 1994", note = "See also \cite{Tracht:1982:RNR}.", acknowledgement = ack-nhfb, } @Article{Morris:1969:TP, author = "J. Morris", title = "{ACM Algorithm 346}: ${F}$-Test Probabilities", journal = j-CACM, volume = "12", number = "3", pages = "184--185", month = mar, year = "1969", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Thu Sep 08 09:47:54 1994", note = "See also \cite{Cormack:1988:RTP}.", } @Article{TadeudeMedeiros:1969:APF, author = "A. {Tadeu de Medeiros} and G. Schwachheim", title = "{Algorithm 349}: Polygamma functions with arbitrary precision", journal = j-CACM, volume = "12", number = "4", pages = "213--214", month = apr, year = "1969", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Fri Jun 16 10:30:24 2000", note = "See certification \cite{Lewis:1975:CPF}.", acknowledgement = ack-nhfb, classcodes = "C7300 (Natural sciences computing)", corpsource = "Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, Brazil", keywords = "mathematics; subroutines", } @Article{Hill:1970:SD, author = "G. W. Hill", title = "{ACM Algorithm 395}: {Student}'s $t$-Distribution", journal = j-CACM, volume = "13", number = "10", pages = "617--619", month = oct, year = "1970", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Thu Sep 08 09:47:54 1994", note = "See also \cite{elLozy:1979:RAS,Hill:1981:RSD}.", } @Article{Hill:1970:SQ, author = "G. W. Hill", title = "{ACM Algorithm 396}: {Student}'s $t$-Quantiles", journal = j-CACM, volume = "13", number = "10", pages = "619--620", month = oct, year = "1970", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Thu Apr 29 15:20:10 1999", note = "See remarks \cite{Hill:1981:RSD,Hill:1981:RSQ,elLozy:1979:RAS}.", acknowledgement = ack-nhfb, } @Article{McNamee:1971:SMP, author = "J. M. McNamee", title = "{ACM Algorithm 408}: {A} Sparse Matrix Package (Part {I})", journal = j-CACM, volume = "14", number = "4", pages = "265--273", month = apr, year = "1971", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Thu Sep 08 09:47:54 1994", note = "See also \cite{Sipala:1977:RSM,Gustavson:1978:RSM,Harms:1980:RSM}.", } @Article{Gentleman:1972:CCQ, author = "W. M. Gentleman", title = "{ACM Algorithm 424}: {Clenshaw-Curtis} Quadrature", journal = j-CACM, volume = "15", number = "5", pages = "353--355", month = may, year = "1972", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Thu Sep 08 09:47:54 1994", note = "See also \cite{Geddes:1979:RCC}.", } @Article{Akima:1972:ISC, author = "H. Akima", title = "{ACM Algorithm 433}: Interpolation and Smooth Curve Fitting Based on Local Procedures", journal = j-CACM, volume = "15", number = "10", pages = "914--918", month = oct, year = "1972", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Thu Sep 08 09:47:55 1994", note = "See also \cite{Anderson:1976:RIS}.", } @Article{March:1972:EPT, author = "D. L. March", title = "{ACM Algorithm 434}: Exact Probabilities for ${R\times{C}}$ Contingency Tables", journal = j-CACM, volume = "15", number = "11", pages = "991--992", month = nov, year = "1972", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Fri Sep 09 14:13:19 1994", note = "See also \cite{Boulton:1976:REP}.", } @Article{Fullerton:1972:MIG, author = "W. Fullerton", title = "{ACM Algorithm 435}: Modified Incomplete Gamma Function", journal = j-CACM, volume = "15", number = "11", pages = "993--995", month = nov, year = "1972", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Thu Sep 08 09:47:55 1994", note = "See also \cite{Schoene:1978:RMI}.", } @Article{MacHura:1973:RFM, author = "M. MacHura and A. Mulawa", title = "{ACM Algorithm 450}: {Rosenbrock} Function Minimization", journal = j-CACM, volume = "16", number = "8", pages = "482--483", month = aug, year = "1973", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Thu Sep 08 09:47:55 1994", note = "See also \cite{Davies:1976:RRF}.", } @Article{Brenner:1973:MTP, author = "N. Brenner", title = "{ACM Algorithm 467}: Matrix Transposition in Place", journal = j-CACM, volume = "16", number = "11", pages = "692--694", month = nov, year = "1973", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Thu Sep 08 09:47:55 1994", note = "See also \cite{Leathers:1979:RAS}.", } @Article{Akima:1974:BIS, author = "H. Akima", title = "{ACM Algorithm 474}: Bivariate Interpolation and Smooth Surface Fitting Based on Local Procedures", journal = j-CACM, volume = "17", number = "1", pages = "26--31", month = jan, year = "1974", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Thu Sep 08 09:47:56 1994", note = "See also \cite{Anderson:1979:RBI}.", } @Article{Loeser:1974:SPT, author = "R. Loeser", title = "Some Performance Tests of `Quicksort' and Descendants", journal = j-CACM, volume = "17", number = "3", pages = "143--152", month = mar, year = "1974", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Thu Apr 29 15:23:43 1999", note = "See remark \cite{Mackay:1977:RPT}.", } @Article{Wright:1974:VSP, author = "T. Wright", title = "{ACM Algorithm 475}: Visible Surface Plotting Program", journal = j-CACM, volume = "17", number = "3", pages = "152--155", month = mar, year = "1974", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Thu Sep 08 09:47:57 1994", note = "See also \cite{Duta:1976:RVS,vanSwieten:1979:RAV}.", } @Article{Page:1974:MST, author = "R. L. Page", title = "{ACM Algorithm 479}: {A} Minimal Spanning Tree Clustering Method", journal = j-CACM, volume = "17", number = "6", pages = "321--323", month = jun, year = "1974", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Thu Sep 08 09:47:57 1994", note = "See also \cite{White:1976:RMS}.", } @Article{Watkins:1974:MTD, author = "S. L. Watkins", title = "{ACM Algorithm 483}: Masked Three-Dimensional Plot Program with Rotations", journal = j-CACM, volume = "17", number = "9", pages = "520--523", month = sep, year = "1974", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Thu Sep 08 09:47:57 1994", note = "See also \cite{Feinstein:1975:RMT}.", } @Article{Veillon:1974:NIL, author = "F. Veillon", title = "{ACM Algorithm 486}: Numerical Inversion of {Laplace} Transform", journal = j-CACM, volume = "17", number = "10", pages = "587--589", month = oct, year = "1974", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Thu Sep 08 09:47:57 1994", note = "See also \cite{Koppelaar:1976:RNI,Veillon:1977:RNI}.", } @Article{Pomeranz:1974:ECD, author = "J. Pomeranz", title = "{ACM Algorithm 487}: Exact Cumulative Distribution of the {Kolmogorov-Smirnov} Statistic for Small Samples", journal = j-CACM, volume = "17", number = "12", pages = "703--704", month = dec, year = "1974", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Thu Sep 08 09:47:57 1994", note = "See also \cite{Pomeranz:1976:REC}.", } @Article{Floyd:1975:ASF, author = "R. W. Floyd and R. L. Rivest", title = "{ACM Algorithm 489}: The Algorithm {SELECT} --- for Finding the $i{\rm th}$ Smallest of $n$ Elements", journal = j-CACM, volume = "18", number = "3", pages = "173--173", month = mar, year = "1975", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Wed Dec 04 12:25:43 1996", note = "See also \cite{Brown:1976:RAS}.", } @Article{Ginsberg:1975:DFR, author = "E. S. Ginsberg and D. Zaborowski", title = "{ACM Algorithm 490}: The Dilogarithm Function of a Real Argument", journal = j-CACM, volume = "18", number = "4", pages = "200--202", month = apr, year = "1975", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Thu Sep 08 09:47:57 1994", note = "See also \cite{Morris:1976:RDF}.", } %%% ==================================================================== %%% Bibliography entries from Software---Practice and Experience @Article{BrinchHansen:1994:MLD, author = "Per {Brinch Hansen}", title = "Multiple-length Division Revisited: a Tour of the Minefield", journal = j-SPE, volume = "24", number = "6", pages = "579--601", month = jun, year = "1994", CODEN = "SPEXBL", ISSN = "0038-0644", bibdate = "Thu Apr 29 15:16:58 1999", note = "This paper derives an algorithm for division of long integers, and implements it as a literate program, although without identifier cross-references. See also related work \cite{Regener:1984:MID} on division.", acknowledgement = ack-nhfb, } %%% ==================================================================== %%% Bibliography entries from ACM Transactions on Mathematical Software. @Article{Rice:1975:PS, author = "John R. Rice", title = "Purpose and Scope", journal = j-TOMS, volume = "1", number = "1", pages = "1--3", month = mar, year = "1975", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Sep 05 21:29:05 1994", URL = "http://doi.acm.org/10.1145/355626.355627", } @Article{Anonymous:1975:ADS, author = "{Anonymous}", title = "Algorithms Distribution Service", journal = j-TOMS, volume = "1", number = "1", pages = "4--4", month = mar, year = "1975", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Sep 05 21:29:05 1994", URL = "http://doi.acm.org/10.1145/355626.355628", } @Article{Fosdick:1975:AP, author = "Lloyd D. Fosdick", title = "Algorithms Policy", journal = j-TOMS, volume = "1", number = "1", pages = "5--6", month = mar, year = "1975", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Sep 05 21:29:05 1994", URL = "http://doi.acm.org/10.1145/355626.355629", } @Article{Anonymous:1975:PMS, author = "{Anonymous}", title = "Papers from {Mathematical Software II}", journal = j-TOMS, volume = "1", number = "1", pages = "7--12", month = mar, year = "1975", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Sep 05 21:29:05 1994", URL = "http://doi.acm.org/10.1145/355626.355630", } @Article{Cody:1975:FPS, author = "W. J. Cody", title = "The {FUNPACK} Package of Special Function Subroutines", journal = j-TOMS, volume = "1", number = "1", pages = "13--25", month = mar, year = "1975", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Aug 26 23:44:16 1994", URL = "http://doi.acm.org/10.1145/355626.355631", acknowledgement = ack-nhfb, } @Article{Jenkins:1975:PTP, author = "M. A. Jenkins and J. F. Traub", title = "Principles for Testing Polynomial Zerofinding Programs", journal = j-TOMS, volume = "1", number = "1", pages = "26--34", month = mar, year = "1975", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "68A10 (65H05)", MRnumber = "53 #2009", bibdate = "Fri Aug 26 23:44:16 1994", URL = "http://doi.acm.org/10.1145/355626.355632", acknowledgement = ack-nhfb, reviewer = "James Howland", } @Article{Parlett:1975:ICC, author = "B. N. Parlett and Y. Wang", title = "The Influence of the Compiler on the Cost of Mathematical Software\emdash in Particular on the Cost of Triangular Factorization", journal = j-TOMS, volume = "1", number = "1", pages = "35--46", month = mar, year = "1975", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Aug 26 23:35:13 1994", URL = "http://doi.acm.org/10.1145/355626.355633", acknowledgement = ack-nhfb, keywords = "cs; lud; nla; software", } @Article{Glover:1975:RWA, author = "Fred Glover and Darwin Klingman", title = "Real World Applications of Network Related Problems and Breakthroughs in Solving Them Efficiently", journal = j-TOMS, volume = "1", number = "1", pages = "47--55", month = mar, year = "1975", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Aug 26 23:44:16 1994", URL = "http://doi.acm.org/10.1145/355626.355634", acknowledgement = ack-nhfb, } @Article{Ng:1975:CCM, author = "Edward W. Ng", title = "A Comparison of Computational Methods and Algorithms for the Complex Gamma Function", journal = j-TOMS, volume = "1", number = "1", pages = "56--70", month = mar, year = "1975", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D20", MRnumber = "52 #2148", bibdate = "Fri Aug 26 23:44:16 1994", URL = "http://doi.acm.org/10.1145/355626.355635", acknowledgement = ack-nhfb, reviewer = "R. H. Bartels", } @Article{Byrne:1975:PNS, author = "G. D. Byrne and A. C. Hindmarsh", title = "A Polyalgorithm for the Numerical Solution of Ordinary Differential Equations", journal = j-TOMS, volume = "1", number = "1", pages = "71--96", month = mar, year = "1975", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65L99 (68A10)", MRnumber = "51 #14600", bibdate = "Fri Aug 26 23:44:16 1994", URL = "http://doi.acm.org/10.1145/355626.355636", acknowledgement = ack-nhfb, reviewer = "Sean McKee", } @Article{Powell:1975:VUM, author = "M. J. D. Powell", title = "A View of Unconstrained Minimization Algorithms that Do Not Require Derivatives", journal = j-TOMS, volume = "1", number = "2", pages = "97--107", month = jun, year = "1975", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "(Reviewer: R. P. Brent (CR {17} \#29471)) 65K05", MRnumber = "53 #14908", bibdate = "Sat Dec 20 10:45:23 1997", URL = "http://doi.acm.org/10.1145/355637.355638", acknowledgement = ack-nhfb, } @Article{Miller:1975:SRA, author = "Webb Miller", title = "Software for Roundoff Analysis", journal = j-TOMS, volume = "1", number = "2", pages = "108--128", month = jun, year = "1975", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65G05", MRnumber = "53 #9622", bibdate = "Fri Aug 26 23:44:16 1994", URL = "http://doi.acm.org/10.1145/355637.355639", acknowledgement = ack-nhfb, reviewer = "James H. Wilkinson", } @Article{Malcolm:1975:LVG, author = "Michael A. Malcolm and R. Bruce Simpson", title = "Local Versus Global Strategies for Adaptive Quadrature", journal = j-TOMS, volume = "1", number = "2", pages = "129--146", month = jun, year = "1975", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D30", MRnumber = "51 #7248", bibdate = "Fri Aug 26 23:44:16 1994", URL = "http://doi.acm.org/10.1145/355637.355640", acknowledgement = ack-nhfb, reviewer = "Thomas A. Atchison", } @Article{Stoutemyer:1975:AOU, author = "David R. Stoutemyer", title = "Analytical Optimization Using Computer Algebraic Manipulation", journal = j-TOMS, volume = "1", number = "2", pages = "147--164", month = jun, year = "1975", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "90C99", MRnumber = "58 #4363", bibdate = "Fri Aug 26 23:44:16 1994", URL = "http://doi.acm.org/10.1145/355637.355641", acknowledgement = ack-nhfb, } @Article{Barinka:1975:SEC, author = "Lawrence L. Barinka", title = "Some Experience with Constructing, Testing, and Certifying a Standard Mathematical Subroutine Library", journal = j-TOMS, volume = "1", number = "2", pages = "165--177", month = jun, year = "1975", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Aug 26 23:44:16 1994", URL = "http://doi.acm.org/10.1145/355637.355642", acknowledgement = ack-nhfb, } @Article{Jenkins:1975:AZR, author = "M. A. Jenkins", title = "{Algorithm 493}: Zeros of a Real Polynomial [{C2}]", journal = j-TOMS, volume = "1", number = "2", pages = "178--189", month = jun, year = "1975", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 00:27:23 1994", URL = "http://doi.acm.org/10.1145/355637.355643", acknowledgement = ack-nhfb, } @Article{Rice:1975:SPP, author = "John R. Rice", title = "Software Package Policy", journal = j-TOMS, volume = "1", number = "3", pages = "193--195", month = sep, year = "1975", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Aug 26 23:44:16 1994", URL = "http://doi.acm.org/10.1145/355644.355645", acknowledgement = ack-nhfb, } @Article{Bailey:1975:UAM, author = "Carl B. Bailey and Rondall E. Jones", title = "Usage and Argument Monitoring of Mathematical Library Routines", journal = j-TOMS, volume = "1", number = "3", pages = "196--209", month = sep, year = "1975", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Aug 26 23:44:16 1994", URL = "http://doi.acm.org/10.1145/355644.355646", acknowledgement = ack-nhfb, } @Article{George:1975:ARR, author = "James E. George", title = "Algorithms to Reveal the Representation of Characters, Integers, and Floating-Point Numbers", journal = j-TOMS, volume = "1", number = "3", pages = "210--216", month = sep, year = "1975", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Aug 26 23:44:16 1994", URL = "http://doi.acm.org/10.1145/355644.355647", acknowledgement = ack-nhfb, } @Article{Aird:1975:CAU, author = "T. J. Aird and Robert E. Lynch", title = "Computable Accurate Upper and Lower Error Bounds for Approximate Solutions of Linear Algebraic Systems", journal = j-TOMS, volume = "1", number = "3", pages = "217--231", month = sep, year = "1975", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65F35", MRnumber = "52 #2176", bibdate = "Fri Aug 26 23:44:16 1994", URL = "http://doi.acm.org/10.1145/355644.355648", acknowledgement = ack-nhfb, reviewer = "Ian Gladwell", } @Article{Sincovec:1975:SNP, author = "Richard F. Sincovec and Niel K. Madsen", title = "Software for Nonlinear Partial Differential Equations", journal = j-TOMS, volume = "1", number = "3", pages = "232--260", month = sep, year = "1975", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Aug 26 23:44:16 1994", URL = "http://doi.acm.org/10.1145/355644.355649", acknowledgement = ack-nhfb, } @Article{Sincovec:1975:APS, author = "Richard F. Sincovec and Niel K. Madsen", title = "{Algorithm 494}: {PDEONE}, Solutions of Systems of Partial Differential Equations [{D3}]", journal = j-TOMS, volume = "1", number = "3", pages = "261--263", month = sep, year = "1975", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 18:06:09 1994", URL = "http://doi.acm.org/10.1145/355644.355650", acknowledgement = ack-nhfb, } @Article{Barrodale:1975:ASO, author = "I. Barrodale and C. Phillips", title = "{Algorithm 495}: Solution of an Overdetermined System of Linear Equations in the {Chebychev} Norm [{F4}]", journal = j-TOMS, volume = "1", number = "3", pages = "264--270", month = sep, year = "1975", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 16:10:20 1994", URL = "http://doi.acm.org/10.1145/355644.355651", acknowledgement = ack-nhfb, keywords = "Chebyshev approximation; nla", } @Article{Kaufman:1975:ALA, author = "Linda Kaufman", title = "{Algorithm 496}: The {LZ} Algorithm to Solve the Generalized Eigenvalue Problem for Complex Matrices [{F2}]", journal = j-TOMS, volume = "1", number = "3", pages = "271--281", month = sep, year = "1975", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Thu Apr 29 15:21:30 1999", note = "See remark \cite{Kaufman:1976:RLA}.", URL = "http://doi.acm.org/10.1145/355644.355652", } @Article{Skovgaard:1975:RBF, author = "Ove Skovgaard", title = "Remark on ``{Algorithm 236}: {Bessel} Functions of the First Kind [{S17}]''", journal = j-TOMS, volume = "1", number = "3", pages = "282--284", month = sep, year = "1975", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Aug 30 00:27:11 1994", note = "See \cite{Gautschi:1964:BFF}.", URL = "http://doi.acm.org/10.1145/355644.355653", acknowledgement = ack-nhfb, } @Article{Feinstein:1975:RMT, author = "Robert Feinstein", title = "Remark on ``{Algorithm 483}: Masked Three-Dimensional Plot Program with Rotations [{J6}]''", journal = j-TOMS, volume = "1", number = "3", pages = "285--285", month = sep, year = "1975", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Aug 30 00:27:09 1994", note = "See \cite{Watkins:1974:MTD}.", URL = "http://doi.acm.org/10.1145/355644.355654", acknowledgement = ack-nhfb, } @Article{Misra:1975:RG, author = "Jayadev Misra", title = "Remark on ``{Algorithm 246}: {Graycode} [{Z}]''", journal = j-TOMS, volume = "1", number = "3", pages = "285--285", month = sep, year = "1975", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Sep 05 20:42:41 1994", note = "See \cite{Boothroyd:1964:G,Er:1985:RG}.", URL = "http://doi.acm.org/10.1145/355644.356449", acknowledgement = ack-nhfb, } @Article{Stone:1975:PTE, author = "Harold S. Stone", title = "Parallel Tridiagonal Equation Solvers", journal = j-TOMS, volume = "1", number = "4", pages = "289--307", month = dec, year = "1975", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "68A10 (68A20)", MRnumber = "52 #9676", bibdate = "Fri Aug 26 23:35:17 1994", URL = "http://doi.acm.org/10.1145/355656.355657", acknowledgement = ack-nhfb, keywords = "nla; prll; tridiagonal matrix", reviewer = "V. A. Valkovskii", } @Article{Lambiotte:1975:STL, author = "Jules J. {Lambiotte, Jr.} and Robert G. Voigt", title = "The Solution of Tridiagonal Linear Systems on the {CDC STAR 100} Computer", journal = j-TOMS, volume = "1", number = "4", pages = "308--329", month = dec, year = "1975", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "68A10 (68A20)", MRnumber = "52 #9677", bibdate = "Sat Aug 27 00:20:57 1994", URL = "http://doi.acm.org/10.1145/355656.355658", acknowledgement = ack-nhfb, keywords = "linear system; nla; tridiagonal matrix; vect", reviewer = "V. A. Valkovskii", } @Article{Bus:1975:TEA, author = "J. C. P. Bus and T. J. Dekker", title = "Two Efficient Algorithms with Guaranteed Convergence for Finding a Zero of a Function", journal = j-TOMS, volume = "1", number = "4", pages = "330--345", month = dec, year = "1975", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65H05", MRnumber = "52 #7112", bibdate = "Fri Aug 26 23:12:30 1994", URL = "http://doi.acm.org/10.1145/355656.355659", acknowledgement = ack-nhfb, keywords = "nlop", reviewer = "Ian Gladwell", } @Article{Norman:1975:CFP, author = "A. C. Norman", title = "Computing with Formal Power Series", journal = j-TOMS, volume = "1", number = "4", pages = "346--356", month = dec, year = "1975", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 00:22:26 1994", URL = "http://doi.acm.org/10.1145/355656.355660", acknowledgement = ack-nhfb, } @Article{Neves:1975:AIF, author = "Kenneth W. Neves", title = "Automatic Integration of Functional Differential Equations: An Approach", journal = j-TOMS, volume = "1", number = "4", pages = "357--368", month = dec, year = "1975", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65Q05", MRnumber = "52 #7171", bibdate = "Sat Aug 27 00:22:51 1994", URL = "http://doi.acm.org/10.1145/355656.355661", acknowledgement = ack-nhfb, reviewer = "W. C. Rheinboldt", } @Article{Neves:1975:AAI, author = "Kenneth W. Neves", title = "{Algorithm 497}: Automatic Integration of Functional Differential Equations [{D2}]", journal = j-TOMS, volume = "1", number = "4", pages = "369--371", month = dec, year = "1975", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 00:24:04 1994", URL = "http://doi.acm.org/10.1145/355656.355662", acknowledgement = ack-nhfb, } @Article{Prince:1975:AAF, author = "P. J. Prince", title = "{Algorithm 498}: {Airy} Functions Using {Chebyshev} Series Approximations", journal = j-TOMS, volume = "1", number = "4", pages = "372--379", month = dec, year = "1975", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 00:24:33 1994", note = "See also \cite{Razaz:1981:RAF}.", URL = "http://doi.acm.org/10.1145/355656.355663", acknowledgement = ack-nhfb, } @Article{Lewis:1975:CPF, author = "John Gregg Lewis", title = "Certification of ``{Algorithm 349}: Polygamma Functions with Arbitrary Precision''", journal = j-TOMS, volume = "1", number = "4", pages = "380--381", month = dec, year = "1975", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Mar 28 11:10:19 2003", note = "See \cite{TadeudeMedeiros:1969:APF}.", URL = "http://doi.acm.org/10.1145/355656.355664", acknowledgement = ack-nhfb, } @Article{Bromage:1975:CVS, author = "Gordon E. Bromage", title = "Certification of ``{Algorithm 475}: Visible Surface Plotting Program [{J6}]''", journal = j-TOMS, volume = "1", number = "4", pages = "381--382", month = dec, year = "1975", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 00:22:51 1994", URL = "http://doi.acm.org/10.1145/355656.355665", acknowledgement = ack-nhfb, } @Article{Rice:1976:PAA, author = "John R. Rice", title = "Parallel Algorithms for Adaptive Quadrature. {III}. Program Correctness", journal = j-TOMS, volume = "2", number = "1", pages = "1--30", month = mar, year = "1976", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D30 (68A10)", MRnumber = "54 #9058c", bibdate = "Sat Aug 27 00:30:21 1994", URL = "http://doi.acm.org/10.1145/355666.355667", acknowledgement = ack-nhfb, reviewer = "Frederick N. Fritsch", } @Article{Griss:1976:ASS, author = "Martin L. Griss", title = "The Algebraic Solution of Sparse Linear Systems via Minor Expansion", journal = j-TOMS, volume = "2", number = "1", pages = "31--49", month = mar, year = "1976", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65F05", MRnumber = "54 #4073", bibdate = "Sat Aug 27 00:30:21 1994", URL = "http://doi.acm.org/10.1145/355666.355668", acknowledgement = ack-nhfb, reviewer = "Charles R. Johnson", } @Article{Duris:1976:GCP, author = "Charles S. Duris", title = "Generating and Compounding Product-Type {Newton-Coates} Quadrature Formulas", journal = j-TOMS, volume = "2", number = "1", pages = "50--58", month = mar, year = "1976", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D30", MRnumber = "53 #1919", bibdate = "Sat Aug 27 00:30:21 1994", URL = "http://doi.acm.org/10.1145/355666.355669", acknowledgement = ack-nhfb, reviewer = "Thomas A. Atchison", } @Article{Bays:1976:IPR, author = "Carter Bays and S. D. Durham", title = "Improving a Poor Random Number Generator", journal = j-TOMS, volume = "2", number = "1", pages = "59--64", month = mar, year = "1976", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 00:30:21 1994", URL = "http://doi.acm.org/10.1145/355666.355670", acknowledgement = ack-nhfb, } @Article{Lyness:1976:CNA, author = "J. N. Lyness and J. J. Kaganove", title = "Comments on the Nature of Automatic Quadrature Routines", journal = j-TOMS, volume = "2", number = "1", pages = "65--81", month = mar, year = "1976", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D30", MRnumber = "53 #1921", bibdate = "Sat Aug 27 00:30:21 1994", URL = "http://doi.acm.org/10.1145/355666.355671", acknowledgement = ack-nhfb, reviewer = "Henning Esser", } @Article{Kinsner:1976:AES, author = "W. Kinsner and E. Della Torre", title = "{Algorithm 499}: An Efficient Scanning Technique [{Z}]", journal = j-TOMS, volume = "2", number = "1", pages = "82--86", month = mar, year = "1976", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 00:35:20 1994", URL = "http://doi.acm.org/10.1145/355666.355672", acknowledgement = ack-nhfb, } @Article{Shanno:1976:AMU, author = "D. F. Shanno and K. H. Phua", title = "{Algorithm 500}: Minimization of Unconstrained Multivariate Functions [{E4}]", journal = j-TOMS, volume = "2", number = "1", pages = "87--94", month = mar, year = "1976", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Thu Apr 29 15:25:28 1999", note = "See remarks \cite{Dunham:1977:RMU,Shanno:1980:RMU}.", URL = "http://doi.acm.org/10.1145/355666.355673", acknowledgement = ack-nhfb, } @Article{Simpson:1976:AFT, author = "Joseph C. Simpson", title = "{Algorithm 501}: {Fortran} Translation of {Algorithm 409}, Discrete {Chebychev} Curve Fit [{E2}]", journal = j-TOMS, volume = "2", number = "1", pages = "95--97", month = mar, year = "1976", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Sep 05 23:07:07 1994", note = "See remark \cite{Futrell:1978:RTA}.", URL = "http://doi.acm.org/10.1145/355666.355674", acknowledgement = ack-nhfb, } @Article{Kubicek:1976:ADS, author = "Milan Kub{\'\i}{\v{c}}ek", title = "{Algorithm 502}: Dependence of Solution of Nonlinear Systems on a Parameter [{C5}]", journal = j-TOMS, volume = "2", number = "1", pages = "98--107", month = mar, year = "1976", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 18:03:58 1994", URL = "http://doi.acm.org/10.1145/355666.355675", acknowledgement = ack-nhfb, } @Article{Boulton:1976:REP, author = "D. M. Boulton", title = "Remark on ``{Algorithm 434}: Exact Probabilities for ${R}\times{C}$ Contingency Tables [{G2}]''", journal = j-TOMS, volume = "2", number = "1", pages = "108--108", month = mar, year = "1976", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Aug 30 00:27:20 1994", note = "See \cite{March:1972:EPT}.", URL = "http://doi.acm.org/10.1145/355666.355676", acknowledgement = ack-nhfb, } @Article{Duta:1976:RVS, author = "Lucian D. Duta", title = "Remark on ``{Algorithm 475}: Visible Surface Plotting Program [{J6}]''", journal = j-TOMS, volume = "2", number = "1", pages = "109--110", month = mar, year = "1976", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Aug 30 00:27:22 1994", note = "See \cite{Wright:1974:VSP}.", URL = "http://doi.acm.org/10.1145/355666.355677", acknowledgement = ack-nhfb, } @Article{White:1976:RMS, author = "G. M. White and S. Goudreau and J. L. Legros", title = "Remark on ``{Algorithm 479}: {A} Minimal Spanning Tree Clustering Method [{Z}]''", journal = j-TOMS, volume = "2", number = "1", pages = "110--111", month = mar, year = "1976", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Aug 30 00:27:24 1994", note = "See \cite{Page:1974:MST}.", URL = "http://doi.acm.org/10.1145/355666.355678", acknowledgement = ack-nhfb, } @Article{Pomeranz:1976:REC, author = "J. Pomeranz", title = "Remark on ``{Algorithm 487}: Exact Cumulative Distribution of the {Kolmogorov-Smirnov} Statistic for Small Samples [{S14}]''", journal = j-TOMS, volume = "2", number = "1", pages = "111--111", month = mar, year = "1976", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Aug 30 00:27:25 1994", note = "See \cite{Pomeranz:1974:ECD}.", URL = "http://doi.acm.org/10.1145/355666.355679", acknowledgement = ack-nhfb, } @Article{Morris:1976:RDF, author = "Robert Morris", title = "Remark on ``{Algorithm 490}: The Dilogarithm Function of a Real Argument [{S22}]''", journal = j-TOMS, volume = "2", number = "1", pages = "112--112", month = mar, year = "1976", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Aug 30 00:27:18 1994", note = "See \cite{Ginsberg:1975:DFR}.", URL = "http://doi.acm.org/10.1145/355666.355680", acknowledgement = ack-nhfb, } @Article{Rice:1976:TPS, author = "John R. Rice", title = "{TOMS} Policy Statement: The Rights of Program Authors in the Evaluation of Programs", journal = j-TOMS, volume = "2", number = "2", pages = "113--114", month = jun, year = "1976", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 00:30:21 1994", URL = "http://doi.acm.org/10.1145/355681.355682", acknowledgement = ack-nhfb, } @Article{Ford:1976:DSN, author = "B. Ford and D. K. Sayers", title = "Developing a Single Numerical Algorithms Library for Different Machine Ranges", journal = j-TOMS, volume = "2", number = "2", pages = "115--131", month = jun, year = "1976", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 00:30:21 1994", URL = "http://doi.acm.org/10.1145/355681.355683", acknowledgement = ack-nhfb, } @Article{Paul:1976:SEF, author = "George Paul and M. Wayne Wilson", title = "Should the Elementary Function Library Be Incorporated Into Computer Instruction Sets?", journal = j-TOMS, volume = "2", number = "2", pages = "132--142", month = jun, year = "1976", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 00:30:21 1994", URL = "http://doi.acm.org/10.1145/355681.355684", acknowledgement = ack-nhfb, } @Article{Janko:1976:LIS, author = "Wolfgang Janko", title = "A List Insertion Sort for Keys With Arbitrary Key Distribution", journal = j-TOMS, volume = "2", number = "2", pages = "143--153", month = jun, year = "1976", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 00:30:21 1994", URL = "http://doi.acm.org/10.1145/355681.355685", acknowledgement = ack-nhfb, } @Article{Atkinson:1976:APL, author = "Kendall Atkinson", title = "An Automatic Program for Linear {Fredholm} Integral Equations of the Second Kind", journal = j-TOMS, volume = "2", number = "2", pages = "154--171", month = jun, year = "1976", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65R05", MRnumber = "54 #6528", bibdate = "Sat Aug 27 00:30:21 1994", URL = "http://doi.acm.org/10.1145/355681.355686", acknowledgement = ack-nhfb, reviewer = "Christopher T. H. Baker", } @Article{Shampine:1976:GEE, author = "L. F. Shampine and H. A. Watts", title = "Global Error Estimates for Ordinary Differential Equations", journal = j-TOMS, volume = "2", number = "2", pages = "172--186", month = jun, year = "1976", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65L05", MRnumber = "54 #1621", bibdate = "Sat Aug 27 00:30:21 1994", URL = "http://doi.acm.org/10.1145/355681.355687", acknowledgement = ack-nhfb, reviewer = "J. Hurt", } @Article{Ericksen:1976:ICP, author = "J. H. Ericksen and R. Wilhelmson", title = "Implementation of a Convective Problem Requiring Auxiliary Storage", journal = j-TOMS, volume = "2", number = "2", pages = "187--195", month = jun, year = "1976", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 10:18:18 1994", URL = "http://doi.acm.org/10.1145/355681.355688", acknowledgement = ack-nhfb, } @Article{Atkinson:1976:AAP, author = "Kendall Atkinson", title = "{Algorithm 503}: An Automatic Program for {Fredholm} Integral Equations of the Second Kind [{D5}]", journal = j-TOMS, volume = "2", number = "2", pages = "196--199", month = jun, year = "1976", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 00:51:30 1994", URL = "http://doi.acm.org/10.1145/355681.355689", acknowledgement = ack-nhfb, } @Article{Shampine:1976:AGG, author = "L. F. Shampine and H. A. Watts", title = "{Algorithm 504}: {GERK}: Global Error Estimation For Ordinary Differential Equations [{D}]", journal = j-TOMS, volume = "2", number = "2", pages = "200--203", month = jun, year = "1976", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 00:52:29 1994", URL = "http://doi.acm.org/10.1145/355681.355690", acknowledgement = ack-nhfb, } @Article{Janko:1976:ALI, author = "Wolfgang Janko", title = "{Algorithm 505}: {A} List Insertion Sort for Keys with Arbitrary Key Distribution [{S20}]", journal = j-TOMS, volume = "2", number = "2", pages = "204--206", month = jun, year = "1976", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 00:52:49 1994", URL = "http://doi.acm.org/10.1145/355681.355691", acknowledgement = ack-nhfb, } @Article{Pike:1976:RIB, author = "Malcolm C. Pike and Jennie SooHoo", title = "Remark on ``{Algorithm 179}: Incomplete Beta Ratio [{S14}]''", journal = j-TOMS, volume = "2", number = "2", pages = "207--208", month = jun, year = "1976", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Aug 30 00:27:26 1994", note = "See \cite{Ludwig:1963:IBR}.", URL = "http://doi.acm.org/10.1145/355681.355692", acknowledgement = ack-nhfb, } @Article{Anderson:1976:RIS, author = "Michael R. Anderson", title = "Remark on ``{Algorithm 433}: Interpolation and Smooth Curve Fitting Based on Local Procedures [{E2}]''", journal = j-TOMS, volume = "2", number = "2", pages = "208--208", month = jun, year = "1976", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Aug 30 00:27:27 1994", note = "See \cite{Akima:1972:ISC}.", URL = "http://doi.acm.org/10.1145/355681.355693", acknowledgement = ack-nhfb, } @Article{Wyatt:1976:PEP, author = "W. T. {Wyatt, Jr.} and D. W. Lozier and D. J. Orser", title = "A Portable Extended Precision Arithmetic Package and Library With {Fortran} Precompiler", journal = j-TOMS, volume = "2", number = "3", pages = "209--231", month = sep, year = "1976", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 00:30:21 1994", URL = "http://doi.acm.org/10.1145/355694.355695", acknowledgement = ack-nhfb, } @Article{Gentleman:1976:AAC, author = "W. M. Gentleman and S. C. Johnson", title = "Analysis of Algorithms, {A} Case Study: Determinants of Matrices with Polynomial Entries", journal = j-TOMS, volume = "2", number = "3", pages = "232--241", month = sep, year = "1976", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65F30", MRnumber = "54 #1575", bibdate = "Sat Aug 27 00:30:21 1994", URL = "http://doi.acm.org/10.1145/355694.355696", acknowledgement = ack-nhfb, reviewer = "K. Moszynski", } @Article{Barwell:1976:CAS, author = "Victor Barwell and Alan George", title = "A Comparison of Algorithms for Solving Symmetric Indefinite Systems of Linear Equations", journal = j-TOMS, volume = "2", number = "3", pages = "242--251", month = sep, year = "1976", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65F05", MRnumber = "54 #6472", bibdate = "Fri Aug 26 23:35:17 1994", URL = "http://doi.acm.org/10.1145/355694.355697", acknowledgement = ack-nhfb, keywords = "indefinite system; linear system; nla; symmetric matrix", reviewer = "F. Szidarovszky", } @Article{Bartels:1976:HIU, author = "Richard Bartels and Alec Steingart", title = "{Hermite} Interpolation Using a Triangular Polynomial Basis", journal = j-TOMS, volume = "2", number = "3", pages = "252--256", month = sep, year = "1976", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D15 (65D20)", MRnumber = "55 #4602", bibdate = "Sat Aug 27 00:30:21 1994", URL = "http://doi.acm.org/10.1145/355694.355698", acknowledgement = ack-nhfb, reviewer = "Hwa-Shan Ho", } @Article{Hall:1976:NSS, author = "C. A. Hall and R. W. Luczak and A. G. Serdy", title = "Numerical Solution of Steady State Heat Flow Problems Over Curved Domains", journal = j-TOMS, volume = "2", number = "3", pages = "257--274", month = sep, year = "1976", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65N10", MRnumber = "54 #4135", bibdate = "Sat Aug 27 00:30:21 1994", URL = "http://doi.acm.org/10.1145/355694.355699", acknowledgement = ack-nhfb, reviewer = "Stephen Hilbert", } @Article{Stewart:1976:AHE, author = "G. W. Stewart", title = "{Algorithm 506}: {HQR3} and {EXCHNG}: {Fortran} Subroutines for Calculating and Ordering the Eigenvalues of a Real Upper {Hessenberg} Matrix [{F2}]", journal = j-TOMS, volume = "2", number = "3", pages = "275--280", month = sep, year = "1976", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 18:03:53 1994", note = "See also \cite{Flamm:1982:RHE}.", URL = "http://doi.acm.org/10.1145/355694.355700", acknowledgement = ack-nhfb, keywords = "eig; Hessenberg matrix; nla; QR algorithm; software", } @Article{Herriot:1976:APQ, author = "John G. Herriot and Christian H. Reinsch", title = "{Algorithm 507}: Procedures for Quintic Natural Spline Interpolation [{E1}]", journal = j-TOMS, volume = "2", number = "3", pages = "281--289", month = sep, year = "1976", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 01:01:50 1994", note = "See also \cite{Hanson:1982:RPQ}.", URL = "http://doi.acm.org/10.1145/355694.355701", acknowledgement = ack-nhfb, } @Article{Loeser:1976:SAQ, author = "Rudolf Loeser", title = "Survey on Algorithms 347, 426, and Quicksort", journal = j-TOMS, volume = "2", number = "3", pages = "290--299", month = sep, year = "1976", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 00:30:21 1994", URL = "http://doi.acm.org/10.1145/355694.355702", acknowledgement = ack-nhfb, } @Article{Davies:1976:RRF, author = "Alan M. Davies", title = "Remark on ``{Algorithm 450}: {Rosenbrock} Function Minimization [{E4}]''", journal = j-TOMS, volume = "2", number = "3", pages = "300--301", month = sep, year = "1976", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Aug 30 00:27:28 1994", note = "See \cite{MacHura:1973:RFM}.", URL = "http://doi.acm.org/10.1145/355694.355703", acknowledgement = ack-nhfb, } @Article{Brown:1976:RAS, author = "Theodore Brown", title = "Remark on ``{Algorithm 489}: The Algorithm {SELECT}\emdash for Finding the $i$th Smallest of $n$ Elements [{M1}]''", journal = j-TOMS, volume = "2", number = "3", pages = "301--304", month = sep, year = "1976", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Aug 30 00:27:31 1994", note = "See \cite{Floyd:1975:ASF}.", URL = "http://doi.acm.org/10.1145/355694.355704", acknowledgement = ack-nhfb, } @Article{Pavlidis:1976:UAP, author = "Theodosios Pavlidis", title = "The Use of Algorithms of Piecewise Approximations for Picture Processing Applications", journal = j-TOMS, volume = "2", number = "4", pages = "305--321", month = dec, year = "1976", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 00:30:21 1994", URL = "http://doi.acm.org/10.1145/355705.355706", acknowledgement = ack-nhfb, } @Article{Gibbs:1976:CSB, author = "Norman E. Gibbs and William G. {Poole Jr.} and Paul K. Stockmeyer", title = "A Comparison of Several Bandwidth and Profile Reduction Algorithms", journal = j-TOMS, volume = "2", number = "4", pages = "322--330", month = dec, year = "1976", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 01:07:27 1994", URL = "http://doi.acm.org/10.1145/355705.355707", acknowledgement = ack-nhfb, keywords = "band matrix; band reduction; nla; profile reduction; sparse", } @Article{Mahendrarajah:1976:CTA, author = "A. Mahendrarajah and F. Fiala", title = "A Comparison of Three Algorithms for Linear Zero-One Programs", journal = j-TOMS, volume = "2", number = "4", pages = "331--334", month = dec, year = "1976", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 01:08:17 1994", URL = "http://doi.acm.org/10.1145/355705.355708", acknowledgement = ack-nhfb, } @Article{Weinberger:1976:FPA, author = "P. J. Weinberger and L. P. Rothschild", title = "Factoring Polynomials Over Algebraic Number Fields", journal = j-TOMS, volume = "2", number = "4", pages = "335--350", month = dec, year = "1976", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "12A20 (12-04)", MRnumber = "56 #8521", bibdate = "Sat Aug 27 00:30:21 1994", URL = "http://doi.acm.org/10.1145/355705.355709", acknowledgement = ack-nhfb, reviewer = "I. Gerst", } @Article{Pinkert:1976:EMF, author = "James R. Pinkert", title = "An Exact Method for Finding the Roots of a Complex Polynomial", journal = j-TOMS, volume = "2", number = "4", pages = "351--363", month = dec, year = "1976", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "12-04 (12D10 30A08 65H05)", MRnumber = "56 #299", bibdate = "Sat Aug 27 00:30:21 1994", URL = "http://doi.acm.org/10.1145/355705.355710", acknowledgement = ack-nhfb, reviewer = "E. Frank", } @Article{Rubin:1976:PI, author = "Frank Rubin", title = "Partition of Integers", journal = j-TOMS, volume = "2", number = "4", pages = "364--374", month = dec, year = "1976", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "68A10 (05A17 10A45)", MRnumber = "57 #4605", bibdate = "Sat Aug 27 00:30:21 1994", URL = "http://doi.acm.org/10.1145/355705.355711", acknowledgement = ack-nhfb, reviewer = "S. Zaks", } @Article{Crane:1976:AMB, author = "H. L. {Crane Jr.} and Norman E. Gibbs and William G. {Poole Jr.} and Paul K. Stockmeyer", title = "{Algorithm 508}: Matrix Bandwidth and Profile Reduction [{F1}]", journal = j-TOMS, volume = "2", number = "4", pages = "375--377", month = dec, year = "1976", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 01:11:54 1994", note = "See also \cite{Lewis:1982:RMB}.", URL = "http://doi.acm.org/10.1145/355705.355712", acknowledgement = ack-nhfb, } @Article{Gibbs:1976:AHP, author = "Norman E. Gibbs", title = "{Algorithm 509}: {A} Hybrid Profile Reduction Algorithm [{F1}]", journal = j-TOMS, volume = "2", number = "4", pages = "378--387", month = dec, year = "1976", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 01:11:35 1994", note = "See also \cite{Lewis:1982:RMB}.", URL = "http://doi.acm.org/10.1145/355705.355713", acknowledgement = ack-nhfb, } @Article{Wilson:1976:APL, author = "D. G. Wilson", title = "{Algorithm 510}: Piecewise Linear Approximation to Tabulated Data [{E2}]", journal = j-TOMS, volume = "2", number = "4", pages = "388--391", month = dec, year = "1976", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 01:12:13 1994", URL = "http://doi.acm.org/10.1145/355705.355714", acknowledgement = ack-nhfb, } @Article{Ito:1976:RIT, author = "M. R. Ito", title = "Remark on ``{Algorithm 284}: Interchange of Two Blocks of Data [{K2}]''", journal = j-TOMS, volume = "2", number = "4", pages = "392--393", month = dec, year = "1976", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Aug 30 00:27:34 1994", note = "See \cite{Fletcher:1966:ITB}.", URL = "http://doi.acm.org/10.1145/355705.355715", acknowledgement = ack-nhfb, } @Article{elLozy:1976:RAC, author = "Mohamed {el Lozy}", title = "Remark on ``{Algorithm 299}: Chi-Squared Integral [{S15}]''", journal = j-TOMS, volume = "2", number = "4", pages = "393--395", month = dec, year = "1976", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Mar 28 11:04:46 2003", bibdate = "Mon Sep 05 20:40:11 1994", note = "See \cite{Hill:1967:CSI,Hill:1985:RCS}.", URL = "http://doi.acm.org/10.1145/355705.355716", acknowledgement = ack-nhfb, } @Article{Koppelaar:1976:RNI, author = "Henk Koppelaar and Peter Molenaar", title = "Remark on ``{Algorithm 486}: Numerical Inversion of {Laplace} Transform [{D5}]''", journal = j-TOMS, volume = "2", number = "4", pages = "395--396", month = dec, year = "1976", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Thu Apr 29 15:27:20 1999", note = "See \cite{Veillon:1974:NIL,Piessens:1984:RNI}.", URL = "http://doi.acm.org/10.1145/355705.355717", acknowledgement = ack-nhfb, } @Article{Kaufman:1976:RLA, author = "Linda Kaufman", title = "Remark on ``{Algorithm 496}: The {LZ} Algorithm to Solve the Generalized Eigenvalue Problem for Complex Matrices [{F2}]''", journal = j-TOMS, volume = "2", number = "4", pages = "396--396", month = dec, year = "1976", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Aug 30 00:27:42 1994", note = "See \cite{Kaufman:1975:ALA}.", URL = "http://doi.acm.org/10.1145/355705.355718", acknowledgement = ack-nhfb, } @Article{McClellan:1977:ESL, author = "Michael T. McClellan", title = "The Exact Solution of Linear Equations with Rational Function Coefficients", journal = j-TOMS, volume = "3", number = "1", pages = "1--25", month = mar, year = "1977", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "68A15", MRnumber = "55 #11696", bibdate = "Sat Aug 27 22:12:55 1994", URL = "http://doi.acm.org/10.1145/355719.355720", acknowledgement = ack-nhfb, reviewer = "Jo Ann Howell", } @Article{Stoutemyer:1977:AEA, author = "David R. Stoutemyer", title = "Automatic Error Analysis Using Computer Algebraic Manipulation", journal = j-TOMS, volume = "3", number = "1", pages = "26--43", month = mar, year = "1977", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65G05", MRnumber = "55 #13765", bibdate = "Fri Sep 02 22:30:11 1994", URL = "http://doi.acm.org/10.1145/355719.355721", abstract = "This paper shows how the inherent error and the fixed-point or floating-point roundoff of chopoff error of an expression can be determined automatically using a computer algebra language such as {REDUCE}.", acknowledgement = ack-nhfb, reviewer = "R. P. Brent", } @Article{Shampine:1977:SND, author = "L. F. Shampine", title = "Stiff and Nonstiff Differential Equation Solvers, {II}: Detecting Stiffness with {Runge-Kutta} Methods", journal = j-TOMS, volume = "3", number = "1", pages = "44--53", month = mar, year = "1977", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65L05", MRnumber = "56 #4175", bibdate = "Sat Aug 27 22:12:55 1994", URL = "http://doi.acm.org/10.1145/355719.355722", acknowledgement = ack-nhfb, reviewer = "W. H. Enright", } @Article{Tran-Thong:1977:FPF, author = "Tr{\^a}\`n-Th{\^o}\'ng and Bede Liu", title = "Floating Point Fast {Fourier} Transform Computation Using Double Precision Floating Point Accumulators", journal = j-TOMS, volume = "3", number = "1", pages = "54--59", month = mar, year = "1977", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65T05", MRnumber = "55 #11658", bibdate = "Sat Aug 27 22:12:55 1994", URL = "http://doi.acm.org/10.1145/355719.355723", acknowledgement = ack-nhfb, } @Article{Gonzalez:1977:EAK, author = "Teofilo Gonzalez and Sartaj Sahni and W. R. Franta", title = "An Efficient Algorithm for the {Kolmogorov-Smirnov} and {Lilliefors} Tests", journal = j-TOMS, volume = "3", number = "1", pages = "60--64", month = mar, year = "1977", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65C99", MRnumber = "55 #11561", bibdate = "Sat Aug 27 22:12:55 1994", URL = "http://doi.acm.org/10.1145/355719.355724", acknowledgement = ack-nhfb, reviewer = "Hannah Chen", } @Article{Kaufman:1977:STQ, author = "Linda Kaufman", title = "Some Thoughts on the {QZ} Algorithm for Solving the Generalized Eigenvalue Problem", journal = j-TOMS, volume = "3", number = "1", pages = "65--75", month = mar, year = "1977", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65F15", MRnumber = "55 #6814", URL = "http://doi.acm.org/10.1145/355719.355725", acknowledgement = ack-nhfb, keywords = "gieg; nla; QZ algorithm", reviewer = "W. Niethammer", } @Article{Amos:1977:CSI, author = "D. E. Amos and S. L. Daniel and M. K. Weston", title = "{CDC} 6600 Subroutines {IBESS} and {JBESS} for {Bessel} Functions {$I_\nu(x)$} and {$J_\nu(x)$}, {$x\ge0,\nu\ge0$}", journal = j-TOMS, volume = "3", number = "1", pages = "76--92", month = mar, year = "1977", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D20", MRnumber = "55 #6781", bibdate = "Tue Sep 06 19:20:02 1994", URL = "http://doi.acm.org/10.1145/355719.355726", acknowledgement = ack-nhfb, reviewer = "Sven-{\AA}ke Gustafson", } @Article{Amos:1977:ACS, author = "D. E. Amos and S. L. Daniel and M. K. Weston", title = "{Algorithm 511}: {CDC} 6600 Subroutines {IBESS} and {JBESS} for {Bessel} Functions {$I_\nu(x)$} and {$J_\nu(x)$}, {$x \ge 0, \nu \ge 0$} [{S18}]", journal = j-TOMS, volume = "3", number = "1", pages = "93--95", month = mar, year = "1977", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Thu Apr 29 15:14:12 1999", note = "See erratum \cite{Amos:1978:ECS}.", URL = "http://doi.acm.org/10.1145/355719.355727", } @Article{Benson:1977:ANA, author = "A. Benson and D. J. Evans", title = "{Algorithm 512}: {A} Normalized Algorithm for Solution of the Positive Definite Symmetric Quindiagonal Systems of Linear Equations [{F4}]", journal = j-TOMS, volume = "3", number = "1", pages = "96--103", month = mar, year = "1977", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 22:22:47 1994", URL = "http://doi.acm.org/10.1145/355719.355728", acknowledgement = ack-nhfb, } @Article{Cate:1977:AAS, author = "Esko G. Cate and David W. Twigg", title = "{Algorithm 513}: Analysis of In-Situ Transposition [{F1}]", journal = j-TOMS, volume = "3", number = "1", pages = "104--110", month = mar, year = "1977", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "68A10", MRnumber = "55 #13866", bibdate = "Thu Apr 29 15:17:56 1999", note = "See remark \cite{Leathers:1979:RAS}.", URL = "http://doi.acm.org/10.1145/355719.355729", acknowledgement = ack-nhfb, reviewer = "Ralph A. Willoughby", } @Article{Veillon:1977:RNI, author = "Fran{\c{c}}oise Veillon", title = "Remark on ``{Algorithm 486}: Numerical Inversion of {Laplace} Transform''", journal = j-TOMS, volume = "3", number = "1", pages = "111--111", month = mar, year = "1977", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Aug 30 00:27:43 1994", note = "See \cite{Veillon:1974:NIL,Piessens:1984:RNI}.", URL = "http://doi.acm.org/10.1145/355719.355730", acknowledgement = ack-nhfb, } @Article{Dunham:1977:RMU, author = "Charles Dunham", title = "Remark on ``{Algorithm 500}: Minimization of Unconstrained Multivariate Functions [{E4}]''", journal = j-TOMS, volume = "3", number = "1", pages = "112--112", month = mar, year = "1977", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Aug 30 00:27:59 1994", note = "See \cite{Shanno:1976:AMU}.", URL = "http://doi.acm.org/10.1145/355719.355731", acknowledgement = ack-nhfb, } @Article{Aird:1977:PMS, author = "Thomas J. Aird", title = "Portability of Mathematical Software Coded in {Fortran}", journal = j-TOMS, volume = "3", number = "2", pages = "113--127", month = jun, year = "1977", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 22:26:34 1994", URL = "http://doi.acm.org/10.1145/355732.355733", acknowledgement = ack-nhfb, } @Article{Stoutemyer:1977:ASI, author = "David R. Stoutemyer", title = "Analytically Solving Integral Equations by Using Computer Algebra", journal = j-TOMS, volume = "3", number = "2", pages = "128--146", month = jun, year = "1977", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65R05", MRnumber = "56 #4205", bibdate = "Sat Aug 27 22:26:34 1994", URL = "http://doi.acm.org/10.1145/355732.355734", acknowledgement = ack-nhfb, reviewer = "Sean McKee", } @Article{McClellan:1977:CAE, author = "Michael T. McClellan", title = "A Comparison of Algorithms for the Exact Solution of Linear Equations", journal = j-TOMS, volume = "3", number = "2", pages = "147--158", month = jun, year = "1977", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65F05", MRnumber = "55 #13753", bibdate = "Sat Aug 27 22:26:34 1994", URL = "http://doi.acm.org/10.1145/355732.355735", acknowledgement = ack-nhfb, reviewer = "H. R. Schwarz", } @Article{Farden:1977:SSS, author = "David C. Farden", title = "The Solution of a Special Set of {Hermitian} {Toeplitz} Linear Equations", journal = j-TOMS, volume = "3", number = "2", pages = "159--163", month = jun, year = "1977", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 22:26:34 1994", URL = "http://doi.acm.org/10.1145/355732.355736", acknowledgement = ack-nhfb, } @Article{Ichida:1977:CFO, author = "Kozo Ichida and Takeshi Kiyono and Fujiichi Yoshimoto", title = "Curve Fitting by a One-Pass Method With a Piecewise Cubic Polynomial", journal = j-TOMS, volume = "3", number = "2", pages = "164--174", month = jun, year = "1977", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 22:26:34 1994", URL = "http://doi.acm.org/10.1145/355732.355737", acknowledgement = ack-nhfb, } @Article{Ellis:1977:ANM, author = "T. M. R. Ellis and D. H. McLain", title = "{Algorithm 514}: {A} New Method of Cubic Curve Fitting Using Local Data [{E2}]", journal = j-TOMS, volume = "3", number = "2", pages = "175--179", month = jun, year = "1977", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/355732.355738", } @Article{Buckles:1977:AGV, author = "B. P. Buckles and M. Lybanon", title = "{Algorithm 515}: Generation of a Vector from the Lexicographical Index [{G6}]", journal = j-TOMS, volume = "3", number = "2", pages = "180--182", month = jun, year = "1977", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/355732.355739", } @Article{McKean:1977:AAO, author = "J. W. McKean and T. A. {Ryan, Jr.}", title = "{Algorithm 516}: An Algorithm for Obtaining Confidence Intervals and Point Estimates Based on Ranks in the Two Sample Location Problem [{G1}]", journal = j-TOMS, volume = "3", number = "2", pages = "183--185", month = jun, year = "1977", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/355732.355740", } @Article{Chan:1977:APC, author = "S. P. Chan and R. Feldman and B. N. Parlett", title = "{Algorithm 517}: {A} Program for Computing the Condition Numbers of Matrix Eigenvalues Without Computing Eigenvectors [{F2}]", journal = j-TOMS, volume = "3", number = "2", pages = "186--203", month = jun, year = "1977", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 22:34:22 1994", URL = "http://doi.acm.org/10.1145/355732.355741", acknowledgement = ack-nhfb, keywords = "condition estimation; eig; nla; nonsymmetric matrix; pert; software", } @Article{Mackay:1977:RPT, author = "M. Mackay and J. E. Radue", title = "Remark on ``{Some} Performance Tests of `{Quicksort}' and Descendants''", journal = j-TOMS, volume = "3", number = "2", pages = "204--204", month = jun, year = "1977", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Nov 19 13:07:36 1994", note = "See \cite{Loeser:1974:SPT}.", URL = "http://doi.acm.org/10.1145/355732.355742", acknowledgement = ack-nhfb, } @Article{Jansen:1977:RLF, author = "J. K. M. Jansen", title = "Remark on ``{Algorithm 259}: {Legendre} Functions for Arguments Larger than One''", journal = j-TOMS, volume = "3", number = "2", pages = "204--205", month = jun, year = "1977", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Sep 30 00:59:04 1994", note = "See \cite{Gautschi:1965:LFA}.", URL = "http://doi.acm.org/10.1145/355732.356467", acknowledgement = ack-nhfb, } @Article{Friedman:1977:AFB, author = "Jerome H. Friedman and Jon Louis Bentley and Raphael Ari Finkel", title = "An Algorithm for Finding Best Matches in Logarithmic Expected Time", journal = j-TOMS, volume = "3", number = "3", pages = "209--226", month = sep, year = "1977", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 22:53:20 1994", URL = "http://doi.acm.org/10.1145/355744.355745", acknowledgement = ack-nhfb, } @Article{Ito:1977:MRP, author = "Tetsuro Ito and Makoto Kizawa", title = "The Matrix Rearrangement Procedure for Graph-Theoretical Algorithms and Its Application to the Generation of Fundamental Cycles", journal = j-TOMS, volume = "3", number = "3", pages = "227--231", month = sep, year = "1977", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 22:26:34 1994", URL = "http://doi.acm.org/10.1145/355744.355746", acknowledgement = ack-nhfb, } @Article{Cody:1977:CRF, author = "W. J. Cody and Rose M. Motley and L. Wayne Fullerton", title = "The Computation of Real Fractional Order {Bessel} Functions of the Second Kind", journal = j-TOMS, volume = "3", number = "3", pages = "232--239", month = sep, year = "1977", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 22:26:34 1994", URL = "http://doi.acm.org/10.1145/355744.355747", acknowledgement = ack-nhfb, } @Article{Gautschi:1977:ERI, author = "Walter Gautschi", title = "Evaluation of Repeated Integrals of the Coerror Function", journal = j-TOMS, volume = "3", number = "3", pages = "240--252", month = sep, year = "1977", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 22:26:34 1994", URL = "http://doi.acm.org/10.1145/355744.355748", acknowledgement = ack-nhfb, } @Article{Walker:1977:EMG, author = "Alastair J. Walker", title = "An Efficient Method for Generating Discrete Random Variables with General Distributions", journal = j-TOMS, volume = "3", number = "3", pages = "253--256", month = sep, year = "1977", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 22:26:34 1994", URL = "http://doi.acm.org/10.1145/355744.355749", acknowledgement = ack-nhfb, } @Article{Kinderman:1977:CGR, author = "A. J. Kinderman and J. F. Monahan", title = "Computer Generation of Random Variables Using the Ratio of Uniform Deviates", journal = j-TOMS, volume = "3", number = "3", pages = "257--260", month = sep, year = "1977", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 22:58:34 1994", URL = "http://doi.acm.org/10.1145/355744.355750", acknowledgement = ack-nhfb, country = "USA", date = "13/05/93", descriptors = "RVG;", enum = "7496", language = "English", location = "SEL: Wi", references = "0", revision = "16/01/94", } @Article{Cohen:1977:SSF, author = "Jacques Cohen and Joel Katcoff", title = "Symbolic Solution of Finite-Difference Equations", journal = j-TOMS, volume = "3", number = "3", pages = "261--271", month = sep, year = "1977", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 22:26:34 1994", URL = "http://doi.acm.org/10.1145/355744.355751", acknowledgement = ack-nhfb, } @Article{Fateman:1977:ADC, author = "Richard J. Fateman", title = "An Algorithm for Deciding the Convergence of the Rational Iteration $x_{n+1} = f(x_n)$", journal = j-TOMS, volume = "3", number = "3", pages = "272--278", month = sep, year = "1977", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 22:26:34 1994", URL = "http://doi.acm.org/10.1145/355744.355752", acknowledgement = ack-nhfb, } @Article{Hill:1977:AIB, author = "G. W. Hill", title = "{Algorithm 518}: Incomplete {Bessel} Function {$I_0$}. {The von Mises} Distribution [{S14}]", journal = j-TOMS, volume = "3", number = "3", pages = "279--284", month = sep, year = "1977", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Oct 24 15:46:06 1998", URL = "http://doi.acm.org/10.1145/355744.355753", acknowledgement = ack-nhfb, } @Article{Kallman:1977:ATA, author = "Ralph Kallman", title = "{Algorithm 519}: Three Algorithms for Computing {Kolmogorov-Smirnov} Probabilities with Arbitrary Boundaries and a Certification of {Algorithm 487} [{S14}]", journal = j-TOMS, volume = "3", number = "3", pages = "285--294", month = sep, year = "1977", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 23:01:47 1994", URL = "http://doi.acm.org/10.1145/355744.355754", acknowledgement = ack-nhfb, } @Article{Weglarz:1977:AAR, author = "Jan Weglarz and Jacek Blazewicz and Wojciech Cellary and Roman Slowinski", title = "{Algorithm 520}: An Automatic Revised Simplex Method for Constrained Resource Network Scheduling [{H}]", journal = j-TOMS, volume = "3", number = "3", pages = "295--300", month = sep, year = "1977", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/355744.355755", } @Article{Gautschi:1977:ARI, author = "Walter Gautschi", title = "{Algorithm 521}: Repeated Integrals of the Coerror Function [{S15}]", journal = j-TOMS, volume = "3", number = "3", pages = "301--302", month = sep, year = "1977", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 23:03:07 1994", URL = "http://doi.acm.org/10.1145/355744.355756", acknowledgement = ack-nhfb, } @Article{Sipala:1977:RSM, author = "Paolo Sipala", title = "Remark on ``{Algorithm 408}: {A} Sparse Matrix Package (Part {I}) [{F4}]''", journal = j-TOMS, volume = "3", number = "3", pages = "303--303", month = sep, year = "1977", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Aug 30 00:28:02 1994", note = "See \cite{McNamee:1971:SMP}.", URL = "http://doi.acm.org/10.1145/355744.355757", acknowledgement = ack-nhfb, } @Article{Tenney:1977:RTO, author = "Dennis Tenney", title = "Remark on ``{Algorithm 219}: Topological Ordering for {PERT} Networks''", journal = j-TOMS, volume = "3", number = "3", pages = "303--303", month = sep, year = "1977", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Aug 30 00:28:02 1994", note = "See \cite{Kase:1963:TOP}.", URL = "http://doi.acm.org/10.1145/355744.356472", acknowledgement = ack-nhfb, } @Article{Hillstrom:1977:STA, author = "Kenneth E. Hillstrom", title = "A Simulation Test Approach to the Evaluation of Nonlinear Optimization Algorithms", journal = j-TOMS, volume = "3", number = "4", pages = "305--315", month = dec, year = "1977", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 23:06:22 1994", URL = "http://doi.acm.org/10.1145/355759.355760", acknowledgement = ack-nhfb, } @Article{Powell:1977:PQA, author = "M. J. D. Powell and M. A. Sabin", title = "Piecewise Quadratic Approximations on Triangles", journal = j-TOMS, volume = "3", number = "4", pages = "316--325", month = dec, year = "1977", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D15", MRnumber = "58 #3319", bibdate = "Sat Aug 27 23:07:03 1994", URL = "http://doi.acm.org/10.1145/355759.355761", acknowledgement = ack-nhfb, } @Article{Skeel:1977:BLM, author = "Robert D. Skeel and Antony K. Kong", title = "Blended Linear Multistep Methods", journal = j-TOMS, volume = "3", number = "4", pages = "326--345", month = dec, year = "1977", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65L05", MRnumber = "57 #1904", bibdate = "Fri Sep 30 01:01:06 1994", URL = "http://doi.acm.org/10.1145/355759.355762", acknowledgement = ack-nhfb, reviewer = "R. Leonard Brown", } @Article{Payne:1977:NRN, author = "W. H. Payne", title = "Normal Random Numbers: Using Machine Analysis to Choose the Best Algorithm", journal = j-TOMS, volume = "3", number = "4", pages = "346--358", month = dec, year = "1977", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65C10", MRnumber = "57 #1827", bibdate = "Sat Aug 27 23:09:02 1994", URL = "http://doi.acm.org/10.1145/355759.355763", acknowledgement = ack-nhfb, country = "USA", date = "13/05/93", descriptors = "RVG;", enum = "7752", language = "English", location = "SEL: Wi", references = "0", reviewer = "Artenio De Matteis", revision = "16/01/94", } @Article{Boyce:1977:IPF, author = "William M. Boyce", title = "An Improved Program for the Full {Steiner} Tree Problem", journal = j-TOMS, volume = "3", number = "4", pages = "359--385", month = dec, year = "1977", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "90B10 (05C30)", MRnumber = "57 #11690", bibdate = "Sat Aug 27 23:07:03 1994", URL = "http://doi.acm.org/10.1145/355759.355764", acknowledgement = ack-nhfb, reviewer = "Fan R. K. Chung", } @Article{Cabay:1977:CTE, author = "S. Cabay and T. P. L. Lam", title = "Congruence Techniques for the Exact Solution of Integer Systems of Linear Equations", journal = j-TOMS, volume = "3", number = "4", pages = "386--397", month = dec, year = "1977", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65F05", MRnumber = "57 #7962a", bibdate = "Fri Sep 30 01:01:45 1994", URL = "http://doi.acm.org/10.1145/355759.355765", acknowledgement = ack-nhfb, reviewer = "W. Borsch-Supan", } @Article{Eddy:1977:NCH, author = "William F. Eddy", title = "A New Convex Hull Algorithm for Planar Sets", journal = j-TOMS, volume = "3", number = "4", pages = "398--403", month = dec, year = "1977", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 23:07:03 1994", URL = "http://doi.acm.org/10.1145/355759.355766", acknowledgement = ack-nhfb, } @Article{Cabay:1977:AEC, author = "S. Cabay and T. P. L. Lam", title = "{Algorithm 522}: {ESOLVE}, Congruence Techniques for the Exact Solution of Integer Systems of Linear Equations [{F4}]", journal = j-TOMS, volume = "3", number = "4", pages = "404--410", month = dec, year = "1977", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65F05", MRnumber = "57 #7962b", URL = "http://doi.acm.org/10.1145/355759.355767", acknowledgement = ack-nhfb, reviewer = "W. Borsch-Supan", } @Article{Eddy:1977:ACN, author = "W. F. Eddy", title = "{Algorithm 523}: {CONVEX}, {A} New Convex Hull Algorithm for Planar Sets [{Z}]", journal = j-TOMS, volume = "3", number = "4", pages = "411--412", month = dec, year = "1977", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/355759.355768", } @Article{Dinkel:1978:SAP, author = "John J. Dinkel and Gary A. Kochenberger and S. N. Wong", title = "Sensitivity Analysis Procedures for Geometric Programs: Computational Aspects", journal = j-TOMS, volume = "4", number = "1", pages = "1--14", month = mar, year = "1978", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 23:13:25 1994", URL = "http://doi.acm.org/10.1145/355769.355770", acknowledgement = ack-nhfb, } @Article{Blue:1978:PFP, author = "James L. Blue", title = "A Portable {Fortran} Program to Find the {Euclidean} Norm of a Vector", journal = j-TOMS, volume = "4", number = "1", pages = "15--23", month = mar, year = "1978", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "68A10", MRnumber = "57 #18205", bibdate = "Sat Aug 27 23:14:36 1994", URL = "http://doi.acm.org/10.1145/355769.355771", acknowledgement = ack-nhfb, keywords = "blas; nla; norm; software", reviewer = "A. D. Booth", } @Article{Ivie:1978:SMP, author = "John Ivie", title = "Some {MACSYMA} Programs for Solving Recurrence Relations", journal = j-TOMS, volume = "4", number = "1", pages = "24--33", month = mar, year = "1978", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 20:42:29 1994", note = "See also \cite{Celis:1984:RCE}.", URL = "http://doi.acm.org/10.1145/355769.355772", acknowledgement = ack-nhfb, } @Article{Lasdon:1978:DTG, author = "L. S. Lasdon and A. D. Waren and A. Jain and M. Ratner", title = "Design and Testing of a Generalized Reduced Gradient Code for Nonlinear Programming", journal = j-TOMS, volume = "4", number = "1", pages = "34--50", month = mar, year = "1978", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 23:13:25 1994", URL = "http://doi.acm.org/10.1145/355769.355773", acknowledgement = ack-nhfb, } @Article{Tsao:1978:MNI, author = "Nai-Kuan Tsao and Rose Marie Prior", title = "On Multipoint Numerical Interpolation", journal = j-TOMS, volume = "4", number = "1", pages = "51--56", month = mar, year = "1978", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 23:13:25 1994", URL = "http://doi.acm.org/10.1145/355769.355774", acknowledgement = ack-nhfb, } @Article{Brent:1978:FMP, author = "Richard P. Brent", title = "{A Fortran} Multiple-Precision Arithmetic Package", journal = j-TOMS, volume = "4", number = "1", pages = "57--70", month = mar, year = "1978", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 23:13:25 1994", URL = "http://doi.acm.org/10.1145/355769.355775", acknowledgement = ack-nhfb, } @Article{Brent:1978:AMF, author = "Richard P. Brent", title = "{Algorithm 524}: {MP}, {A Fortran} Multiple-Precision Arithmetic Package [{A1}]", journal = j-TOMS, volume = "4", number = "1", pages = "71--81", month = mar, year = "1978", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Mar 09 10:35:50 1999", note = "See also \cite{Brent:1979:RMF,Brent:1980:AIB,Smith:1998:AMP}.", URL = "http://doi.acm.org/10.1145/355769.355776", acknowledgement = ack-nhfb, } @Article{Rice:1978:AAA, author = "John R. Rice", title = "{Algorithm 525}: {ADAPT}, Adaptive Smooth Curve Fitting [{E2}]", journal = j-TOMS, volume = "4", number = "1", pages = "82--94", month = mar, year = "1978", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/355769.355777", } @Article{Futrell:1978:RTA, author = "R. Futrell", title = "Remark on ``{Fortran} Translation of {Algorithm 409}: Discrete {Chebychev} Curve Fit [{E2}]''", journal = j-TOMS, volume = "4", number = "1", pages = "95--95", month = mar, year = "1978", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Sep 05 23:07:36 1994", note = "See \cite{Simpson:1976:AFT}.", URL = "http://doi.acm.org/10.1145/355769.355778", acknowledgement = ack-nhfb, } @Article{Skovgaard:1978:RCE, author = "Ove Skovgaard", title = "Remark on ``{Algorithm 149}: Complete Elliptic Integral [{S21}]''", journal = j-TOMS, volume = "4", number = "1", pages = "95--95", month = mar, year = "1978", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Aug 30 00:28:02 1994", note = "See \cite{Merner:1962:CEI}.", URL = "http://doi.acm.org/10.1145/355769.356473", acknowledgement = ack-nhfb, } @Article{Krogh:1978:AP, author = "Fred T. Krogh", title = "Algorithms Policy", journal = j-TOMS, volume = "4", number = "2", pages = "97--99", month = jun, year = "1978", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 23:23:41 1994", URL = "http://doi.acm.org/10.1145/355780.355781", acknowledgement = ack-nhfb, } @Article{Ford:1978:PET, author = "Brian Ford", title = "Parametrization of the Environment for Transportable Numerical Software", journal = j-TOMS, volume = "4", number = "2", pages = "100--103", month = jun, year = "1978", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 23:13:25 1994", URL = "http://doi.acm.org/10.1145/355780.355782", acknowledgement = ack-nhfb, } @Article{Fox:1978:PMS, author = "P. A. Fox and A. D. Hall and N. L. Schryer", title = "The {PORT} Mathematical Subroutine Library", journal = j-TOMS, volume = "4", number = "2", pages = "104--126", month = jun, year = "1978", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 23:13:25 1994", URL = "http://doi.acm.org/10.1145/355780.355783", acknowledgement = ack-nhfb, } @Article{Enright:1978:IEM, author = "W. H. Enright", title = "Improving the Efficiency of Matrix Operations in the Numerical Solution of Stiff Ordinary Differential Equations", journal = j-TOMS, volume = "4", number = "2", pages = "127--136", month = jun, year = "1978", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65L10", MRnumber = "58 #3483", bibdate = "Sat Aug 27 23:13:25 1994", URL = "http://doi.acm.org/10.1145/355780.355784", acknowledgement = ack-nhfb, reviewer = "Henning Esser", } @Article{Duff:1978:ITA, author = "I. S. Duff and J. K. Reid", title = "An Implementation of {Tarjan}'s Algorithm for the Block Triangularization of a Matrix", journal = j-TOMS, volume = "4", number = "2", pages = "137--147", month = jun, year = "1978", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 19:40:23 1994", URL = "http://doi.acm.org/10.1145/355780.355785", acknowledgement = ack-nhfb, keywords = "graph; sparse", } @Article{Akima:1978:MBI, author = "Hiroshi Akima", title = "A Method of Bivariate Interpolation and Smooth Surface Fitting for Irregularly Distributed Data Points", journal = j-TOMS, volume = "4", number = "2", pages = "148--159", month = jun, year = "1978", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 23:13:25 1994", URL = "http://doi.acm.org/10.1145/355780.355786", acknowledgement = ack-nhfb, } @Article{Akima:1978:ABI, author = "Hiroshi Akima", title = "{Algorithm 526}: Bivariate Interpolation and Smooth Surface Fitting for Irregularly Distributed Data Points [{E1}]", journal = j-TOMS, volume = "4", number = "2", pages = "160--164", month = jun, year = "1978", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 4 20:54:19 1994", note = "See also \cite{Akima:1979:RBI,Preusser:1985:RBI}.", URL = "http://doi.acm.org/10.1145/355780.355787", acknowledgement = ack-nhfb, } @Article{Bank:1978:AFI, author = "Randolph E. Bank", title = "{Algorithm 527}: {A Fortran} Implementation of the Generalized Marching Algorithm [{D3}]", journal = j-TOMS, volume = "4", number = "2", pages = "165--176", month = jun, year = "1978", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 23:30:03 1994", URL = "http://doi.acm.org/10.1145/355780.355788", acknowledgement = ack-nhfb, } @Article{Fox:1978:AFP, author = "P. A. Fox and A. D. Hall and N. L. Schryer", title = "{Algorithm 528}: Framework for a Portable Library [{Z}]", journal = j-TOMS, volume = "4", number = "2", pages = "177--188", month = jun, year = "1978", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 23:30:46 1994", note = "See remarks \cite{Fox:1979:RFP,Gay:1999:SAF}.", URL = "http://doi.acm.org/10.1145/355780.355789", acknowledgement = ack-nhfb, annote = "The three program packages presented here provide a framework for a portable FORTRAN subroutine library. They were developed for the BELL Laboratories library PORT(1). The packages are: machine-dependent constants, automatic error handling, and dynamic storage allocation using a stack.", country = "USA", date = "19/03/80", descriptors = "Reliability; program construction; mathematical method; FORTRAN; portability; error handling; memory management; library;", enum = "988", language = "English", location = "RWTH-AC-DFV: TELL", references = "1", revision = "20/03/92", } @Article{Duff:1978:APB, author = "I. S. Duff and J. K. Reid", title = "{Algorithm 529}: Permutations To Block Triangular Form [{F1}]", journal = j-TOMS, volume = "4", number = "2", pages = "189--192", month = jun, year = "1978", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 23:31:27 1994", URL = "http://doi.acm.org/10.1145/355780.355790", acknowledgement = ack-nhfb, } @Article{Bailey:1978:ASS, author = "P. B. Bailey and M. K. Gordon and L. F. Shampine", title = "Automatic Solution of the {Sturm-Liouville} Problem", journal = j-TOMS, volume = "4", number = "3", pages = "193--208", month = sep, year = "1978", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65L15", MRnumber = "80a:65181", bibdate = "Sat Aug 27 23:13:25 1994", URL = "http://doi.acm.org/10.1145/355791.355792", acknowledgement = ack-nhfb, } @Article{Polak:1978:TPP, author = "S. J. Polak and J. Schrooten and C. Barneveld Binkhuysen", title = "{TEDDY2}, {A} Program Package for Parabolic Composite Region Problems", journal = j-TOMS, volume = "4", number = "3", pages = "209--227", month = sep, year = "1978", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65-04", MRnumber = "80a:65009", bibdate = "Sat Aug 27 23:13:25 1994", URL = "http://doi.acm.org/10.1145/355791.355793", acknowledgement = ack-nhfb, } @Article{Larson:1978:ECE, author = "John Larson and Ahmed Sameh", title = "Efficient Calculation of the Effects of Roundoff Errors", journal = j-TOMS, volume = "4", number = "3", pages = "228--236", month = sep, year = "1978", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65G05", MRnumber = "80a:65092a", bibdate = "Thu Apr 29 15:22:59 1999", note = "See errata \cite{Larson:1979:ECE}.", URL = "http://doi.acm.org/10.1145/355791.355794", acknowledgement = ack-nhfb, keywords = "na; rounding error", } @Article{Brown:1978:SPA, author = "W. S. Brown", title = "The Subresultant {PRS} Algorithm", journal = j-TOMS, volume = "4", number = "3", pages = "237--249", month = sep, year = "1978", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "12-04 (68C20)", MRnumber = "82g:12001", bibdate = "Sat Aug 27 23:13:25 1994", URL = "http://doi.acm.org/10.1145/355791.355795", acknowledgement = ack-nhfb, } @Article{Gustavson:1978:TFA, author = "Fred G. Gustavson", title = "Two Fast Algorithms for Sparse Matrices: Multiplication and Permuted Transposition", journal = j-TOMS, volume = "4", number = "3", pages = "250--269", month = sep, year = "1978", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65F30 (65-04)", MRnumber = "80a:65086", bibdate = "Sat Aug 27 23:13:25 1994", URL = "http://doi.acm.org/10.1145/355791.355796", acknowledgement = ack-nhfb, } @Article{Chen:1978:PPB, author = "S. C. Chen and D. J. Kuck and A. H. Sameh", title = "Practical Parallel Band Triangular Systems Solvers", journal = j-TOMS, volume = "4", number = "3", pages = "270--277", month = sep, year = "1978", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65F05 (65-04)", MRnumber = "80a:65065", bibdate = "Fri Aug 26 23:35:36 1994", URL = "http://doi.acm.org/10.1145/355791.355797", acknowledgement = ack-nhfb, keywords = "linear system; nla; prll; tridiagonal matrix", } @Article{Ward:1978:ECS, author = "R. C. Ward and L. J. Gray", title = "Eigensystem Computation for Skew-Symmetric and a Class of Symmetric Matrices", journal = j-TOMS, volume = "4", number = "3", pages = "278--285", month = sep, year = "1978", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65F15", MRnumber = "80a:65082", bibdate = "Sat Aug 27 23:37:26 1994", URL = "http://doi.acm.org/10.1145/355791.355798", acknowledgement = ack-nhfb, keywords = "eig; nla; skew-symmetric matrix; symmetric matrix", } @Article{Ward:1978:AAC, author = "R. C. Ward and L. J. Gray", title = "{Algorithm 530}: An Algorithm for Computing the Eigensystem of Skew-Symmetric Matrices and a Class of Symmetric Matrices [{F2}]", journal = j-TOMS, volume = "4", number = "3", pages = "286--289", month = sep, year = "1978", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 23:37:47 1994", URL = "http://doi.acm.org/10.1145/355791.355799", acknowledgement = ack-nhfb, } @Article{Snyder:1978:ACP, author = "William V. Snyder", title = "{Algorithm 531}: Contour Plotting [{J6}]", journal = j-TOMS, volume = "4", number = "3", pages = "290--294", month = sep, year = "1978", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 23:38:29 1994", URL = "http://doi.acm.org/10.1145/355791.355800", acknowledgement = ack-nhfb, } @Article{Coleman:1978:RSN, author = "John P. Coleman", title = "Remark on ``{Algorithm 49}: Spherical {Neumann} Function''", journal = j-TOMS, volume = "4", number = "3", pages = "295--295", month = sep, year = "1978", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Aug 30 00:28:02 1994", note = "See \cite{Herndon:1961:SNF}.", URL = "http://doi.acm.org/10.1145/355791.355801", acknowledgement = ack-nhfb, } @Article{Gustavson:1978:RSM, author = "Fred G. Gustavson", title = "Remark on ``{Algorithm 408}: {A} Sparse Matrix Package (Part {I}) [{F4}]''", journal = j-TOMS, volume = "4", number = "3", pages = "295--295", month = sep, year = "1978", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Aug 30 00:28:02 1994", note = "See \cite{McNamee:1971:SMP}.", URL = "http://doi.acm.org/10.1145/355791.356474", acknowledgement = ack-nhfb, } @Article{Schoene:1978:RMI, author = "Andrew Y. Schoene", title = "Remark on ``{Algorithm 435}: Modified Incomplete Gamma Function [{S14}]''", journal = j-TOMS, volume = "4", number = "3", pages = "296--304", month = sep, year = "1978", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Aug 30 00:28:02 1994", note = "See \cite{Fullerton:1972:MIG}.", URL = "http://doi.acm.org/10.1145/355791.355803", acknowledgement = ack-nhfb, } @Article{Baker:1978:SAC, author = "Christopher T. H. Baker and Malcolm S. Keech", title = "Stability Analysis of Certain {Runge-Kutta} Procedures for {Volterra} Integral Equations", journal = j-TOMS, volume = "4", number = "4", pages = "305--315", month = dec, year = "1978", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65R20", MRnumber = "80a:65264", bibdate = "Sat Aug 27 23:13:25 1994", URL = "http://doi.acm.org/10.1145/356502.356476", acknowledgement = ack-nhfb, } @Article{Fairweather:1978:IRQ, author = "Graeme Fairweather", title = "An Investigation of {Romberg} Quadrature", journal = j-TOMS, volume = "4", number = "4", pages = "316--322", month = dec, year = "1978", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 23:13:25 1994", URL = "http://doi.acm.org/10.1145/356502.356477", acknowledgement = ack-nhfb, } @Article{Shampine:1978:SPA, author = "Lawrence F. Shampine", title = "Stability Properties of {Adams} Codes", journal = j-TOMS, volume = "4", number = "4", pages = "323--329", month = dec, year = "1978", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65L05", MRnumber = "80c:65157", bibdate = "Sat Aug 27 23:13:25 1994", URL = "http://doi.acm.org/10.1145/356502.356478", acknowledgement = ack-nhfb, } @Article{Sherman:1978:ASG, author = "Andrew H. Sherman", title = "Algorithms for Sparse {Gaussian} Elimination with Partial Pivoting", journal = j-TOMS, volume = "4", number = "4", pages = "330--338", month = dec, year = "1978", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 23:13:25 1994", URL = "http://doi.acm.org/10.1145/356502.356494", acknowledgement = ack-nhfb, } @Article{Tendler:1978:SSI, author = "Joel M. Tendler and Theodore A. Bickart and Zdenek Picel", title = "A Stiffly Stable Integration Process Using Cyclic Composite Methods", journal = j-TOMS, volume = "4", number = "4", pages = "339--368", month = dec, year = "1978", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 23:13:25 1994", URL = "http://doi.acm.org/10.1145/356502.356495", acknowledgement = ack-nhfb, } @Article{Miller:1978:SRA, author = "Webb Miller and David Spooner", title = "Software for Roundoff Analysis. {II}", journal = j-TOMS, volume = "4", number = "4", pages = "369--387", month = dec, year = "1978", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65G05 (65F99)", MRnumber = "81i:65035", bibdate = "Sat Aug 27 23:48:16 1994", URL = "http://doi.acm.org/10.1145/356502.356496", acknowledgement = ack-nhfb, keywords = "cs; rounding error; software", } @Article{Miller:1978:ASR, author = "Webb Miller and David Spooner", title = "{Algorithm 532}: Software for Roundoff Analysis [{Z}]", journal = j-TOMS, volume = "4", number = "4", pages = "388--390", month = dec, year = "1978", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 23:48:45 1994", URL = "http://doi.acm.org/10.1145/356502.356497", acknowledgement = ack-nhfb, } @Article{Sherman:1978:ANF, author = "Andrew H. Sherman", title = "{Algorithm 533}: {NSPIV}, {A Fortran} Subroutine for Sparse {Gaussian} Elimination with Partial Pivoting [{F4}]", journal = j-TOMS, volume = "4", number = "4", pages = "391--398", month = dec, year = "1978", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 23:49:20 1994", URL = "http://doi.acm.org/10.1145/356502.356498", acknowledgement = ack-nhfb, } @Article{Tendler:1978:ASS, author = "Joel M. Tendler and Theodore A. Bickart and Zdenek Picel", title = "{Algorithm 534}: {STINT}: {STiff} (differential equations) {INTegrator} [{D2}]", journal = j-TOMS, volume = "4", number = "4", pages = "399--403", month = dec, year = "1978", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 23:50:02 1994", URL = "http://doi.acm.org/10.1145/356502.356499", acknowledgement = ack-nhfb, } @Article{Garbow:1978:AQA, author = "Burton S. Garbow", title = "{Algorithm 535}: The {QZ} Algorithm to Solve the Generalized Eigenvalue Problem for Complex Matrices [{F2}]", journal = j-TOMS, volume = "4", number = "4", pages = "404--410", month = dec, year = "1978", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 20:40:17 1994", note = "See also \cite{Garbow:1982:RQA,Garbow:1984:RQA}.", URL = "http://doi.acm.org/10.1145/356502.356500", acknowledgement = ack-nhfb, } @Article{Amos:1978:ECS, author = "Donald E. Amos", title = "Erratum: ``{Algorithm 511}: {CDC} 6600 Subroutines {IBESS} and {JBESS} for {Bessel} Functions {$I_\nu(x)$} and {$J_\nu(x)$}, {$x\ge0,\nu\ge0$} [{S18}]''", journal = j-TOMS, volume = "4", number = "4", pages = "411--411", month = dec, year = "1978", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Aug 30 00:28:02 1994", note = "See \cite{Amos:1977:ACS}.", URL = "http://doi.acm.org/10.1145/356502.356501", acknowledgement = ack-nhfb, } @Article{Zave:1979:DAP, author = "Pamela Zave and Werner C. Rheinboldt", title = "Design of an Adaptive, Parallel Finite-Element System", journal = j-TOMS, volume = "5", number = "1", pages = "1--17", month = mar, year = "1979", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65N30 (65-04)", MRnumber = "80c:65213", bibdate = "Sat Aug 27 23:13:25 1994", URL = "http://doi.acm.org/10.1145/355815.355816", acknowledgement = ack-nhfb, } @Article{Duff:1979:SDF, author = "I. S. Duff and J. K. Reid", title = "Some Design Features of a Sparse Matrix Code", journal = j-TOMS, volume = "5", number = "1", pages = "18--35", month = mar, year = "1979", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 23:13:25 1994", URL = "http://doi.acm.org/10.1145/355815.355817", acknowledgement = ack-nhfb, } @Article{Proskurowski:1979:NSH, author = "Wlodzimierz Proskurowski", title = "Numerical Solution of {Helmholtz}'s Equation by Implicit Capacitance Matrix Methods", journal = j-TOMS, volume = "5", number = "1", pages = "36--49", month = mar, year = "1979", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65N20", MRnumber = "80b:65129", bibdate = "Sat Aug 27 23:13:25 1994", URL = "http://doi.acm.org/10.1145/355815.355818", acknowledgement = ack-nhfb, reviewer = "John Crank", } @Article{Yohe:1979:SIA, author = "J. M. Yohe", title = "Software for Interval Arithmetic: {A} Reasonably Portable Package", journal = j-TOMS, volume = "5", number = "1", pages = "50--63", month = mar, year = "1979", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 23:55:38 1994", URL = "http://doi.acm.org/10.1145/355815.355819", acknowledgement = ack-nhfb, keywords = "interval arithmetic; na; software", } @Article{More:1979:NSN, author = "Jorge J. Mor{\'e} and Michel Y. Cosnard", title = "Numerical Solution of Nonlinear Equations", journal = j-TOMS, volume = "5", number = "1", pages = "64--85", month = mar, year = "1979", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65H05", MRnumber = "80c:65110", bibdate = "Sat Aug 27 23:13:25 1994", URL = "http://doi.acm.org/10.1145/355815.355820", acknowledgement = ack-nhfb, } @Article{Kahaner:1979:EAD, author = "David K. Kahaner and Mark B. Wells", title = "An Experimental Algorithm for ${N}$-Dimensional Adaptive Quadrature", journal = j-TOMS, volume = "5", number = "1", pages = "86--96", month = mar, year = "1979", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Aug 30 00:41:04 1994", URL = "http://doi.acm.org/10.1145/355815.355821", acknowledgement = ack-nhfb, } @Article{Knoble:1979:EOW, author = "H. D. Knoble and C. {Forney, Jr.} and F. S. Bader", title = "An Efficient One-Way Enciphering Algorithm", journal = j-TOMS, volume = "5", number = "1", pages = "97--107", month = mar, year = "1979", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 23:13:25 1994", URL = "http://doi.acm.org/10.1145/355815.355822", acknowledgement = ack-nhfb, } @Article{Knoble:1979:AEO, author = "H. D. Knoble", title = "{Algorithm 536}: An Efficient One-Way Enciphering Algorithm [{Z}]", journal = j-TOMS, volume = "5", number = "1", pages = "108--111", month = mar, year = "1979", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 23:58:53 1994", URL = "http://doi.acm.org/10.1145/355815.355823", acknowledgement = ack-nhfb, } @Article{Leeb:1979:ACV, author = "Walter R. Leeb", title = "{Algorithm 537}: Characteristic Values of {Mathieu}'s Differential Equation", journal = j-TOMS, volume = "5", number = "1", pages = "112--117", month = mar, year = "1979", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/355815.355824", } @Article{Nikolai:1979:AEE, author = "Paul J. Nikolai", title = "{Algorithm 538}: Eigenvectors and Eigenvalues of Real Generalized Symmetric Matrices by Simultaneous Iteration [{F2}]", journal = j-TOMS, volume = "5", number = "1", pages = "118--125", month = mar, year = "1979", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/355815.355825", } @Article{Krogh:1979:AAP, author = "Fred T. Krogh", title = "{ACM} Algorithms Policy", journal = j-TOMS, volume = "5", number = "2", pages = "129--131", month = jun, year = "1979", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Aug 28 00:01:38 1994", URL = "http://doi.acm.org/10.1145/355826.355827", acknowledgement = ack-nhfb, } @Article{Schrage:1979:MPF, author = "Linus Schrage", title = "A More Portable {Fortran} Random Number Generator", journal = j-TOMS, volume = "5", number = "2", pages = "132--138", month = jun, year = "1979", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 23:13:25 1994", URL = "http://doi.acm.org/10.1145/355826.355828", acknowledgement = ack-nhfb, } @Article{George:1979:DUI, author = "Alan George and Joseph W. H. Liu", title = "The Design of a User Interface for a Sparse Matrix Package", journal = j-TOMS, volume = "5", number = "2", pages = "139--162", month = jun, year = "1979", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 23:13:25 1994", URL = "http://doi.acm.org/10.1145/355826.355829", acknowledgement = ack-nhfb, } @Article{Payne:1979:CG, author = "W. H. Payne and F. M. Ives", title = "Combination Generators", journal = j-TOMS, volume = "5", number = "2", pages = "163--172", month = jun, year = "1979", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 23:13:25 1994", URL = "http://doi.acm.org/10.1145/355826.355830", acknowledgement = ack-nhfb, } @Article{deBoor:1979:ECM, author = "Carl {de Boor}", title = "Efficient Computer Manipulation of Tensor Products", journal = j-TOMS, volume = "5", number = "2", pages = "173--182", month = jun, year = "1979", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65-04", MRnumber = "80d:65006a", bibdate = "Thu Apr 29 15:18:18 1999", note = "See corrigenda \cite{deBoor:1979:CCM}.", URL = "http://doi.acm.org/10.1145/355826.355831", acknowledgement = ack-nhfb, } @Article{Cleary:1979:AAF, author = "John Gerald Cleary", title = "Analysis of an Algorithm for Finding Nearest Neighbors in {Euclidean} Space", journal = j-TOMS, volume = "5", number = "2", pages = "183--192", month = jun, year = "1979", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "68H05 (68G10)", MRnumber = "80e:68236", bibdate = "Sun Aug 28 00:06:29 1994", URL = "http://doi.acm.org/10.1145/355826.355832", acknowledgement = ack-nhfb, } @Article{Crowder:1979:RCE, author = "Harlan Crowder and Ron S. Dembo and John M. Mulvey", title = "On Reporting Computational Experiments with Mathematical Software", journal = j-TOMS, volume = "5", number = "2", pages = "193--203", month = jun, year = "1979", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Aug 28 00:06:29 1994", URL = "http://doi.acm.org/10.1145/355826.355833", acknowledgement = ack-nhfb, } @Article{Crary:1979:VPN, author = "Fred D. Crary", title = "A Versatile Precompiler for Nonstandard Arithmetics", journal = j-TOMS, volume = "5", number = "2", pages = "204--217", month = jun, year = "1979", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Aug 28 00:06:29 1994", URL = "http://doi.acm.org/10.1145/355826.355834", acknowledgement = ack-nhfb, } @Article{Geddes:1979:SCP, author = "K. O. Geddes", title = "Symbolic Computation of Pad{\'e} Approximants", journal = j-TOMS, volume = "5", number = "2", pages = "218--233", month = jun, year = "1979", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65-04 (65F99 68C20)", MRnumber = "80c:65005", bibdate = "Sun Aug 28 00:06:29 1994", URL = "http://doi.acm.org/10.1145/355826.355835", acknowledgement = ack-nhfb, } @Article{Bogen:1979:ASI, author = "Richard A. Bogen", title = "Addendum to ``{Analytically} Solving Integral Equations by Using Computer Algebra''", journal = j-TOMS, volume = "5", number = "2", pages = "234--237", month = jun, year = "1979", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65R20", MRnumber = "80k:65102", bibdate = "Sat Nov 19 13:07:40 1994", URL = "http://doi.acm.org/10.1145/355826.355836", acknowledgement = ack-nhfb, } @Article{elLozy:1979:RAS, author = "Mohamed {el Lozy}", title = "Remark on ``{Algorithm 395}: {Student}'s $t$-Distribution'' and Remark on ``{Algorithm 396}: {Student}'s Quantiles [{S14}]''", journal = j-TOMS, volume = "5", number = "2", pages = "238--239", month = jun, year = "1979", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Mar 28 11:05:53 2003", note = "See \cite{Hill:1970:SD,Hill:1970:SQ,Hill:1981:RSD,Hill:1985:RCS}.", URL = "http://doi.acm.org/10.1145/355826.355837", acknowledgement = ack-nhfb, } @Article{Geddes:1979:RCC, author = "K. O. Geddes", title = "Remark on ``{Algorithm 424}: {Clenshaw-Curtis} Quadrature [{O1}]''", journal = j-TOMS, volume = "5", number = "2", pages = "240--240", month = jun, year = "1979", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Aug 30 00:28:02 1994", note = "See \cite{Gentleman:1972:CCQ}.", URL = "http://doi.acm.org/10.1145/355826.355838", acknowledgement = ack-nhfb, } @Article{Anderson:1979:RBI, author = "M. R. Anderson", title = "Remark on ``{Algorithm 474}: Bivariate Interpolation and Smooth Surface Fitting Based on Local Procedures''", journal = j-TOMS, volume = "5", number = "2", pages = "241--241", month = jun, year = "1979", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Aug 30 00:28:02 1994", note = "See \cite{Akima:1974:BIS}.", URL = "http://doi.acm.org/10.1145/355826.355839", acknowledgement = ack-nhfb, } @Article{Akima:1979:RBI, author = "Hiroshi Akima", title = "Remark on ``{Algorithm} 526: Bivariate Interpolation and Smooth Surface Fitting for Irregularly Distributed Data Points [{E1}]''", journal = j-TOMS, volume = "5", number = "2", pages = "242--243", month = jun, year = "1979", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Aug 30 00:28:03 1994", note = "See \cite{Akima:1978:ABI,Preusser:1985:RBI}.", URL = "http://doi.acm.org/10.1145/355826.355840", acknowledgement = ack-nhfb, } @Article{Shampine:1979:SRR, author = "L. F. Shampine", title = "Storage Reduction for {Runge-Kutta} Codes", journal = j-TOMS, volume = "5", number = "3", pages = "245--250", month = sep, year = "1979", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Aug 28 00:06:29 1994", URL = "http://doi.acm.org/10.1145/355841.355842", acknowledgement = ack-nhfb, } @Article{Ehrlich:1979:SBE, author = "L. W. Ehrlich", title = "Solving the Biharmonic Equation on Irregular Regions", journal = j-TOMS, volume = "5", number = "3", pages = "251--258", month = sep, year = "1979", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65N20", MRnumber = "80e:65093", bibdate = "Sun Aug 28 00:06:29 1994", URL = "http://doi.acm.org/10.1145/355841.355843", acknowledgement = ack-nhfb, } @Article{Gill:1979:DSF, author = "Philip E. Gill and Walter Murray and Susan M. Picken and Margaret H. Wright", title = "The Design and Structure of a {Fortran} Program Library for Optimization", journal = j-TOMS, volume = "5", number = "3", pages = "259--283", month = sep, year = "1979", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Aug 28 00:06:29 1994", URL = "http://doi.acm.org/10.1145/355841.355844", acknowledgement = ack-nhfb, } @Article{George:1979:IPN, author = "Alan George and Joseph W. H. Liu", title = "An Implementation of a Pseudoperipheral Node Finder", journal = j-TOMS, volume = "5", number = "3", pages = "284--295", month = sep, year = "1979", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Aug 28 00:06:29 1994", URL = "http://doi.acm.org/10.1145/355841.355845", acknowledgement = ack-nhfb, } @Article{Bennett:1979:SPE, author = "James Michael Bennett and Robert Neff Bryan", title = "A Single-Point Exchange Algorithm for Approximating Functions of Two Variables", journal = j-TOMS, volume = "5", number = "3", pages = "296--307", month = sep, year = "1979", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D15", MRnumber = "80e:65020", bibdate = "Sun Aug 28 00:06:29 1994", URL = "http://doi.acm.org/10.1145/355841.355846", acknowledgement = ack-nhfb, } @Article{Lawson:1979:BLA, author = "C. L. Lawson and R. J. Hanson and D. R. Kincaid and F. T. Krogh", title = "{Basic Linear Algebra Subprograms} for {Fortran} Usage", journal = j-TOMS, volume = "5", number = "3", pages = "308--323", month = sep, year = "1979", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 19:42:33 1994", URL = "http://doi.acm.org/10.1145/355841.355847", acknowledgement = ack-nhfb, keywords = "blas; nla; software", } @Article{Lawson:1979:ABL, author = "C. L. Lawson and R. J. Hanson and D. R. Kincaid and F. T. Krogh", title = "{Algorithm 539}: {Basic Linear Algebra Subprograms} for {Fortran} Usage [{F1}]", journal = j-TOMS, volume = "5", number = "3", pages = "324--325", month = sep, year = "1979", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Sep 05 21:11:34 1994", note = "See also \cite{Dodson:1982:RBL,Dodson:1983:CRB,Hanson:1987:ATA,Louter-Nool:1988:ATA}.", URL = "http://doi.acm.org/10.1145/355841.355848", acknowledgement = ack-nhfb, } @Article{Madsen:1979:APG, author = "N. K. Madsen and R. F. Sincovec", title = "{Algorithm 540}: {PDECOL}, General Collocation Software for Partial Differential Equations [{D3}]", journal = j-TOMS, volume = "5", number = "3", pages = "326--351", month = sep, year = "1979", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Sep 05 09:21:53 1994", note = "See also \cite{Hopkins:1992:RPG}.", URL = "http://doi.acm.org/10.1145/355841.355849", acknowledgement = ack-nhfb, } @Article{Swartztrauber:1979:AEF, author = "Paul N. Swartztrauber and Roland A. Sweet", title = "{Algorithm 541}: Efficient {Fortran} Subprograms for the Solution of Separable Elliptic Partial Differential Equations [{D3}]", journal = j-TOMS, volume = "5", number = "3", pages = "352--364", month = sep, year = "1979", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 19:43:36 1994", URL = "http://doi.acm.org/10.1145/355841.355850", acknowledgement = ack-nhfb, } @Article{Steuerwalt:1979:CEF, author = "Michael Steuerwalt", title = "Certification of ``{Algorithm} 541: Efficient {Fortran} Subprograms for the Solution of Separable Elliptic Partial Differential Equations [{D3}]''", journal = j-TOMS, volume = "5", number = "3", pages = "365--371", month = sep, year = "1979", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Feb 24 09:58:08 1996", URL = "http://doi.acm.org/10.1145/355841.355851", acknowledgement = ack-nhfb, } @Article{Larson:1979:ECE, author = "John Larson", title = "Errata: ``{Efficient} Calculation of the Effects of Roundoff Errors''", journal = j-TOMS, volume = "5", number = "3", pages = "372--372", month = sep, year = "1979", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "372. 65G05", MRnumber = "80a:65092b", bibdate = "Sat Nov 19 13:07:42 1994", note = "See \cite{Larson:1978:ECE}.", URL = "http://doi.acm.org/10.1145/355841.355852", acknowledgement = ack-nhfb, } @Article{Gear:1979:EN, author = "C. W. Gear", title = "{Editor}'s Note", journal = j-TOMS, volume = "5", number = "4", pages = "373--373", month = dec, year = "1979", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Aug 28 00:32:50 1994", URL = "http://doi.acm.org/10.1145/355853.355854", acknowledgement = ack-nhfb, } @Article{Enright:1979:APS, author = "W. H. Enright and M. S. Kamel", title = "Automatic Partitioning of Stiff Systems and Exploiting the Resulting Structure", journal = j-TOMS, volume = "5", number = "4", pages = "374--385", month = dec, year = "1979", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Aug 28 00:32:50 1994", URL = "http://doi.acm.org/10.1145/355853.355855", acknowledgement = ack-nhfb, } @Article{Gladwell:1979:IVR, author = "Ian Gladwell", title = "Initial Value Routines in the {NAG} Library", journal = j-TOMS, volume = "5", number = "4", pages = "386--400", month = dec, year = "1979", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Aug 28 00:32:50 1994", URL = "http://doi.acm.org/10.1145/355853.355856", acknowledgement = ack-nhfb, } @Article{Zlatev:1979:ASD, author = "Zahari Zlatev and Per Grove Thomsen", title = "Automatic Solution of Differential Equations Based on the User of Linear Multistep Methods", journal = j-TOMS, volume = "5", number = "4", pages = "401--414", month = dec, year = "1979", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Aug 28 00:32:50 1994", URL = "http://doi.acm.org/10.1145/355853.355857", acknowledgement = ack-nhfb, } @Article{Stetter:1979:GEE, author = "Hans J. Stetter", title = "Global Error Estimation in {Adams PC}-Codes", journal = j-TOMS, volume = "5", number = "4", pages = "415--430", month = dec, year = "1979", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Aug 28 00:32:50 1994", URL = "http://doi.acm.org/10.1145/355853.355858", acknowledgement = ack-nhfb, } @Article{Houstis:1979:HOF, author = "E. N. Houstis and T. S. Papatheodorou", title = "High-Order Fast Elliptic Equation Solvers", journal = j-TOMS, volume = "5", number = "4", pages = "431--441", month = dec, year = "1979", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Aug 28 00:32:50 1994", URL = "http://doi.acm.org/10.1145/355853.355859", acknowledgement = ack-nhfb, } @Article{Kaufman:1979:ADH, author = "L. Kaufman", title = "Application of Dense {Householder} Transformation to a Sparse Matrix", journal = j-TOMS, volume = "5", number = "4", pages = "442--450", month = dec, year = "1979", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Aug 26 23:38:08 1994", URL = "http://doi.acm.org/10.1145/355853.355860", acknowledgement = ack-nhfb, keywords = "Householder transformation; nla; qrd; sparse", } @Article{Rayward-Smith:1979:CSN, author = "V. J. Rayward-Smith", title = "On Computing the {Smith} Normal Form of an Integer Matrix", journal = j-TOMS, volume = "5", number = "4", pages = "451--456", month = dec, year = "1979", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Aug 28 00:32:50 1994", URL = "http://doi.acm.org/10.1145/355853.355861", acknowledgement = ack-nhfb, } @Article{Wampler:1979:SWL, author = "Roy H. Wampler", title = "Solutions to Weighted Least Squares Problems by Modified {Gram-Schmidt} with Iterative Refinement", journal = j-TOMS, volume = "5", number = "4", pages = "457--465", month = dec, year = "1979", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 19:44:12 1994", URL = "http://doi.acm.org/10.1145/355853.355862", acknowledgement = ack-nhfb, keywords = "Gram-Schmidt algorithm; iterative refinement; lsq; nla; qrd; weights", } @Article{Gautschi:1979:CPI, author = "Walter Gautschi", title = "A Computational Procedure for Incomplete Gamma Functions", journal = j-TOMS, volume = "5", number = "4", pages = "466--481", month = dec, year = "1979", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Aug 28 00:32:50 1994", URL = "http://doi.acm.org/10.1145/355853.355863", acknowledgement = ack-nhfb, } @Article{Gautschi:1979:AIG, author = "W. Gautschi", title = "{Algorithm 542}: Incomplete Gamma Functions [{S14}]", journal = j-TOMS, volume = "5", number = "4", pages = "482--489", month = dec, year = "1979", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Aug 28 00:39:50 1994", URL = "http://doi.acm.org/10.1145/355853.355864", acknowledgement = ack-nhfb, } @Article{Houstis:1979:AFF, author = "E. N. Houstis and T. S. Papatheodorou", title = "{Algorithm 543}: {FFT9}, Fast Solution of {Helmholtz}-Type Partial Differential Equations [{D3}]", journal = j-TOMS, volume = "5", number = "4", pages = "490--493", month = dec, year = "1979", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Aug 28 00:40:38 1994", URL = "http://doi.acm.org/10.1145/355853.355865", acknowledgement = ack-nhfb, } @Article{Wampler:1979:ALL, author = "Roy H. Wampler", title = "{Algorithm 544}: {L2A} and {L2B}, Weighted Least Squares Solutions by Modified {Gram-Schmidt} with Iterative Refinement [{F4}]", journal = j-TOMS, volume = "5", number = "4", pages = "494--499", month = dec, year = "1979", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Sep 30 01:04:18 1994", URL = "http://doi.acm.org/10.1145/355853.355866", acknowledgement = ack-nhfb, keywords = "Gram-Schmidt algorithm; iterative refinement; lsq; nla; qrd; weights", } @Article{Fraser:1979:AOM, author = "D. Fraser", title = "{Algorithm 545}: An Optimized Mass Storage {FFT} [{C6}]", journal = j-TOMS, volume = "5", number = "4", pages = "500--517", month = dec, year = "1979", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Aug 28 00:41:29 1994", URL = "http://doi.acm.org/10.1145/355853.355867", acknowledgement = ack-nhfb, } @Article{Brent:1979:RMF, author = "R. P. Brent", title = "Remark on ``{Algorithm} 524: {MP}, {A Fortran} Multiple-Precision Arithmetic Package [{A1}]''", journal = j-TOMS, volume = "5", number = "4", pages = "518--519", month = dec, year = "1979", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Mar 09 10:35:42 1999", note = "See \cite{Brent:1978:AMF,Brent:1980:AIB,Smith:1998:AMP}.", URL = "http://doi.acm.org/10.1145/355853.355868", acknowledgement = ack-nhfb, } @Article{Leathers:1979:RAS, author = "Burton L. Leathers", title = "Remark on ``{Algorithm} 513: Analysis of In-Situ Transposition [{F1}]'' and Remark on ``{Algorithm} 467: Matrix Transposition in Place''", journal = j-TOMS, volume = "5", number = "4", pages = "520--520", month = dec, year = "1979", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Aug 30 00:28:03 1994", note = "See \cite{Cate:1977:AAS,Brenner:1973:MTP}.", URL = "http://doi.acm.org/10.1145/355853.355869", acknowledgement = ack-nhfb, } @Article{vanSwieten:1979:RAV, author = "A. C. M. {van Swieten} and J. Th. M. {de Hosson}", title = "Remark on ``{Algorithm} 475: Visible Surface Plotting Program''", journal = j-TOMS, volume = "5", number = "4", pages = "521--523", month = dec, year = "1979", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Aug 30 00:28:03 1994", note = "See \cite{Wright:1974:VSP}.", URL = "http://doi.acm.org/10.1145/355853.355870", acknowledgement = ack-nhfb, } @Article{Fox:1979:RFP, author = "Phyllis Fox", title = "Remark on ``{Algorithm} 528: Framework for a Portable Library [{Z}]''", journal = j-TOMS, volume = "5", number = "4", pages = "524--524", month = dec, year = "1979", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Aug 30 00:28:06 1994", note = "See \cite{Fox:1978:AFP}.", URL = "http://doi.acm.org/10.1145/355853.355871", acknowledgement = ack-nhfb, } @Article{deBoor:1979:CCM, author = "Carl {de Boor}", title = "Corrigenda: ``{Efficient} Computer Manipulation of Tensor Products''", journal = j-TOMS, volume = "5", number = "4", pages = "525--525", month = dec, year = "1979", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "525. 65-04", MRnumber = "80d:65006b", bibdate = "Sat Oct 24 15:50:17 1998", note = "See \cite{deBoor:1979:ECM}.", URL = "http://doi.acm.org/10.1145/355853.355872", acknowledgement = ack-nhfb, } @Article{Cheung:1980:CCE, author = "To-Yat Cheung", title = "Computational Comparison of Eight Methods for the Maximum Network Flow Problem", journal = j-TOMS, volume = "6", number = "1", pages = "1--16", month = mar, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "90B10 (68E10)", MRnumber = "80m:90046", bibdate = "Mon Aug 29 08:58:06 1994", URL = "http://doi.acm.org/10.1145/355873.355874", acknowledgement = ack-nhfb, keywords = "breadth-first; computational comparison; depth-first; Dinic; Karzanov; Kinariwala-Rao; maximum network flow", } @Article{Ho:1980:CST, author = "James K. Ho and Etienne Loute", title = "A Comparative Study of Two Methods for Staircase Linear Problems", journal = j-TOMS, volume = "6", number = "1", pages = "17--30", month = mar, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 08:58:06 1994", URL = "http://doi.acm.org/10.1145/355873.355875", acknowledgement = ack-nhfb, keywords = "comparison of algorithms; decomposition; factorization; large-scale systems; structured linear programs", } @Article{Michaels:1980:MPG, author = "William M. Michaels and Richard P. O'Neill", title = "A Mathematical Program Generator {MPGENR}", journal = j-TOMS, volume = "6", number = "1", pages = "31--44", month = mar, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 08:58:06 1994", URL = "http://doi.acm.org/10.1145/355873.355876", acknowledgement = ack-nhfb, keywords = "large-scale optimization; linear and nonlinear programming; software verification; test problem generation", } @Article{Chung:1980:ACF, author = "Won L. Chung", title = "Automatic Curve Fittings Using an Adaptive Local Algorithm", journal = j-TOMS, volume = "6", number = "1", pages = "45--57", month = mar, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 11:55:50 1994", URL = "http://doi.acm.org/10.1145/355873.355877", acknowledgement = ack-nhfb, keywords = "adaptive approximation; automatic curve fitting; data compression; interactive display; {$L_2$} approximation with continuity constraints; modeling and simulation systems; numerical stability; one-sided algorithm; piecewise cubic polynomials", } @Article{Clark:1980:REV, author = "Gordon M. Clark", title = "Recursive Estimation of the Variance of the Sample Average", journal = j-TOMS, volume = "6", number = "1", pages = "58--67", month = mar, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "68J05 (65C20)", MRnumber = "80m:68086", bibdate = "Mon Aug 29 08:58:06 1994", URL = "http://doi.acm.org/10.1145/355873.355878", acknowledgement = ack-nhfb, keywords = "recursive calculation; sample autocovariances; simulation output analysis; variance estimation", } @Article{Power:1980:ISU, author = "Leigh R. Power", title = "Internal Sorting Using a Minimal Tree Merge Strategy", journal = j-TOMS, volume = "6", number = "1", pages = "68--79", month = mar, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "68E05", MRnumber = "80m:68056", bibdate = "Mon Aug 29 08:58:06 1994", URL = "http://doi.acm.org/10.1145/355873.355879", acknowledgement = ack-nhfb, keywords = "internal sort; linked list; list processing; merge; minimal tree; natural merge sort; sort; straight merge sort", } @Article{deBoor:1980:SPS, author = "Carl {de Boor} and Richard Weiss", title = "{SOLVEBLOK}: {A} Package for Solving Almost Block Diagonal Linear Systems", journal = j-TOMS, volume = "6", number = "1", pages = "80--87", month = mar, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Oct 24 15:50:20 1998", URL = "http://doi.acm.org/10.1145/355873.355880", acknowledgement = ack-nhfb, keywords = "almost block diagonal systems; Gaussian elimination; ordinary differential equations; spline approximation", } @Article{deBoor:1980:AS, author = "Carl {de Boor} and Richard Weiss", title = "{Algorithm 546}: {SOLVEBLOK} [{F4}]", journal = j-TOMS, volume = "6", number = "1", pages = "88--91", month = mar, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Oct 24 15:50:24 1998", URL = "http://doi.acm.org/10.1145/355873.355881", acknowledgement = ack-nhfb, keywords = "almost block diagonal systems; Gaussian elimination; ordinary differential equations; spline approximation", } @Article{Duris:1980:AFR, author = "Charles S. Duris", title = "{Algorithm 547}: {FORTRAN} Routines for Discrete Cubic Spline Interpolation and Smoothing [{E1}], [{E3}]", journal = j-TOMS, volume = "6", number = "1", pages = "92--103", month = mar, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 10:29:10 1994", URL = "http://doi.acm.org/10.1145/355873.355882", acknowledgement = ack-nhfb, keywords = "discrete cubic splines; discrete natural splines; discrete splines; interpolation; smoothing", } @Article{Carpaneto:1980:ASA, author = "Giorgio Carpaneto and Paolo Toth", title = "{Algorithm 548}: Solution of the Assignment Problem [{H}]", journal = j-TOMS, volume = "6", number = "1", pages = "104--111", month = mar, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 10:29:23 1994", URL = "http://doi.acm.org/10.1145/355873.355883", acknowledgement = ack-nhfb, keywords = "assignment problem; Hungarian algorithm", } @Article{Eckhardt:1980:AWE, author = "Ulrich Eckhardt", title = "{Algorithm 549}: {Weierstrass}' Elliptic Functions [{S21}]", journal = j-TOMS, volume = "6", number = "1", pages = "112--120", month = mar, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 10:31:24 1994", URL = "http://doi.acm.org/10.1145/355873.355884", acknowledgement = ack-nhfb, keywords = "Weierstrass' elliptic functions", } @Article{Messner:1980:ASP, author = "A. M. Messner and G. Q. Taylor", title = "{Algorithm 550}: Solid Polyhedron Measure [{Z}]", journal = j-TOMS, volume = "6", number = "1", pages = "121--130", month = mar, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 14:44:11 1994", URL = "http://doi.acm.org/10.1145/355873.355885", acknowledgement = ack-nhfb, keywords = "graphics; numerical integration; polyhedron", } @Article{Anonymous:1980:AAD, author = "{Anonymous}", title = "{ACM Algorithms Distribution Service} Expanded", journal = j-TOMS, volume = "6", number = "1", pages = "131--132", month = mar, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 08:58:06 1994", URL = "http://doi.acm.org/10.1145/355873.355886", acknowledgement = ack-nhfb, } @Article{Chan:1980:NLS, author = "Tony F. Chan and William M. {Coughran, Jr.} and Eric H. Grosse and Michael T. Heath", title = "A Numerical Library and Its Support", journal = j-TOMS, volume = "6", number = "2", pages = "135--145", month = jun, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 10:33:27 1994", URL = "http://doi.acm.org/10.1145/355887.355888", acknowledgement = ack-nhfb, keywords = "library management and organization; mathematical software; numerical analysis", } @Article{Brent:1980:AIB, author = "Richard P. Brent and Judith A. Hooper and J. Michael Yohe", title = "An {AUGMENT} Interface for {Brent}'s Multiple Precision Arithmetic Package", journal = j-TOMS, volume = "6", number = "2", pages = "146--149", month = jun, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Mar 09 10:35:33 1999", note = "See \cite{Brent:1978:AMF,Brent:1979:RMF,Smith:1998:AMP}.", URL = "http://doi.acm.org/10.1145/355887.355889", acknowledgement = ack-nhfb, keywords = "arithmetic; AUGMENT interface; extended precision; floating point; multiple precision; portable software; precompiler interface; software package", } @Article{Kedem:1980:ADC, author = "Gershon Kedem", title = "Automatic Differentiation of Computer Programs", journal = j-TOMS, volume = "6", number = "2", pages = "150--165", month = jun, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "68C20 (68F25)", MRnumber = "81g:68058", bibdate = "Mon Aug 29 10:33:27 1994", URL = "http://doi.acm.org/10.1145/355887.355890", acknowledgement = ack-nhfb, keywords = "automatic differentiation; factorable functions", } @Article{Rheinboldt:1980:DSA, author = "Werner C. Rheinboldt and Charles K. Mesztenyi", title = "On a Data Structure for Adaptive Finite Element Mesh Refinements", journal = j-TOMS, volume = "6", number = "2", pages = "166--187", month = jun, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 10:33:27 1994", URL = "http://doi.acm.org/10.1145/355887.355891", acknowledgement = ack-nhfb, keywords = "access algorithms; finite elements; mesh refinements; tree structure", } @Article{Verwer:1980:ICS, author = "J. G. Verwer", title = "An Implementation of a Class of Stabilized Explicit Methods for the Time Integration of Parabolic Equations", journal = j-TOMS, volume = "6", number = "2", pages = "188--205", month = jun, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 10:33:27 1994", URL = "http://doi.acm.org/10.1145/355887.355892", acknowledgement = ack-nhfb, keywords = "implementation of time integrators; numerical analysis; parabolic partial differential equations; semidiscretization", } @Article{Munksgaard:1980:SSS, author = "N. Munksgaard", title = "Solving Sparse Symmetric Sets of Linear Equations by Preconditioned Conjugate Gradients", journal = j-TOMS, volume = "6", number = "2", pages = "206--219", month = jun, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 10:33:27 1994", URL = "http://doi.acm.org/10.1145/355887.355893", acknowledgement = ack-nhfb, keywords = "conjugate gradients; fixed space factorization; linear equations; numerical drop tolerance modification; positive definite; preconditioning; sparse", } @Article{Abdelmalek:1980:SOS, author = "Nabih N. Abdelmalek", title = "{$L_1$} Solution of Overdetermined Systems of Linear Equations", journal = j-TOMS, volume = "6", number = "2", pages = "220--227", month = jun, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 10:33:27 1994", URL = "http://doi.acm.org/10.1145/355887.355894", acknowledgement = ack-nhfb, keywords = "discrete linear {$L_1$} approximation; dual simplex algorithms; linear programming; overdetermined system of linear equations; triangular decomposition", } @Article{Abdelmalek:1980:AFS, author = "Nabih N. Abdelmalek", title = "{Algorithm 551}: {A FORTRAN} Subroutine for the {$L_1$} Solution of Overdetermined Systems of Linear Equations [{F4}]", journal = j-TOMS, volume = "6", number = "2", pages = "228--230", month = jun, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 10:44:41 1994", URL = "http://doi.acm.org/10.1145/355887.355895", acknowledgement = ack-nhfb, keywords = "discrete linear {$L_1$} approximation; dual simplex algorithms; linear programming; overdetermined system of linear equations; triangular decomposition", } @Article{Barrodale:1980:ASC, author = "I. Barrodale and F. D. K. Roberts", title = "{Algorithm 552}: Solution of the Constrained $\ell_1$ Linear Approximation Problem [{F4}]", journal = j-TOMS, volume = "6", number = "2", pages = "231--235", month = jun, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 10:46:51 1994", URL = "http://doi.acm.org/10.1145/355887.355896", acknowledgement = ack-nhfb, keywords = "constrained $\ell_1$ approximation; linear programming; simplex method", } @Article{Verwer:1980:AME, author = "J. G. Verwer", title = "{Algorithm 553}: {M3RK}, An Explicit Time Integrator for Semidiscrete Parabolic Equations [{D3}]", journal = j-TOMS, volume = "6", number = "2", pages = "236--239", month = jun, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 10:49:22 1994", URL = "http://doi.acm.org/10.1145/355887.355897", acknowledgement = ack-nhfb, keywords = "explicit time integrator; parabolic partial differential equations; semidiscretization", } @Article{More:1980:ABF, author = "J. J. Mor{\'e} and M. Y. Cosnard", title = "{Algorithm 554}: {BRENTM}, {A Fortran} Subroutine for the Numerical Solution of Nonlinear Equations [{F5}]", journal = j-TOMS, volume = "6", number = "2", pages = "240--251", month = jun, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 10:49:42 1994", URL = "http://doi.acm.org/10.1145/355887.355898", keywords = "Brent's method; nonlinear equations; numerical solution", } @Article{Watson:1980:ACY, author = "L. T. Watson and D. Fenner", title = "{Algorithm 555}: {Chow-Yorke} Algorithm for Fixed Points or Zeros of ${C}^2$ Maps [{C5}]", journal = j-TOMS, volume = "6", number = "2", pages = "252--259", month = jun, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 10:17:11 1994", URL = "http://doi.acm.org/10.1145/355887.355899", acknowledgement = ack-nhfb, keywords = "continuation method; fixed point; fixed points of nonlinear systems; homotopy method; nonlinear systems; parameterized nonlinear system; zero; zero curve of a homotopy map; zeros of nonlinear systems", } @Article{Gear:1980:RKS, author = "C. W. Gear", title = "{Runge-Kutta} Starters for Multistep Methods", journal = j-TOMS, volume = "6", number = "3", pages = "263--279", month = sep, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65L05", MRnumber = "81m:65119", bibdate = "Mon Aug 29 10:57:24 1994", URL = "http://doi.acm.org/10.1145/355900.355901", acknowledgement = ack-nhfb, keywords = "integration; multistep; ordinary differential equations; Runge-Kutta", reviewer = "J. Sprekels", } @Article{Barton:1980:TSS, author = "David Barton", title = "On {Taylor} Series and Stiff Equations", journal = j-TOMS, volume = "6", number = "3", pages = "280--294", month = sep, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65L05", MRnumber = "82e:65078", bibdate = "Mon Aug 29 10:57:24 1994", URL = "http://doi.acm.org/10.1145/355900.355902", acknowledgement = ack-nhfb, keywords = "stiff ordinary differential equations; Taylor series", reviewer = "P. M. Dew", } @Article{Jackson:1980:AIV, author = "K. R. Jackson and R. Sacks-Davis", title = "An Alternative Implementation of Variable Step-Size Multistep Formulas for Stiff {ODE}s", journal = j-TOMS, volume = "6", number = "3", pages = "295--318", month = sep, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65L05", MRnumber = "81m:65120", bibdate = "Mon Aug 29 10:57:24 1994", URL = "http://doi.acm.org/10.1145/355900.355903", acknowledgement = ack-nhfb, keywords = "backward differential formulas; stiff ODEs; variable step-size methods", reviewer = "Hans J. Stetter", } @Article{Gupta:1980:NAO, author = "G. K. Gupta", title = "A Note About Overhead Costs in {ODE} Solvers", journal = j-TOMS, volume = "6", number = "3", pages = "319--326", month = sep, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 10:57:24 1994", URL = "http://doi.acm.org/10.1145/355900.355904", acknowledgement = ack-nhfb, keywords = "Adams methods; mathematical software; ordinary differential equations; Runge-Kutta methods; software evaluation", } @Article{Coleman:1980:SSI, author = "David Coleman and Paul Holland and Neil Kaden and Virginia Klema and Stephen C. Peters", title = "A System of Subroutines for Iteratively Reweighted Least Squares Computations", journal = j-TOMS, volume = "6", number = "3", pages = "327--336", month = sep, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 10:57:24 1994", URL = "http://doi.acm.org/10.1145/355900.355905", acknowledgement = ack-nhfb, keywords = "curve fitting; data analysis; least squares; linear algebra; mathematical software; portability; robust estimation; weight functions", } @Article{George:1980:FIM, author = "Alan George and Joseph W. H. Liu", title = "A Fast Implementation of the Minimum Degree Algorithm Using Quotient Graphs", journal = j-TOMS, volume = "6", number = "3", pages = "337--358", month = sep, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65F05 (68E10)", MRnumber = "82i:65022", bibdate = "Mon Aug 29 10:57:24 1994", URL = "http://doi.acm.org/10.1145/355900.355906", acknowledgement = ack-nhfb, keywords = "graph algorithms; mathematical software; ordering algorithms; quotient graphs; sparse linear equations", reviewer = "Niels Munksgaard", } @Article{Bentley:1980:GSL, author = "Jon Louis Bentley and James B. Saxe", title = "Generating Sorted Lists of Random Numbers", journal = j-TOMS, volume = "6", number = "3", pages = "359--364", month = sep, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65C10 (68-01)", MRnumber = "81k:65010", bibdate = "Mon Aug 29 10:57:24 1994", URL = "http://doi.acm.org/10.1145/355900.355907", acknowledgement = ack-nhfb, keywords = "linear-time algorithm; probabilistic methods in algorithm design; random number generation; sorting", reviewer = "George Marsaglia", } @Article{Amos:1980:CEI, author = "Donald E. Amos", title = "Computation of Exponential Integrals", journal = j-TOMS, volume = "6", number = "3", pages = "365--377", month = sep, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D30 (68-04)", MRnumber = "82b:65011", bibdate = "Mon Aug 29 10:57:24 1994", URL = "http://doi.acm.org/10.1145/355900.355908", acknowledgement = ack-nhfb, keywords = "exponential integral; Miller algorithm; recursion; Taylor series", reviewer = "M. M. Chawla", } @Article{Arthur:1980:PPA, author = "Jeffrey L. Arthur and A. Ravindran", title = "{PAGP}, {A} Partitioning Algorithm for (Linear) Goal Programming Problems", journal = j-TOMS, volume = "6", number = "3", pages = "378--386", month = sep, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "90C05", MRnumber = "81i:90122", bibdate = "Mon Aug 29 10:57:24 1994", URL = "http://doi.acm.org/10.1145/355900.355909", acknowledgement = ack-nhfb, keywords = "constraint partitioning; goal program; multiple objective optimization; simplex method", } @Article{Cheung:1980:MLP, author = "To-Yat Cheung", title = "Multifacility Location Problem with Rectilinear Distance by the Minimum-Cut Approach", journal = j-TOMS, volume = "6", number = "3", pages = "387--390", month = sep, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 10:57:24 1994", URL = "http://doi.acm.org/10.1145/355900.355910", acknowledgement = ack-nhfb, keywords = "minimum cut; multifacility; optimal location; rectilinear distance", } @Article{Betts:1980:CAC, author = "J. T. Betts", title = "A Compact Algorithm for Computing the Stationary Point of a Quadratic Function Subject to Linear Constraints", journal = j-TOMS, volume = "6", number = "3", pages = "391--397", month = sep, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "90C20 (65K05)", MRnumber = "81i:90162", bibdate = "Mon Aug 29 10:57:24 1994", URL = "http://doi.acm.org/10.1145/355900.355911", acknowledgement = ack-nhfb, keywords = "orthogonal decomposition; quadratic programming", } @Article{Kaagstrom:1980:ANC, author = "Bo K{\aa}gstr{\"o}m and Axel Ruhe", title = "An Algorithm for Numerical Computation of the {Jordan} Normal Form of a Complex Matrix", journal = j-TOMS, volume = "6", number = "3", pages = "398--419", month = sep, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65F15 (15A21)", MRnumber = "81m:65054", bibdate = "Fri Aug 26 23:38:10 1994", URL = "http://doi.acm.org/10.1145/355900.355912", acknowledgement = ack-nhfb, keywords = "block diagonal form; canonical form; eig; eigenvalues; eigenvectors; Jordan form; Jordan normal form; nla; numerical multiple eigenvalues; principal vectors; software", reviewer = "Petr Liebl", } @Article{Amos:1980:AEI, author = "Donald E. Amos", title = "{Algorithm 556}: Exponential Integrals [{S13}]", journal = j-TOMS, volume = "6", number = "3", pages = "420--428", month = sep, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 11:13:05 1994", note = "See remark in \cite{Amos:1983:REI}.", URL = "http://doi.acm.org/10.1145/355900.355913", acknowledgement = ack-nhfb, keywords = "confluent hypergeometric functions; exponential integrals; Miller algorithm", } @Article{Arthur:1980:APP, author = "J. L. Arthur and A. Ravindran", title = "{Algorithm 557}: {PAGP}, {A} Partitioning Algorithm for (Linear) Goal Programming Problems [{H}]", journal = j-TOMS, volume = "6", number = "3", pages = "429--429", month = sep, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 11:13:53 1994", URL = "http://doi.acm.org/10.1145/355900.355914", acknowledgement = ack-nhfb, keywords = "constraint partitioning; goal program; multiple objective optimization; simplex method", } @Article{Cheung:1980:APM, author = "To-Yat Cheung", title = "{Algorithm 558}: {A} Program for the Multifacility Location Problem with Rectilinear Distance by the Minimum-Cut Approach [{H}]", journal = j-TOMS, volume = "6", number = "3", pages = "430--431", month = sep, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 11:14:45 1994", URL = "http://doi.acm.org/10.1145/355900.355915", acknowledgement = ack-nhfb, keywords = "minimum cut; multifacility; optimal location; rectilinear distance", } @Article{Betts:1980:ASP, author = "J. T. Betts", title = "{Algorithm 559}: The Stationary Point of a Quadratic Function Subject to Linear Constraints [{E4}]", journal = j-TOMS, volume = "6", number = "3", pages = "432--436", month = sep, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 11:15:40 1994", URL = "http://doi.acm.org/10.1145/355900.355916", acknowledgement = ack-nhfb, keywords = "orthogonal decomposition; quadratic programming", } @Article{Kaagstroem:1980:AJA, author = "Bo K{\aa{}}gstr{\"o}m and Axel Ruhe", title = "{Algorithm 560}: {JNF}, An Algorithm for Numerical Computation of the {Jordan} Normal Form of a Complex Matrix [{F2}]", journal = j-TOMS, volume = "6", number = "3", pages = "437--443", month = sep, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 15:16:29 1994", URL = "http://doi.acm.org/10.1145/355900.355917", acknowledgement = ack-nhfb, keywords = "block diagonal form; canonical form; eig; eigenvalues; eigenvectors; Jordan form; Jordan normal form; nla; principal vectors; software", } @Article{Kahaner:1980:AFI, author = "D. K. Kahaner", title = "{Algorithm 561}: {FORTRAN} Implementation of Heap Programs for Efficient Table Maintenance [{Z}]", journal = j-TOMS, volume = "6", number = "3", pages = "444--449", month = sep, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 11:17:27 1994", URL = "http://doi.acm.org/10.1145/355900.355918", acknowledgement = ack-nhfb, keywords = "heap; table maintenance", } @Article{Pape:1980:ASP, author = "U. Pape", title = "{Algorithm 562}: Shortest Path Lengths [{H}]", journal = j-TOMS, volume = "6", number = "3", pages = "450--455", month = sep, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 11:17:56 1994", note = "See also \cite{Pape:1983:RSP}.", URL = "http://doi.acm.org/10.1145/355900.355919", acknowledgement = ack-nhfb, keywords = "shortest path; shortest route problem", } @Article{Harms:1980:RSM, author = "U. Harms and H. Kollakowski and G. M{\"o}ller", title = "Remark on ``{Algorithm} 408: {A} Sparse Matrix Package (Part 1) [{F4}]''", journal = j-TOMS, volume = "6", number = "3", pages = "456--457", month = sep, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Aug 30 00:28:06 1994", note = "See \cite{McNamee:1971:SMP}.", URL = "http://doi.acm.org/10.1145/355900.355920", acknowledgement = ack-nhfb, } @Article{Machura:1980:SSP, author = "Marek Machura and Roland A. Sweet", title = "A Survey of Software for Partial Differential Equations", journal = j-TOMS, volume = "6", number = "4", pages = "461--488", month = dec, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65M99 (65-04 65N99)", MRnumber = "81k:65106", bibdate = "Mon Aug 29 11:23:03 1994", URL = "http://doi.acm.org/10.1145/355921.355922", acknowledgement = ack-nhfb, keywords = "partial differential equations; software; survey", } @Article{Kurator:1980:PIS, author = "William G. Kurator and Richard P. O'Neill", title = "{PERUSE}: An Interactive System for Mathematical Programs", journal = j-TOMS, volume = "6", number = "4", pages = "489--509", month = dec, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 11:23:03 1994", URL = "http://doi.acm.org/10.1145/355921.355923", acknowledgement = ack-nhfb, keywords = "interactive mathematical programming; model auditing; model debugging; model verification", } @Article{Brown:1980:EPB, author = "W. S. Brown and S. I. Feldman", title = "Environment Parameters and Basic Functions for Floating-Point Computation", journal = j-TOMS, volume = "6", number = "4", pages = "510--523", month = dec, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 11:23:03 1994", URL = "http://doi.acm.org/10.1145/355921.355924", acknowledgement = ack-nhfb, keywords = "environment parameters; floating-point arithmetic; software portability", } @Article{Luk:1980:CSV, author = "Franklin T. Luk", title = "Computing the Singular-Value Decomposition on the {ILLIAC IV}", journal = j-TOMS, volume = "6", number = "4", pages = "524--539", month = dec, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65F15", MRnumber = "81k:65044", bibdate = "Mon Aug 29 11:27:44 1994", URL = "http://doi.acm.org/10.1145/355921.355925", acknowledgement = ack-nhfb, keywords = "Golub-Reinsch algorithm; Illiac; ILLIAC IV computer; Jacobi-like method; nla; parallel matrix computations; prll; singular-value decomposition; svd", } @Article{Sacks-Davis:1980:FLC, author = "R. Sacks-Davis", title = "Fixed Leading Coefficient Implementation of {SD}-Formulas for Stiff {ODE}s", journal = j-TOMS, volume = "6", number = "4", pages = "540--562", month = dec, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65L05", MRnumber = "81k:65084", bibdate = "Mon Aug 29 11:23:03 1994", URL = "http://doi.acm.org/10.1145/355921.355926", acknowledgement = ack-nhfb, keywords = "ordinary differential equations; second-derivative method", } @Article{Bentley:1980:OET, author = "Jon Louis Bentley and Bruce W. Weide and Andrew C. Yao", title = "Optimal Expected-Time Algorithms for Closest Point Problems", journal = j-TOMS, volume = "6", number = "4", pages = "563--580", month = dec, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "68G10 (52-04 52A45 68E10 90C10)", MRnumber = "82g:68084", bibdate = "Mon Aug 29 11:23:03 1994", URL = "http://doi.acm.org/10.1145/355921.355927", acknowledgement = ack-nhfb, keywords = "closest point problems; computational geometry; minimum spanning trees; nearest neighbor searching; optimal algorithms; probabilistic analysis of algorithms; Voronoi diagrams", reviewer = "Wolfgang Boehm", } @Article{Campbell:1980:TAM, author = "J. B. Campbell", title = "On {Temme}'s Algorithm for the Modified {Bessel} Function of the Third Kind", journal = j-TOMS, volume = "6", number = "4", pages = "581--586", month = dec, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D20", MRnumber = "82d:65019", bibdate = "Mon Aug 29 11:23:03 1994", URL = "http://doi.acm.org/10.1145/355921.355928", acknowledgement = ack-nhfb, keywords = "mathematical software; Miller's algorithm; modified Bessel functions of the third kind", } @Article{Hoffman:1980:TPG, author = "K. L. Hoffman and D. R. Shier", title = "A Test Problem Generator for Discrete Linear {$L_1$} Approximation Problems", journal = j-TOMS, volume = "6", number = "4", pages = "587--593", month = dec, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D99 (65K05)", MRnumber = "81m:65042", bibdate = "Mon Aug 29 11:23:03 1994", URL = "http://doi.acm.org/10.1145/355921.355929", acknowledgement = ack-nhfb, keywords = "{$L_1$} approximation; least absolute deviation; problem generator; test data", } @Article{Bartels:1980:LCD, author = "Richard H. Bartels and Andrew R. Conn", title = "Linearly Constrained Discrete $\ell_1$ Problems", journal = j-TOMS, volume = "6", number = "4", pages = "594--608", month = dec, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "90C33 (65K05)", MRnumber = "82a:90165", bibdate = "Sat Aug 27 15:41:12 1994", URL = "http://doi.acm.org/10.1145/355921.355930", acknowledgement = ack-nhfb, keywords = "data filling; discrete approximation; $\ell_1$ norm; l1 approximation; linearly constrained approximation; nlop; software", } @Article{Bartels:1980:APL, author = "Richard H. Bartels and Andrew R. Conn", title = "{Algorithm 563}: {A} Program for Linearly Constrained Discrete $\ell_1$ Problems", journal = j-TOMS, volume = "6", number = "4", pages = "609--614", month = dec, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Mar 09 10:22:14 1999", note = "See remark \cite{Koenker:1996:RBC}.", URL = "http://doi.acm.org/10.1145/355921.355931", acknowledgement = ack-nhfb, keywords = "discrete $\ell_1$ approximation; l1 approximation; linear constraints; nlop; numerical analysis; overdetermined linear systems; software", } @Article{Hoffman:1980:ATP, author = "K. L. Hoffman and D. R. Shier", title = "{Algorithm 564}: {A} Test Problem Generator for Discrete Linear {$L_1$} Approximation Problems", journal = j-TOMS, volume = "6", number = "4", pages = "615--617", month = dec, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/355921.355932", keywords = "{$L_1$} approximation; least absolute deviation; problem generator; test data", } @Article{Shanno:1980:RMU, author = "D. F. Shanno and K. H. Phua", title = "Remark on ``{Algorithm} 500: Minimization of Unconstrained Multivariate Functions [{E4}]''", journal = j-TOMS, volume = "6", number = "4", pages = "618--622", month = dec, year = "1980", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Sep 30 01:07:08 1994", note = "See \cite{Shanno:1976:AMU}.", URL = "http://doi.acm.org/10.1145/355921.355933", acknowledgement = ack-nhfb, } @Article{Hiebert:1981:EMS, author = "K. L. Hiebert", title = "An Evaluation of Mathematical Software that Solves Nonlinear Least Squares Problems", journal = j-TOMS, volume = "7", number = "1", pages = "1--16", month = mar, year = "1981", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Sep 30 01:46:37 1994", URL = "http://doi.acm.org/10.1145/355934.355935", acknowledgement = ack-nhfb, keywords = "augmented Gauss-Newton; Gauss-Newton; Levenberg-Marquardt; lsq; nllsq; nlop; nonlinear data fitting; nonlinear least squares; nonlinear regression; quasi-Newton; software evaluation", } @Article{More:1981:TUO, author = "Jorge J. Mor{\'e} and Burton S. Garbow and Kenneth E. Hillstrom", title = "Testing Unconstrained Optimization Software", journal = j-TOMS, volume = "7", number = "1", pages = "17--41", month = mar, year = "1981", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "90C30", MRnumber = "83b:90144", bibdate = "Mon Aug 29 22:02:12 1994", URL = "http://doi.acm.org/10.1145/355934.355936", acknowledgement = ack-nhfb, keywords = "nonlinear least squares; optimization software; performance testing; systems of nonlinear equations; unconstrained minimization", } @Article{Akl:1981:CCG, author = "Selim G. Akl", title = "A Comparison of Combination Generation Methods", journal = j-TOMS, volume = "7", number = "1", pages = "42--45", month = mar, year = "1981", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 22:02:12 1994", URL = "http://doi.acm.org/10.1145/355934.355937", acknowledgement = ack-nhfb, keywords = "algorithm; combinations", } @Article{Fritsch:1981:DIU, author = "F. N. Fritsch and D. K. Kahaner and J. N. Lyness", title = "Double Integration Using One-Dimensional Adaptive Quadrature Routines: {A} Software Interface Problem", journal = j-TOMS, volume = "7", number = "1", pages = "46--75", month = mar, year = "1981", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D30", MRnumber = "83c:65033a", bibdate = "Sat Nov 19 13:07:46 1994", note = "See also \cite{Fritsch:1981:CIU}.", URL = "http://doi.acm.org/10.1145/355934.355938", acknowledgement = ack-nhfb, keywords = "adaptive integration; automatic quadrature routine; double integration; quadrature; software interface", } @Article{Friedman:1981:NPP, author = "Jerome H. Friedman and Margaret H. Wright", title = "A Nested Partitioning Procedure for Numerical Multiple Integration", journal = j-TOMS, volume = "7", number = "1", pages = "76--92", month = mar, year = "1981", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D30", MRnumber = "83d:65058", bibdate = "Mon Aug 29 22:02:12 1994", URL = "http://doi.acm.org/10.1145/355934.355939", acknowledgement = ack-nhfb, keywords = "bounds-constrained optimization; numerical integration; quadrature; recursive partitioning", reviewer = "C. Dagnino", } @Article{Smith:1981:ERA, author = "J. M. Smith and F. W. J. Olver and D. W. Lozier", title = "Extended-Range Arithmetic and Normalized {Legendre} Polynomials", journal = j-TOMS, volume = "7", number = "1", pages = "93--105", month = mar, year = "1981", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D20 (65G05)", MRnumber = "83a:65017", bibdate = "Mon Aug 29 22:02:12 1994", URL = "http://doi.acm.org/10.1145/355934.355940", acknowledgement = ack-nhfb, keywords = "angular momentum; extended-range arithmetic; Legendre polynomials; overflow; underflow", } @Article{Melgaard:1981:GST, author = "David K. Melgaard and Richard F. Sincovec", title = "General Software for Two-Dimensional Nonlinear Partial Differential Equations", journal = j-TOMS, volume = "7", number = "1", pages = "106--125", month = mar, year = "1981", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65M20", MRnumber = "83a:65082", bibdate = "Mon Aug 29 22:02:12 1994", URL = "http://doi.acm.org/10.1145/355934.355941", acknowledgement = ack-nhfb, keywords = "finite differences; method of lines; ordinary differential equations; partial differential equations", } @Article{Melgaard:1981:APS, author = "David K. Melgaard and Richard F. Sincovec", title = "{Algorithm 565}: {PDETWO}\slash {PSETM}\slash {GEARB}: Solution of Systems of Two-Dimensional Nonlinear Partial Differential Equations [{D3}]", journal = j-TOMS, volume = "7", number = "1", pages = "126--135", month = mar, year = "1981", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 22:16:02 1994", URL = "http://doi.acm.org/10.1145/355934.355942", acknowledgement = ack-nhfb, keywords = "finite differences; method of lines; ordinary differential equations; partial differential equations", } @Article{More:1981:AFS, author = "J. J. Mor{\'e} and B. S. Garbow and K. E. Hillstrom", title = "{Algorithm 566}: {FORTRAN} Subroutines for Testing Unconstrained Optimization Software [{C5} [{E4}]]", journal = j-TOMS, volume = "7", number = "1", pages = "136--140", month = mar, year = "1981", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Nov 19 13:13:44 1994", note = "See also \cite{Averbukh:1994:RA}.", URL = "http://doi.acm.org/10.1145/355934.355943", acknowledgement = ack-nhfb, keywords = "nonlinear least squares; optimization software; performance testing; systems of nonlinear equations; unconstrained minimization", } @Article{Lozier:1981:AER, author = "D. W. Lozier and J. M. Smith", title = "{Algorithm 567}: Extended-Range Arithmetic and Normalized {Legendre} Polynomials [{A1}], [{C1}]", journal = j-TOMS, volume = "7", number = "1", pages = "141--146", month = mar, year = "1981", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 22:17:34 1994", URL = "http://doi.acm.org/10.1145/355934.355944", acknowledgement = ack-nhfb, keywords = "angular momentum; extended-range arithmetic; Legendre polynomials; overflow; underflow", } @Article{Golub:1981:BLM, author = "Gene H. Golub and Franklin T. Luk and Michael L. Overton", title = "A Block {L{\'a}nczos} Method for Computing the Singular Values of Corresponding Singular Vectors of a Matrix", journal = j-TOMS, volume = "7", number = "2", pages = "149--169", month = jun, year = "1981", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65F50 (65F15)", MRnumber = "84h:65045", bibdate = "Fri Sep 30 01:47:15 1994", URL = "http://doi.acm.org/10.1145/355945.355946", acknowledgement = ack-nhfb, keywords = "block Lanczos method; Lanczos algorithm; large sparse matrix; nla; singular values; singular vectors; singular-value decomposition; svd; upper-triangular band matrix", } @Article{Wang:1981:PMT, author = "H. H. Wang", title = "A Parallel Method for Tridiagonal Equations", journal = j-TOMS, volume = "7", number = "2", pages = "170--183", month = jun, year = "1981", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65F05", MRnumber = "83d:65092", bibdate = "Mon Aug 29 22:19:35 1994", URL = "http://doi.acm.org/10.1145/355945.355947", acknowledgement = ack-nhfb, keywords = "cyclic reduction method; parallel computers; partition method; recursive doubling method; tridiagonal equations; vectors computers", } @Article{Stewart:1981:SIA, author = "William J. Stewart and Alan Jennings", title = "A Simultaneous Iteration Algorithm for Real Matrices", journal = j-TOMS, volume = "7", number = "2", pages = "184--198", month = jun, year = "1981", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65F15", MRnumber = "83d:65118", bibdate = "Mon Aug 29 22:19:35 1994", URL = "http://doi.acm.org/10.1145/355945.355948", acknowledgement = ack-nhfb, keywords = "eigenvalues; eigenvectors; large sparse matrices; real unsymmetric matrices; simultaneous iteration", } @Article{Hill:1981:EIR, author = "Geoffrey W. Hill", title = "Evaluation and Inversion of the Ratios of Modified {Bessel} Functions, {$I_1(x)/I_0(x)$} and {$I_{1.5}(x)/I_{0.5}(x)$}", journal = j-TOMS, volume = "7", number = "2", pages = "199--208", month = jun, year = "1981", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D20", MRnumber = "83d:65046", bibdate = "Mon Aug 29 22:19:35 1994", URL = "http://doi.acm.org/10.1145/355945.355949", acknowledgement = ack-nhfb, keywords = "approximation; backward recursion; continued fractions; Fisher distribution; function inversion; modified Bessel function ratios; Newton-Raphson; von Mises distribution", } @Article{Ascher:1981:CSB, author = "U. Ascher and J. Christiansen and R. D. Russell", title = "Collocation Software for Boundary Value {ODE}'s", journal = j-TOMS, volume = "7", number = "2", pages = "209--222", month = jun, year = "1981", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Sep 30 01:48:04 1994", URL = "http://doi.acm.org/10.1145/355945.355950", acknowledgement = ack-nhfb, annote = "collocation", keywords = "B-spline; boundary-value problems; collocation; damped Newton's method; error estimates; general-purpose code; mesh selection; ordinary differential equations", } @Article{Ascher:1981:ACC, author = "U. Ascher and J. Christiansen and R. D. Russell", title = "{Algorithm 569}: {COLSYS}: Collocation Software for Boundary-Value {ODEs} [{D2}]", journal = j-TOMS, volume = "7", number = "2", pages = "223--229", month = jun, year = "1981", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 22:26:51 1994", note = "See also \cite{Hake:1986:RCC}.", URL = "http://doi.acm.org/10.1145/355945.355951", acknowledgement = ack-nhfb, keywords = "B-spline; boundary-value problems; collocation; damped Newton's method; error estimates; general-purpose code; mesh selection; ordinary differential equations", } @Article{Stewart:1981:ALS, author = "William J. Stewart and Alan Jennings", title = "{Algorithm 570}: {LOPSI}: {A} Simultaneous Iteration Method for Real Matrices [{F2}]", journal = j-TOMS, volume = "7", number = "2", pages = "230--232", month = jun, year = "1981", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 22:27:33 1994", URL = "http://doi.acm.org/10.1145/355945.355952", acknowledgement = ack-nhfb, keywords = "eigenvalues; eigenvectors; large sparse matrices; real unsymmetric matrices; simultaneous iteration", } @Article{Hill:1981:ASM, author = "Geoffrey W. Hill", title = "{Algorithm 571}: Statistics for von {Mises}' and {Fisher}'s Distributions of Directions: {$I_1(x)/I_0(x)$}, {$I_{1.5}(x)/I_{0.5}(x)$} and Their Inverses [{S14}]", journal = j-TOMS, volume = "7", number = "2", pages = "233--238", month = jun, year = "1981", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 22:28:34 1994", URL = "http://doi.acm.org/10.1145/355945.355953", acknowledgement = ack-nhfb, keywords = "continued fraction; direction statistics; Fisher distribution; function inversion; modified Bessel function ratio; Newton-Raphson; von Mises distribution", } @Article{OLeary:1981:ASH, author = "Dianne P. O'Leary and Olof Widlund", title = "{Algorithm 572}: Solution of the {Helmholtz} Equation for the {Dirichlet} Problem on General Bounded Three-Dimensional Regions [{D3}]", journal = j-TOMS, volume = "7", number = "2", pages = "239--246", month = jun, year = "1981", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 22:31:55 1994", URL = "http://doi.acm.org/10.1145/355945.355954", acknowledgement = ack-nhfb, keywords = "capacitance matrix; conjugate gradients; fast Poisson solvers; Helmholtz equation", } @Article{Hill:1981:RSD, author = "G. W. Hill", title = "Remark on ``{Algorithm} 395: {Student}'s $t$-Distribution''", journal = j-TOMS, volume = "7", number = "2", pages = "247--249", month = jun, year = "1981", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Aug 30 00:28:07 1994", note = "See \cite{Hill:1970:SD,Hill:1970:SQ,elLozy:1979:RAS}.", URL = "http://doi.acm.org/10.1145/355945.355955", acknowledgement = ack-nhfb, } @Article{Hill:1981:RSQ, author = "G. W. Hill", title = "Remark on ``{Algorithm} 396: {Student}'s $t$-Quantiles''", journal = j-TOMS, volume = "7", number = "2", pages = "250--251", month = jun, year = "1981", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Aug 30 00:28:07 1994", note = "See \cite{Hill:1970:SQ}.", URL = "http://doi.acm.org/10.1145/355945.355956", acknowledgement = ack-nhfb, } @Article{Fritsch:1981:CIU, author = "F. N. Fritsch", title = "Corrigendum: ``{Double} Integration Using One-Dimensional Adaptive Quadrature Routines: {A} Software Interface Problem''", journal = j-TOMS, volume = "7", number = "2", pages = "252--252", month = jun, year = "1981", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "252. 65D30", MRnumber = "83c:65033b", bibdate = "Mon Aug 29 22:19:35 1994", note = "See \cite{Fritsch:1981:DIU}.", URL = "http://doi.acm.org/10.1145/355945.355957", acknowledgement = ack-nhfb, } @Article{Ukkonen:1981:CER, author = "Esko Ukkonen", title = "On the Calculation of the Effects of Roundoff Errors", journal = j-TOMS, volume = "7", number = "3", pages = "259--271", month = sep, year = "1981", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65G05", MRnumber = "82i:65030", bibdate = "Mon Aug 29 22:44:37 1994", URL = "http://doi.acm.org/10.1145/355958.355959", acknowledgement = ack-nhfb, keywords = "automatic roundoff analysis; numerical linear algebra; numerical stability", } @Article{Linnainmaa:1981:SDP, author = "Seppo Linnainmaa", title = "Software for Doubled-Precision Floating-Point Computations", journal = j-TOMS, volume = "7", number = "3", pages = "272--283", month = sep, year = "1981", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "68B99 (65G99 68C05)", MRnumber = "82h:68041", bibdate = "Mon Aug 29 22:44:37 1994", URL = "http://doi.acm.org/10.1145/355958.355960", acknowledgement = ack-nhfb, keywords = "exact multiplication; floating-point arithmetic; rounding errors; software portability", } @Article{Lii:1981:CBC, author = "K. S. Lii and K. N. Helland", title = "Cross-Bispectrum Computation and Variance Estimation", journal = j-TOMS, volume = "7", number = "3", pages = "284--294", month = sep, year = "1981", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "62M15", MRnumber = "82m:62213", bibdate = "Mon Aug 29 22:44:37 1994", URL = "http://doi.acm.org/10.1145/355958.355961", acknowledgement = ack-nhfb, keywords = "bispectra; time series analysis", } @Article{Dew:1981:SLR, author = "P. M. Dew and J. E. Walsh", title = "A Set of Library Routines for Solving Parabolic Equations in One Space Variable", journal = j-TOMS, volume = "7", number = "3", pages = "295--314", month = sep, year = "1981", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 11:51:54 1994", URL = "http://doi.acm.org/10.1145/355958.355962", annote = "parabolic equations", keywords = "method of lines; parabolic equations", } @Article{Duff:1981:AOM, author = "I. S. Duff", title = "On Algorithms for Obtaining a Maximum Transversal", journal = j-TOMS, volume = "7", number = "3", pages = "315--330", month = sep, year = "1981", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 22:49:58 1994", URL = "http://doi.acm.org/10.1145/355958.355963", acknowledgement = ack-nhfb, keywords = "block-triangular form; maximum assignment; maximum transversal; perm; sparse; sparse matrices; unsymmetric permutations", } @Article{McAllister:1981:ACS, author = "David F. McAllister and John A. Roulier", title = "An Algorithm for Computing a Shape-Preserving Osculatory Quadratic Spline", journal = j-TOMS, volume = "7", number = "3", pages = "331--347", month = sep, year = "1981", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D07", MRnumber = "82h:65009", bibdate = "Mon Aug 29 22:44:37 1994", URL = "http://doi.acm.org/10.1145/355958.355964", acknowledgement = ack-nhfb, keywords = "Bernstein polynomial; convexity preserving; geometric design; monotonicity preserving; osculation; parametric curve; polynomial interpolation; shape preserving; spline", } @Article{Dennis:1981:ANL, author = "John E. {Dennis, Jr.} and David M. Gay and Roy E. Welsch", title = "An Adaptive Nonlinear Least-squares Algorithm", journal = j-TOMS, volume = "7", number = "3", pages = "348--368", month = sep, year = "1981", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Aug 26 23:38:10 1994", URL = "http://doi.acm.org/10.1145/355958.355965", acknowledgement = ack-nhfb, keywords = "lsq; nllsq; nlop; nonlinear least squares; nonlinear regression; quasi-Newton methods; secant methods; unconstrained optimization", } @Article{Dennis:1981:ANE, author = "John E. {Dennis, Jr.} and David M. Gay and Roy E. Welsch", title = "{Algorithm 573}: {NL2SOL}\emdash An Adaptive Nonlinear Least-Squares Algorithm [{E4}]", journal = j-TOMS, volume = "7", number = "3", pages = "369--383", month = sep, year = "1981", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 22:52:21 1994", note = "See also \cite{Gay:1983:RNE}.", URL = "http://doi.acm.org/10.1145/355958.355966", acknowledgement = ack-nhfb, keywords = "lsq; nllsq; nlop; nonlinear least squares; nonlinear regression; quasi-Newton methods; secant methods; software; unconstrained optimization", } @Article{McAllister:1981:ASP, author = "D. F. McAllister and J. A. Roulier", title = "{Algorithm 574}: Shape-Preserving Osculatory Quadratic Splines [{E1}, {E2}]", journal = j-TOMS, volume = "7", number = "3", pages = "384--386", month = sep, year = "1981", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 22:55:24 1994", URL = "http://doi.acm.org/10.1145/355958.355967", acknowledgement = ack-nhfb, keywords = "Bernstein polynomial; convexity preserving; monotonicity preserving; osculation; polynomial interpolation; shape preserving", } @Article{Duff:1981:APZ, author = "I. S. Duff", title = "{Algorithm 575}: Permutations for a Zero-Free Diagonal [{F1}]", journal = j-TOMS, volume = "7", number = "3", pages = "387--390", month = sep, year = "1981", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 22:56:49 1994", URL = "http://doi.acm.org/10.1145/355958.355968", acknowledgement = ack-nhfb, keywords = "block triangular form; maximum assignment; maximum transversal; sparse matrices; unsymmetric permutations", } @Article{Barrodale:1981:AFP, author = "I. Barrodale and G. F. Stuart", title = "{Algorithm 576}: {A FORTRAN} Program for Solving {${\bf Ax} = {\bf b}$} [{F4}]", journal = j-TOMS, volume = "7", number = "3", pages = "391--397", month = sep, year = "1981", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 22:57:25 1994", URL = "http://doi.acm.org/10.1145/355958.355969", acknowledgement = ack-nhfb, keywords = "Gaussian elimination; linear equations; new pivoting strategy", } @Article{Carlson:1981:AAI, author = "B. C. Carlson and Elaine M. Notis", title = "{Algorithm 577}: Algorithms for Incomplete Elliptic Integrals [{S21}]", journal = j-TOMS, volume = "7", number = "3", pages = "398--403", month = sep, year = "1981", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 22:58:27 1994", URL = "http://doi.acm.org/10.1145/355958.355970", acknowledgement = ack-nhfb, keywords = "elliptic integrals; inverse circular functions; inverse hyperbolic functions; logarithms; $R$-functions", } @Article{Razaz:1981:RAF, author = "M. Razaz and J. L. Schonfelder", title = "Remark on ``{Algorithm} 498: {Airy} Functions Using {Chebyshev} Series Approximations''", journal = j-TOMS, volume = "7", number = "3", pages = "404--405", month = sep, year = "1981", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Aug 30 00:28:07 1994", note = "See \cite{Prince:1975:AAF}.", URL = "http://doi.acm.org/10.1145/355958.355971", acknowledgement = ack-nhfb, } @Article{Shampine:1981:ETS, author = "Lawrence F. Shampine", title = "Evaluation of a Test Set for Stiff {ODE} Solvers", journal = j-TOMS, volume = "7", number = "4", pages = "409--420", month = dec, year = "1981", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65L05", MRnumber = "83d:65215", bibdate = "Mon Aug 29 23:03:20 1994", URL = "http://doi.acm.org/10.1145/355972.355973", acknowledgement = ack-nhfb, keywords = "stiff; test set; testing ODE codes", } @Article{Neves:1981:CIE, author = "Kenneth W. Neves", title = "Control of Interpolatory Error in Retarded Differential Equations", journal = j-TOMS, volume = "7", number = "4", pages = "421--444", month = dec, year = "1981", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65L99 (34K99)", MRnumber = "83d:65243", bibdate = "Mon Aug 29 23:03:20 1994", URL = "http://doi.acm.org/10.1145/355972.355974", acknowledgement = ack-nhfb, keywords = "automatic step-size reduction; delay differential equations; derivative jump discontinuities; local error control; Runge-Kutta methods", } @Article{Brown:1981:SRM, author = "W. S. Brown", title = "A Simple but Realistic Model of Floating-Point Computation", journal = j-TOMS, volume = "7", number = "4", pages = "445--480", month = dec, year = "1981", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 23:03:20 1994", URL = "http://doi.acm.org/10.1145/355972.355975", acknowledgement = ack-nhfb, keywords = "computer arithmetic; environment parameters; error analysis; Euclidean norm; floating-point arithmetic; software portability", } @Article{Marsten:1981:DXL, author = "Roy E. Marsten", title = "The Design of the {XMP} Linear Programming Library", journal = j-TOMS, volume = "7", number = "4", pages = "481--497", month = dec, year = "1981", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 23:03:20 1994", URL = "http://doi.acm.org/10.1145/355972.355976", acknowledgement = ack-nhfb, keywords = "linear programming; mathematical programming; optimization; software engineering; software libraries", } @Article{Pallottino:1981:EAD, author = "Stefano Pallottino and Tommaso Toffoli", title = "An Efficient Algorithm for Determining the Length of the Longest Dead Path in a ``{LIFO}'' Branch-and-Bound Exploration Schema", journal = j-TOMS, volume = "7", number = "4", pages = "498--504", month = dec, year = "1981", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Sep 30 01:08:44 1994", URL = "http://doi.acm.org/10.1145/355972.355977", acknowledgement = ack-nhfb, keywords = "branch-and-bound; length of longest dead path; LIFO tree search", } @Article{Duff:1981:MSU, author = "I. S. Duff", title = "{ME28}: {A} Sparse Unsymmetric Linear Equation Solver for Complex Equations", journal = j-TOMS, volume = "7", number = "4", pages = "505--511", month = dec, year = "1981", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 23:03:20 1994", URL = "http://doi.acm.org/10.1145/355972.355978", acknowledgement = ack-nhfb, keywords = "complex sparse linear equations; drop tolerances; ME28; numerical software; real and complex arithmetic; sparse matrix", } @Article{Fornberg:1981:NDA, author = "Bengt Fornberg", title = "Numerical Differentiation of Analytic Functions", journal = j-TOMS, volume = "7", number = "4", pages = "512--526", month = dec, year = "1981", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D25", MRnumber = "83d:65056", bibdate = "Mon Aug 29 23:03:20 1994", URL = "http://doi.acm.org/10.1145/355972.355979", acknowledgement = ack-nhfb, keywords = "analytic functions; numerical differentiation; Taylor series coefficients", } @Article{Croz:1981:SLF, author = "J. J. Du Croz and S. M. Nugent and J. K. Reid and D. B. Taylor", title = "Solving Large Full Sets of Linear Equations in a Paged Virtual Store", journal = j-TOMS, volume = "7", number = "4", pages = "527--536", month = dec, year = "1981", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 23:03:20 1994", URL = "http://doi.acm.org/10.1145/355972.355980", acknowledgement = ack-nhfb, keywords = "Gaussian elimination; paged virtual store", } @Article{Croz:1981:ASR, author = "J. J. Du Croz and S. M. Nugent and J. K. Reid and D. B. Taylor", title = "{Algorithm 578}: Solution of Real Linear Equations in a Paged Virtual Store [{F4}]", journal = j-TOMS, volume = "7", number = "4", pages = "537--541", month = dec, year = "1981", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 23:12:14 1994", URL = "http://doi.acm.org/10.1145/355972.355981", acknowledgement = ack-nhfb, keywords = "Gaussian elimination; paged virtual store", } @Article{Fornberg:1981:ACC, author = "B. Fornberg", title = "{Algorithm 579}: {CPSC}: Complex Power Series Coefficients [{D4}]", journal = j-TOMS, volume = "7", number = "4", pages = "542--547", month = dec, year = "1981", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 23:12:50 1994", URL = "http://doi.acm.org/10.1145/355972.355982", acknowledgement = ack-nhfb, keywords = "analytic functions; numerical differentiation; Taylor series coefficients", } @Article{Buckley:1981:AQS, author = "A. Buckley", title = "{Algorithm 580}: {QRUP}: {A} Set of {FORTRAN} Routines for Updating {QR} Factorizations [{F5}]", journal = j-TOMS, volume = "7", number = "4", pages = "548--549", month = dec, year = "1981", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 23:13:39 1994", note = "See also \cite{Buckley:1982:RQS}.", URL = "http://doi.acm.org/10.1145/355972.355983", acknowledgement = ack-nhfb, keywords = "matrix factorization; orthogonalization", } @Article{Krogh:1982:AAP, author = "Fred T. Krogh", title = "{ACM} Algorithms Policy", journal = j-TOMS, volume = "8", number = "1", pages = "1--4", month = mar, year = "1982", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 23:14:59 1994", URL = "http://doi.acm.org/10.1145/355984.355985", acknowledgement = ack-nhfb, } @Article{Hiebert:1982:EMS, author = "K. L. Hiebert", title = "An Evaluation of Mathematical Software That Solves Systems of Nonlinear Equations", journal = j-TOMS, volume = "8", number = "1", pages = "5--20", month = mar, year = "1982", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 23:14:59 1994", URL = "http://doi.acm.org/10.1145/355984.355986", acknowledgement = ack-nhfb, keywords = "algorithms; Brent's method; Brown's method; performance; quasi-Newton Powell's hybrid method", subject = "D.2.8 [Software Engineering]: Metrics\emdash performance measures; G.1.5 [Numerical Analysis]: Proofs of Nonlinear Equations\emdash systems of equations; G.4 [Mathematics of Computing]: Mathematical Software\emdash certification and testing", } @Article{Dunham:1982:CBC, author = "Charles B. Dunham", title = "Choice of Basis for {Chebyshev} Approximation", journal = j-TOMS, volume = "8", number = "1", pages = "21--25", month = mar, year = "1982", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "41A50 (65D15)", MRnumber = "84i:41038", bibdate = "Mon Aug 29 23:14:59 1994", URL = "http://doi.acm.org/10.1145/355984.355987", acknowledgement = ack-nhfb, keywords = "algorithms; condition numbers; design; Fraser-Hart-Remez algorithm; polynomials; rational functions", subject = "G.1.2 [Numerical Analysis]: Approximation\emdash Chebyshev approximation and theory", } @Article{Deo:1982:AGF, author = "Narsingh Deo and G. M. Prabhu and M. S. Krishnamoorthy", title = "Algorithms for Generating Fundamental Cycles in a Graph", journal = j-TOMS, volume = "8", number = "1", pages = "26--42", month = mar, year = "1982", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "68C05 (05C38 68E10)", MRnumber = "83h:68041", bibdate = "Mon Aug 29 23:14:59 1994", URL = "http://doi.acm.org/10.1145/355984.355988", acknowledgement = ack-nhfb, keywords = "algorithms; design; fundamental-cycle set; NP-complete; spanning tree", reviewer = "Sukhamay Kundu", subject = "F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical algorithms and problems\emdash computations on discrete structures; G.2.2 [Discrete Mathematics]: Graph Theory", } @Article{Paige:1982:LAS, author = "Christopher C. Paige and Michael A. Saunders", title = "{LSQR}: An Algorithm for Sparse Linear Equations and Sparse Least Squares", journal = j-TOMS, volume = "8", number = "1", pages = "43--71", month = mar, year = "1982", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65F10 (65F20)", MRnumber = "83f:65048", bibdate = "Fri Aug 26 23:38:14 1994", URL = "http://doi.acm.org/10.1145/355984.355989", acknowledgement = ack-nhfb, keywords = "algorithms; analysis of variance; conjugate gradients; Lanczos algorithm; lsq; nla", } @Article{Chan:1982:IAC, author = "Tony F. Chan", title = "An Improved Algorithm for Computing the Singular Value Decomposition", journal = j-TOMS, volume = "8", number = "1", pages = "72--83", month = mar, year = "1982", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65F30", MRnumber = "83f:65058", bibdate = "Mon Aug 29 23:23:48 1994", URL = "http://doi.acm.org/10.1145/355984.355990", acknowledgement = ack-nhfb, keywords = "algorithms; Householder transformation; nla; performance; singular values; software; svd", } @Article{Chan:1982:AIA, author = "Tony F. Chan", title = "{Algorithm 581}: An Improved Algorithm for Computing the Singular Value Decomposition [{F1}]", journal = j-TOMS, volume = "8", number = "1", pages = "84--88", month = mar, year = "1982", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Aug 26 23:38:11 1994", URL = "http://doi.acm.org/10.1145/355984.355991", acknowledgement = ack-nhfb, keywords = "algorithms; nla; singular value decomposition; software; svd", } @Article{Tracht:1982:RNR, author = "Allen E. Tracht", title = "Remark on ``{Algorithm} 334: Normal Random Deviates''", journal = j-TOMS, volume = "8", number = "1", pages = "89--89", month = mar, year = "1982", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Aug 30 00:28:07 1994", note = "See \cite{Bell:1968:NRD}.", URL = "http://doi.acm.org/10.1145/355984.355992", acknowledgement = ack-nhfb, } @Article{Shampine:1982:IRM, author = "L. F. Shampine", title = "Implementation of {Rosenbrock} Methods", journal = j-TOMS, volume = "8", number = "2", pages = "93--113", month = jun, year = "1982", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65L05", MRnumber = "83f:65115", bibdate = "Mon Aug 29 23:27:37 1994", URL = "http://doi.acm.org/10.1145/355993.355994", acknowledgement = ack-nhfb, keywords = "algorithms; FORTRAN Codes; Rosenbrock Methods; theory", } @Article{Corliss:1982:SOD, author = "George Corliss and Y. F. Chang", title = "Solving Ordinary Differential Equations Using {Taylor} Series", journal = j-TOMS, volume = "8", number = "2", pages = "114--144", month = jun, year = "1982", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65L05", MRnumber = "83g:65072", bibdate = "Mon Aug 29 23:27:37 1994", URL = "http://doi.acm.org/10.1145/355993.355995", acknowledgement = ack-nhfb, keywords = "algorithms; performance; Taylor series method", reviewer = "L. F. Shampine", } @Article{Hoaglin:1982:EDA, author = "David C. Hoaglin and Virginia C. Klema and Stephen C. Peters", title = "Exploratory Data Analysis in a Study of the Performance of Nonlinear Optimization Routines", journal = j-TOMS, volume = "8", number = "2", pages = "145--162", month = jun, year = "1982", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 23:27:37 1994", URL = "http://doi.acm.org/10.1145/355993.355996", acknowledgement = ack-nhfb, keywords = "experimentation; performance", } @Article{Ahrens:1982:CGP, author = "J. H. Ahrens and U. Dieter", title = "Computer Generation of {Poisson} Deviates from Modified Normal Distributions", journal = j-TOMS, volume = "8", number = "2", pages = "163--179", month = jun, year = "1982", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65C10 (60-04 62E99)", MRnumber = "84c:65016", bibdate = "Mon Aug 29 23:31:37 1994", URL = "http://doi.acm.org/10.1145/355993.355997", acknowledgement = ack-nhfb, country = "USA", date = "13/05/93", descriptors = "RVG;", enum = "6930", keywords = "acceptance-rejection method; algorithms; Poisson distribution; theory", language = "English", location = "SEL: Wi", references = "0", reviewer = "James E. Gentle", revision = "16/01/94", } @Article{Lewis:1982:IGP, author = "John G. Lewis", title = "Implementation of the {Gibbs-Poole-Stockmeyer} and {Gibbs}-King Algorithms", journal = j-TOMS, volume = "8", number = "2", pages = "180--189", month = jun, year = "1982", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 23:27:37 1994", URL = "http://doi.acm.org/10.1145/355993.355998", acknowledgement = ack-nhfb, keywords = "Algorithms; banded matrix; Gibbs-King algorithms; Gibbs-Poole-Stockmeyer algorithms; matrix bandwidth; matrix profile; matrix wavefront", } @Article{Lewis:1982:AGP, author = "John G. Lewis", title = "{Algorithm 582}: The {Gibbs-Poole-Stockmeyer} and {Gibbs-King} Algorithms for Reordering Sparse Matrices", journal = j-TOMS, volume = "8", number = "2", pages = "190--194", month = jun, year = "1982", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 23:34:27 1994", URL = "http://doi.acm.org/10.1145/355993.355999", acknowledgement = ack-nhfb, keywords = "Algorithms; banded matrix; Gibbs-King algorithms; Gibbs-Poole-Stockmeyer algorithms; matrix bandwidth; matrix profile; matrix wavefront", } @Article{Paige:1982:ALS, author = "Christopher C. Paige and Michael A. Saunders", title = "{Algorithm 583}: {LSQR}: Sparse Linear Equations and Least Squares Problems", journal = j-TOMS, volume = "8", number = "2", pages = "195--209", month = jun, year = "1982", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Aug 26 23:38:14 1994", URL = "http://doi.acm.org/10.1145/355993.356000", acknowledgement = ack-nhfb, keywords = "algorithms; analysis of variance; conjugate gradients; conjugate-gradient method; Lanczos algorithm; least squares; linear equations; lsq; nla; regression; software; sparse matrix", } @Article{Laurie:1982:ACA, author = "D. P. Laurie", title = "{Algorithm 584}: {CUBTRI}: Automatic Cubature over a Triangle", journal = j-TOMS, volume = "8", number = "2", pages = "210--218", month = jun, year = "1982", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 23:37:42 1994", note = "See also \cite{Hanson:1986:RCA}.", URL = "http://doi.acm.org/10.1145/355993.356001", acknowledgement = ack-nhfb, keywords = "algorithm; quadrature rule; theory", } @Article{Flamm:1982:RHE, author = "David S. Flamm and Robert A. Walker", title = "Remark on ``{Algorithm} 506: {HQR3} and {EXCHNG}: {Fortran} Subroutines for Calculating and Ordering the Eigenvalues of a Real Upper {Hessenberg} Matrix [{F2}]''", journal = j-TOMS, volume = "8", number = "2", pages = "219--220", month = jun, year = "1982", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Aug 30 00:28:07 1994", note = "See \cite{Stewart:1976:AHE}.", URL = "http://doi.acm.org/10.1145/355993.356002", acknowledgement = ack-nhfb, } @Article{Lewis:1982:RMB, author = "John G. Lewis", title = "Remark on ``{Algorithm}s 508 and 509: Matrix Bandwidth and Profile Reduction [{F1}] and {A} Hybrid Profile Reduction Algorithm [{F1}]''", journal = j-TOMS, volume = "8", number = "2", pages = "221--221", month = jun, year = "1982", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Aug 30 00:28:07 1994", note = "See \cite{Crane:1976:AMB,Gibbs:1976:AHP}.", URL = "http://doi.acm.org/10.1145/355993.356003", acknowledgement = ack-nhfb, } @Article{Ellison:1982:UUI, author = "E. F. D. Ellison and Gautam Mitra", title = "{UIMP}: User Interface for Mathematical Programming", journal = j-TOMS, volume = "8", number = "3", pages = "229--255", month = sep, year = "1982", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 23:27:37 1994", URL = "http://doi.acm.org/10.1145/356004.356005", acknowledgement = ack-nhfb, keywords = "matrix generator; report writer; solution analysis", } @Article{Schreiber:1982:NIS, author = "Robert Schreiber", title = "A New Implementation of Sparse {Gaussian} Elimination", journal = j-TOMS, volume = "8", number = "3", pages = "256--276", month = sep, year = "1982", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65F05", MRnumber = "84d:65020", bibdate = "Mon Aug 29 23:27:37 1994", URL = "http://doi.acm.org/10.1145/356004.356006", acknowledgement = ack-nhfb, keywords = "algorithms; sparse matrix; sparse systems of linear equations; theory", } @Article{Sasaki:1982:EGE, author = "Tateaki Sasaki and Hirokazu Murao", title = "Efficient {Gaussian} Elimination Method for Symbolic Determinants and Linear Systems", journal = j-TOMS, volume = "8", number = "3", pages = "277--289", month = sep, year = "1982", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65F40 (68Q40)", MRnumber = "85b:65037", bibdate = "Mon Aug 29 23:27:37 1994", URL = "http://doi.acm.org/10.1145/356004.356007", acknowledgement = ack-nhfb, keywords = "algorithms; Cramer's method; expansion by minors; Gaussian elimination; symbolic determinant; symbolic linear systems", reviewer = "E. Bareiss", } @Article{Brezinski:1982:ASG, author = "C. Brezinski", title = "{Algorithm 585}: {A} Subroutine for the General Interpolation and Extrapolation Problems", journal = j-TOMS, volume = "8", number = "3", pages = "290--301", month = sep, year = "1982", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 23:49:19 1994", URL = "http://doi.acm.org/10.1145/356004.356008", acknowledgement = ack-nhfb, keywords = "algorithms; convergence acceleration; extrapolation; interpolation; least squares approximation; Neville-Aitken scheme", } @Article{Kincaid:1982:AIF, author = "David R. Kincaid and John R. Respess and David M. Young and Roger G. Grimes", title = "{Algorithm 586}: {ITPACK 2C}: {A FORTRAN} Package for Solving Large Sparse Linear Systems by Adaptive Accelerated Iterative Methods", journal = j-TOMS, volume = "8", number = "3", pages = "302--322", month = sep, year = "1982", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 23:49:22 1994", URL = "http://doi.acm.org/10.1145/356004.356009", acknowledgement = ack-nhfb, keywords = "algorithms; documentation; iterative methods; numerical software; sparse matrix", } @Article{Hanson:1982:ATA, author = "Richard J. Hanson and Karen H. Haskell", title = "{Algorithm 587}: Two Algorithms for the Linearly Constrained Least Squares Problem", journal = j-TOMS, volume = "8", number = "3", pages = "323--333", month = sep, year = "1982", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Sep 05 20:52:33 1994", note = "See also \cite{Dadurkevicius:1989:RA}.", URL = "http://doi.acm.org/10.1145/356004.356010", acknowledgement = ack-nhfb, keywords = "algorithms; covariance matrix; equality constraints; inconsistent constraints; inequality constraints; linear least squares solution", } @Article{Hanson:1982:RPQ, author = "R. J. Hanson", title = "Remark on ``{Algorithm} 507: Procedures for Quintic Natural Spline Interpolation [{E1}]''", journal = j-TOMS, volume = "8", number = "3", pages = "334--334", month = sep, year = "1982", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Aug 30 00:28:07 1994", note = "See \cite{Herriot:1976:APQ}.", URL = "http://doi.acm.org/10.1145/356004.356011", acknowledgement = ack-nhfb, } @Article{Wolfe:1982:CCG, author = "Philip Wolfe", title = "Checking the Calculation of Gradients", journal = j-TOMS, volume = "8", number = "4", pages = "337--343", month = dec, year = "1982", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Aug 30 00:02:03 1994", URL = "http://doi.acm.org/10.1145/356012.356013", acknowledgement = ack-nhfb, keywords = "nonlinearity; optimization", } @Article{Anderson:1982:FHT, author = "Walter L. Anderson", title = "Fast {Hankel} Transforms Using Related and Lagged Convolutions", journal = j-TOMS, volume = "8", number = "4", pages = "344--368", month = dec, year = "1982", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Aug 30 00:02:03 1994", URL = "http://doi.acm.org/10.1145/356012.356014", acknowledgement = ack-nhfb, keywords = "Bessel functions of the first kind; convolution integrals; Hankel transforms of integer order; linear digital filters", } @Article{Anderson:1982:AFH, author = "Walter L. Anderson", title = "{Algorithm 588}: Fast {Hankel} Transforms Using Related and Lagged Convolutions", journal = j-TOMS, volume = "8", number = "4", pages = "369--370", month = dec, year = "1982", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Aug 30 00:05:54 1994", URL = "http://doi.acm.org/10.1145/356012.356015", acknowledgement = ack-nhfb, keywords = "Bessel functions of the first kind; convolution integrals; Hankel transforms of integer order; linear digital filters", } @Article{Dongarra:1982:ASF, author = "Jack J. Dongarra", title = "{Algorithm 589}: {SICEDR}: {A FORTRAN} Subroutine for Improving the Accuracy of Computed Matrix Eigenvalues", journal = j-TOMS, volume = "8", number = "4", pages = "371--375", month = dec, year = "1982", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Aug 30 00:05:58 1994", URL = "http://doi.acm.org/10.1145/356012.356016", acknowledgement = ack-nhfb, keywords = "algorithms; eigensystems improvement; iterative method; matrix eigensystems", } @Article{VanDooren:1982:ADE, author = "P. {Van Dooren}", title = "{Algorithm 590}: {DSUBSP} and {EXCHQZ}: {FORTRAN} Subroutines for Computing Deflating Subspaces with Specified Spectrum", journal = j-TOMS, volume = "8", number = "4", pages = "376--382", month = dec, year = "1982", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 20:17:25 1994", note = "See also \cite{Petkov:1984:RDE}.", URL = "http://doi.acm.org/10.1145/356012.356017", acknowledgement = ack-nhfb, keywords = "algorithm; generalized eigenvalue; QZ algorithm", } @Article{Hemmerle:1982:ACM, author = "William J. Hemmerle", title = "{Algorithm 591}: {A} Comprehensive Matrix-Free Algorithm for Analysis of Variance", journal = j-TOMS, volume = "8", number = "4", pages = "383--401", month = dec, year = "1982", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Aug 30 00:08:00 1994", URL = "http://doi.acm.org/10.1145/356012.356018", acknowledgement = ack-nhfb, keywords = "algebraic-model specification; algorithms; analysis of variance; balanced data operators; G-inverse solution; hypothesis testing; iterative improvement; linear models; missing cells; rank computations; storage-efficient algorithm; unbalanced data", } @Article{Garbow:1982:RQA, author = "B. S. Garbow", title = "Remark on ``{Algorithm} 535: The {QZ} Algorithm to Solve the Generalized Eigenvalue Problem for Complex Matrices [{F2}]''", journal = j-TOMS, volume = "8", number = "4", pages = "402--402", month = dec, year = "1982", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Aug 30 00:28:07 1994", note = "See \cite{Garbow:1978:AQA,Garbow:1984:RQA}.", URL = "http://doi.acm.org/10.1145/356012.356019", acknowledgement = ack-nhfb, } @Article{Dodson:1982:RBL, author = "David S. Dodson and Roger G. Grimes", title = "Remark on ``{Algorithm} 539: {Basic Linear Algebra Subprograms} for {Fortran} Usage [{F1}]''", journal = j-TOMS, volume = "8", number = "4", pages = "403--404", month = dec, year = "1982", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Sep 05 21:11:37 1994", note = "See \cite{Lawson:1979:ABL,Dodson:1983:CRB,Hanson:1987:ATA,Louter-Nool:1988:ATA}.", URL = "http://doi.acm.org/10.1145/356012.356020", acknowledgement = ack-nhfb, } @Article{Buckley:1982:RQS, author = "A. Buckley", title = "Remark on ``{Algorithm} 580: {QRUP}: {A} Set of {FORTRAN} Routines for Updating {QR} Factorizations [{F5}]''", journal = j-TOMS, volume = "8", number = "4", pages = "405--405", month = dec, year = "1982", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Aug 30 00:28:08 1994", note = "See \cite{Buckley:1981:AQS}.", URL = "http://doi.acm.org/10.1145/356012.356021", acknowledgement = ack-nhfb, } @Article{Morgan:1983:MCA, author = "Alexander P. Morgan", title = "A Method for Computing All Solutions to Systems of Polynomials Equations", journal = j-TOMS, volume = "9", number = "1", pages = "1--17", month = mar, year = "1983", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65H10", MRnumber = "85f:65051", bibdate = "Sun Sep 04 19:32:57 1994", URL = "http://doi.acm.org/10.1145/356022.356023", acknowledgement = ack-nhfb, reviewer = "Eugene Allgower", } @Article{Greenberg:1983:FDA, author = "Harvey Greenberg", title = "A Functional Description of {ANALYZE}: {A} Computer-Assisted Analysis System for Linear Programming Models", journal = j-TOMS, volume = "9", number = "1", pages = "18--56", month = mar, year = "1983", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 19:32:57 1994", URL = "http://doi.acm.org/10.1145/356022.356024", acknowledgement = ack-nhfb, } @Article{Beck:1983:RGA, author = "P. Beck and L. Lasdon and M. Engquist", title = "A Reduced Gradient Algorithm for Nonlinear Network Problems", journal = j-TOMS, volume = "9", number = "1", pages = "57--70", month = mar, year = "1983", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65K10", MRnumber = "84m:65077", bibdate = "Sun Sep 04 19:32:57 1994", URL = "http://doi.acm.org/10.1145/356022.356025", acknowledgement = ack-nhfb, reviewer = "Kailash C. Kapur", } @Article{Hanson:1983:CDE, author = "P. M. Hanson and W. H. Enright", title = "Controlling the defect in existing variable-order {Adams} codes for initial-value problems", journal = j-TOMS, volume = "9", number = "1", pages = "71--97", month = mar, year = "1983", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65L05 (65L07)", MRnumber = "85i:65086", bibdate = "Sat Aug 13 17:16:02 MDT 1994", URL = "http://doi.acm.org/10.1145/356022.356026", acknowledgement = ack-nhfb, keywords = "algorithms; reliability; theory", review = "ACM CR 40497", reviewer = "Syvert P. N{\o}rsett", subject = "G.1.4 Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation, Error analysis \\ G.1.7 Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Error analysis \\ G.1.7 Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Initial value problems", } @Article{Gaffney:1983:AFS, author = "Patrick W. Gaffney", title = "{Algorithm 592}: {A FORTRAN} Subroutine for Computing the Optimal Estimate of {$f(x)$}", journal = j-TOMS, volume = "9", number = "1", pages = "98--116", month = mar, year = "1983", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/356022.356027", } @Article{Proskurowski:1983:APH, author = "Wlodzimierz Proskurowski", title = "{Algorithm 593}: {A} Package for the {Helmholtz} Equation in Nonrectangular Planar Regions", journal = j-TOMS, volume = "9", number = "1", pages = "117--124", month = mar, year = "1983", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/356022.356028", } @Article{Larson:1983:ASR, author = "John L. Larson and Mary E. Pasternak and John A. Wisniewski", title = "{Algorithm 594}: Software for Relative Error Analysis", journal = j-TOMS, volume = "9", number = "1", pages = "125--130", month = mar, year = "1983", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/356022.356029", } @Article{Martello:1983:AEA, author = "Silvano Martello", title = "{Algorithm 595}: An Enumerative Algorithm for Finding {Hamiltonian} Circuits in a Directed Graph", journal = j-TOMS, volume = "9", number = "1", pages = "131--138", month = mar, year = "1983", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/356022.356030", } @Article{Gay:1983:RNE, author = "David M. Gay", title = "Remark on ``{Algorithm} 573: {NL2SOL}\emdash An Adaptive Nonlinear Least-Squares Algorithm''", journal = j-TOMS, volume = "9", number = "1", pages = "139--139", month = mar, year = "1983", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 19:32:57 1994", note = "See \cite{Dennis:1981:ANE}.", URL = "http://doi.acm.org/10.1145/356022.356031", acknowledgement = ack-nhfb, keywords = "lsq; nllsq; nlop; software", } @Article{Dodson:1983:CRB, author = "David S. Dodson", title = "Corrigendum: Remark on ``{Algorithm} 539: {Basic Linear Algebra Subroutines} for {FORTRAN} Usage''", journal = j-TOMS, volume = "9", number = "1", pages = "140--140", month = mar, year = "1983", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Sep 05 21:11:39 1994", note = "See \cite{Lawson:1979:ABL,Dodson:1982:RBL,Hanson:1987:ATA,Louter-Nool:1988:ATA}.", URL = "http://doi.acm.org/10.1145/356022.356032", acknowledgement = ack-nhfb, } @Article{Fourer:1983:MLV, author = "Robert Fourer", title = "Modeling Languages Versus Matrix Generators for Linear Programming", journal = j-TOMS, volume = "9", number = "2", pages = "143--183", month = jun, year = "1983", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 19:43:20 1994", URL = "http://doi.acm.org/10.1145/357456.357457", acknowledgement = ack-nhfb, } @Article{Armstrong:1983:CSM, author = "R. D. Armstrong and D. S. Kung and P. Sinha and A. A. Zoltners", title = "A Computational Study of a Multiple-Choice Knapsack Algorithm", journal = j-TOMS, volume = "9", number = "2", pages = "184--198", month = jun, year = "1983", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "90C10", MRnumber = "85a:90163", bibdate = "Sun Sep 04 19:43:20 1994", URL = "http://doi.acm.org/10.1145/357456.357458", acknowledgement = ack-nhfb, } @Article{Cryer:1983:ESL, author = "C. W. Cryer", title = "The Efficient Solution of Linear Complementarity Problems for Tridiagonal {Minkowski} Matrices", journal = j-TOMS, volume = "9", number = "2", pages = "199--214", month = jun, year = "1983", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "90C33 (65F10)", MRnumber = "84j:90088", bibdate = "Sun Sep 04 19:43:20 1994", URL = "http://doi.acm.org/10.1145/357456.357459", acknowledgement = ack-nhfb, } @Article{Rheinboldt:1983:LPC, author = "Werner C. Rheinboldt and John V. Burkardt", title = "A Locally Parametrized Continuation Process", journal = j-TOMS, volume = "9", number = "2", pages = "215--235", month = jun, year = "1983", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65H10", MRnumber = "85f:65052", bibdate = "Sun Sep 04 19:43:20 1994", URL = "http://doi.acm.org/10.1145/357456.357460", acknowledgement = ack-nhfb, reviewer = "Dietrich Braess", } @Article{Rheinboldt:1983:APL, author = "Werner C. Rheinboldt and John V. Burkardt", title = "{Algorithm 596}: {A} Program for a Locally Parametrized Continuation Process", journal = j-TOMS, volume = "9", number = "2", pages = "236--241", month = jun, year = "1983", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Aug 29 12:18:04 1994", URL = "http://doi.acm.org/10.1145/357456.357461", acknowledgement = ack-nhfb, } @Article{Cody:1983:ASM, author = "W. J. Cody", title = "{Algorithm 597}: Sequence of Modified {Bessel} Functions of the First Kind", journal = j-TOMS, volume = "9", number = "2", pages = "242--245", month = jun, year = "1983", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Sep 6 22:16:30 1994", URL = "http://doi.acm.org/10.1145/357456.357462", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "G.1.2 Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation G Mathematics of Computing, MISCELLANEOUS", } @Article{Davis:1983:AAC, author = "George J. Davis", title = "{Algorithm 598}: An Algorithm to Compute Solvents of the Matrix Equation {$AX^2 + BX + C = 0$}", journal = j-TOMS, volume = "9", number = "2", pages = "246--254", month = jun, year = "1983", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/357456.357463", } @Article{Ahrens:1983:ASG, author = "J. H. Ahrens and K. D. Kohrt and U. Dieter", title = "{Algorithm 599}: Sampling from {Gamma} and {Poisson} Distributions", journal = j-TOMS, volume = "9", number = "2", pages = "255--257", month = jun, year = "1983", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 16:10:33 1994", URL = "http://doi.acm.org/10.1145/357456.357464", acknowledgement = ack-nhfb, country = "USA", date = "13/05/93", descriptors = "RVG;", enum = "6932", language = "English", location = "SEL: Wi", references = "0", revision = "16/01/94", } @Article{Herriott:1983:ATA, author = "John G. Herriott and Christian H. Reinsch", title = "{Algorithm 600}: Translation of {Algorithm} 507: {Procedures} for Quintic Natural Spline Interpolation", journal = j-TOMS, volume = "9", number = "2", pages = "258--259", month = jun, year = "1983", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Sep 5 23:07:55 1994", URL = "http://doi.acm.org/10.1145/357456.357465", acknowledgement = ack-nhfb, } @Article{Pape:1983:RSP, author = "U. Pape", title = "Remark on ``{Algorithm} 562: Shortest Path Lengths''", journal = j-TOMS, volume = "9", number = "2", pages = "260--260", month = jun, year = "1983", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 19:43:20 1994", note = "See \cite{Pape:1980:ASP}.", URL = "http://doi.acm.org/10.1145/357456.357466", acknowledgement = ack-nhfb, } @Article{Krogh:1983:AAP, author = "Fred T. Krogh", title = "{ACM} Algorithms Policy", journal = j-TOMS, volume = "9", number = "2", pages = "261--264", month = jun, year = "1983", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 19:43:20 1994", URL = "http://doi.acm.org/10.1145/357456.357467", acknowledgement = ack-nhfb, } @Article{Zave:1983:QEF, author = "Pamela Zave and George E. {Cole, Jr.}", title = "A Quantitative Evaluation of the Feasibility of, and Suitable Hardware Architectures for, an Adaptive, Parallel Finite-Element System", journal = j-TOMS, volume = "9", number = "3", pages = "271--292", month = sep, year = "1983", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65W05 (65N30)", MRnumber = "86g:65244", bibdate = "Sun Sep 04 19:50:51 1994", URL = "http://doi.acm.org/10.1145/356044.356045", acknowledgement = ack-nhfb, reviewer = "Beny Neta", } @Article{Watkins:1983:NSS, author = "David S. Watkins and Ralph W. {HansonSmith}", title = "The Numerical Solution of Separably Stiff Systems by Precise Partitioning", journal = j-TOMS, volume = "9", number = "3", pages = "293--301", month = sep, year = "1983", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65L05 (65-04)", MRnumber = "86g:65136", bibdate = "Sun Sep 04 19:51:59 1994", URL = "http://doi.acm.org/10.1145/356044.356046", acknowledgement = ack-nhfb, keywords = "algorithms; experimentation; measurement; performance", review = "ACM CR 8406-0468", subject = "G.1.7 Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Initial value problems \\ G.1.7 Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Stiff equations", } @Article{Duff:1983:MSI, author = "I. S. Duff and J. K. Reid", title = "The Multifrontal Solution of Indefinite Sparse Symmetric Linear Systems", journal = j-TOMS, volume = "9", number = "3", pages = "302--325", month = sep, year = "1983", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65F50 (65W05)", MRnumber = "86k:65030", bibdate = "Fri Aug 26 23:38:14 1994", URL = "http://doi.acm.org/10.1145/356044.356047", acknowledgement = ack-nhfb, keywords = "indefinite system; nla; sparse; symmetric matrix", reviewer = "Stephen W. Brady", } @Article{Tarjan:1983:SEI, author = "Robert E. Tarjan", title = "Space-Efficient Implementations of Graph Search Methods", journal = j-TOMS, volume = "9", number = "3", pages = "326--339", month = sep, year = "1983", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "68P10", MRnumber = "86m:68023", bibdate = "Sun Sep 04 19:50:51 1994", URL = "http://doi.acm.org/10.1145/356044.356048", acknowledgement = ack-nhfb, } @Article{McNamee:1983:SMP, author = "J. M. McNamee", title = "A Sparse Matrix Package\emdash Part {II}: Special Cases", journal = j-TOMS, volume = "9", number = "3", pages = "340--343", month = sep, year = "1983", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 19:50:51 1994", URL = "http://doi.acm.org/10.1145/356044.356049", acknowledgement = ack-nhfb, } @Article{McNamee:1983:ASM, author = "J. M. McNamee", title = "{Algorithm 601}: {A} Sparse-Matrix Package\emdash Part {II}: Special Cases", journal = j-TOMS, volume = "9", number = "3", pages = "344--345", month = sep, year = "1983", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/356044.356050", } @Article{Fessler:1983:HAA, author = "Theodore Fessler and William F. Ford and David A. Smith", title = "{HURRY}: An Acceleration Algorithm for Scalar Sequences and Series", journal = j-TOMS, volume = "9", number = "3", pages = "346--354", month = sep, year = "1983", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65B10", MRnumber = "791 970", bibdate = "Sun Sep 04 19:50:51 1994", URL = "http://doi.acm.org/10.1145/356044.356051", acknowledgement = ack-nhfb, } @Article{Fessler:1983:AHA, author = "Theodore Fessler and William F. Ford and David A. Smith", title = "{Algorithm 602}: {HURRY}: An Acceleration Algorithm for Scalar Sequences and Series", journal = j-TOMS, volume = "9", number = "3", pages = "355--357", month = sep, year = "1983", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65B10", MRnumber = "791 971", URL = "http://doi.acm.org/10.1145/356044.356052", acknowledgement = ack-nhfb, } @Article{Diaz:1983:FPS, author = "J. C. D{\'i}az and G. Fairweather and P. Keast", title = "{FORTRAN} Packages for Solving Certain Almost Block Diagonal Linear Systems by Modified Alternate Row and Column Elimination", journal = j-TOMS, volume = "9", number = "3", pages = "358--375", month = sep, year = "1983", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65F05 (65-04)", MRnumber = "791 972", bibdate = "Sun Sep 04 19:50:51 1994", URL = "http://doi.acm.org/10.1145/356044.356053", acknowledgement = ack-nhfb, } @Article{Diaz:1983:ACA, author = "J. C. D{\'i}az and G. Fairweather and P. Keast", title = "{Algorithm 603}: {COLROW} and {ARCECO}: {FORTRAN} Packages for Solving Certain Almost Block Diagonal Linear Systems by Modified Alternate Row and Column Elimination", journal = j-TOMS, volume = "9", number = "3", pages = "376--380", month = sep, year = "1983", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65F05 (65-04)", MRnumber = "791 973", bibdate = "Sun Sep 4 22:04:24 1994", note = "See also \cite{Diaz:1988:RCA}.", URL = "http://doi.acm.org/10.1145/356044.356054", acknowledgement = ack-nhfb, } @Article{Sauer:1983:AFP, author = "Frederick W. Sauer", title = "{Algorithm 604}: {A} {FORTRAN} Program for the Calculation of an Extremal Polynomial", journal = j-TOMS, volume = "9", number = "3", pages = "381--383", month = sep, year = "1983", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65-04 (65F10 65K10)", MRnumber = "86g:65007", URL = "http://doi.acm.org/10.1145/356044.356055", acknowledgement = ack-nhfb, } @Article{Hopkins:1983:APV, author = "T. R. Hopkins", title = "{Algorithm 605}: {PBASIC}: {A} Verifier Program for {American National Standard Minimal BASIC}", journal = j-TOMS, volume = "9", number = "4", pages = "391--394", month = dec, year = "1983", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/356056.356057", } @Article{Gaffney:1983:NIT, author = "P. W. Gaffney and J. W. Wooten and K. A. Kessel and W. R. McKinney", title = "{NITPACK}: An Interactive Tree Package", journal = j-TOMS, volume = "9", number = "4", pages = "395--417", month = dec, year = "1983", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 19:56:32 1994", URL = "http://doi.acm.org/10.1145/356056.356058", acknowledgement = ack-nhfb, } @Article{Gaffney:1983:ANI, author = "P. W. Gaffney and J. W. Wooten and K. A. Kessel and W. R. McKinney", title = "{Algorithm 606}: {NITPACK}: An Interactive Tree Package", journal = j-TOMS, volume = "9", number = "4", pages = "418--426", month = dec, year = "1983", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/356056.356059", } @Article{Snyder:1983:ATE, author = "W. V. Snyder and R. J. Hanson", title = "{Algorithm 607}: Text Exchange System: {A} Transportable System for Management and Exchange of Programs and other Text", journal = j-TOMS, volume = "9", number = "4", pages = "427--440", month = dec, year = "1983", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/356056.356060", } @Article{Horn:1983:CLE, author = "B. K. P. Horn", title = "The Curve of Least Energy", journal = j-TOMS, volume = "9", number = "4", pages = "441--460", month = dec, year = "1983", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D07 (65D10)", MRnumber = "87c:65009", bibdate = "Sun Sep 04 19:58:16 1994", URL = "http://doi.acm.org/10.1145/356056.356061", acknowledgement = ack-nhfb, reviewer = "G. P. Bhattacharjee", } @Article{West:1983:AAS, author = "David H. West", title = "{Algorithm 608}: Approximate Solution of the Quadratic Assignment Problem", journal = j-TOMS, volume = "9", number = "4", pages = "461--466", month = dec, year = "1983", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65K05 (90C10)", MRnumber = "791 976", URL = "http://doi.acm.org/10.1145/356056.356062", acknowledgement = ack-nhfb, } @Article{Amos:1983:UAE, author = "D. E. Amos", title = "Uniform Asymptotic Expansions for Exponential Integrals ${E}_n(x)$ and {Bickley} Functions $\hbox{Ki}_n(x)$", journal = j-TOMS, volume = "9", number = "4", pages = "467--479", month = dec, year = "1983", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D20 (33A70)", MRnumber = "87a:65043", bibdate = "Sun Sep 04 19:56:32 1994", URL = "http://doi.acm.org/10.1145/356056.356063", acknowledgement = ack-nhfb, reviewer = "Marietta J. Tretter", } @Article{Amos:1983:APFa, author = "D. E. Amos", title = "{Algorithm 609}: {A} Portable {FORTRAN} Subroutine for the {Bickley} Functions {$\hbox{Ki}_n(x)$}", journal = j-TOMS, volume = "9", number = "4", pages = "480--493", month = dec, year = "1983", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D20 (33A70 65-04)", MRnumber = "87a:65044", bibdate = "Sun Sep 4 20:00:39 1994", URL = "http://doi.acm.org/10.1145/356056.356064", acknowledgement = ack-nhfb, reviewer = "Marietta J. Tretter", } @Article{Amos:1983:APFb, author = "D. E. Amos", title = "{Algorithm 610}: {A} Portable {FORTRAN} Subroutine for Derivatives of the Psi Function", journal = j-TOMS, volume = "9", number = "4", pages = "494--502", month = dec, year = "1983", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D20", MRnumber = "791 979", bibsource = "ACM Computing Archive CD-ROM database (1991)", URL = "http://doi.acm.org/10.1145/356056.356065", acknowledgement = ack-nhfb, catcode = "G.1.0; G.1; G; D.3.2", CRclass = "G.1.0 General; G.1.0 Numerical algorithms; G.1.m Miscellaneous; D.3.2 Language Classifications; D.3.2 FORTRAN", descriptor = "Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms; Mathematics of Computing, NUMERICAL ANALYSIS, Miscellaneous; Mathematics of Computing, MISCELLANEOUS; Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN", genterm = "ALGORITHMS", guideno = "02212", subject = "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.m MISCELLANEOUS; D. Software; D.3 PROGRAMMING LANGUAGES", } @Article{Gay:1983:ASU, author = "David M. Gay", title = "{Algorithm 611}: Subroutines for Unconstrained Minimization Using a Model\slash Trust-Region Approach", journal = j-TOMS, volume = "9", number = "4", pages = "503--524", month = dec, year = "1983", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65K10 (65-04 90C30)", MRnumber = "86f:65111", bibdate = "Fri Aug 26 23:38:14 1994", URL = "http://doi.acm.org/10.1145/356056.356066", acknowledgement = ack-nhfb, keywords = "lsq; nllsq; nlop", } @Article{Amos:1983:REI, author = "Donald E. Amos", title = "Remark on ``{Algorithm} 556: Exponential Integrals''", journal = j-TOMS, volume = "9", number = "4", pages = "525--525", month = dec, year = "1983", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Aug 30 00:28:08 1994", note = "See \cite{Amos:1980:AEI}.", URL = "http://doi.acm.org/10.1145/356056.356067", acknowledgement = ack-nhfb, } @Article{deDoncker:1984:AAI, author = "Elise {de Doncker} and Ian Robinson", title = "An Algorithm for Automatic Integration Over a Triangle Using Nonlinear Extrapolation", journal = j-TOMS, volume = "10", number = "1", pages = "1--16", month = mar, year = "1984", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D30 (65V05)", MRnumber = "86e:65035a", bibdate = "Fri Mar 28 11:00:07 2003", URL = "http://doi.acm.org/10.1145/356068.356069", acknowledgement = ack-nhfb, } @Article{deDoncker:1984:ATI, author = "Elise {de Doncker} and Ian Robinson", title = "{Algorithm 612}: {TRIEX}: Integration Over a {TRIangle} Using Nonlinear {EXtrapolation}", journal = j-TOMS, volume = "10", number = "1", pages = "17--22", month = mar, year = "1984", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D30 (65V05)", MRnumber = "86e:65035b", bibdate = "Sat Oct 24 15:51:01 1998", URL = "http://doi.acm.org/10.1145/356068.356070", acknowledgement = ack-nhfb, } @Article{Gear:1984:SOD, author = "C. W. Gear and O. {\O}sterby", title = "Solving Ordinary Differential Equations with Discontinuities", journal = j-TOMS, volume = "10", number = "1", pages = "23--44", month = mar, year = "1984", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65L05", MRnumber = "86h:65097", bibdate = "Sun Sep 04 20:02:26 1994", URL = "http://doi.acm.org/10.1145/356068.356071", acknowledgement = ack-nhfb, reviewer = "W. C. Rheinboldt", } @Article{Krogh:1984:ARI, author = "Fred T. Krogh and Kris Stewart", title = "Asymptotic ($h\rightarrow\infty$) Absolute Stability for {BDFs} Applied to Stiff Differential Equations", journal = j-TOMS, volume = "10", number = "1", pages = "45--57", month = mar, year = "1984", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65L20 (65-04)", MRnumber = "86j:65103", bibdate = "Sun Sep 04 20:02:26 1994", URL = "http://doi.acm.org/10.1145/356068.356072", acknowledgement = ack-nhfb, reviewer = "Gh. Adam", } @Article{Gaffney:1984:PES, author = "Patrick W. Gaffney", title = "A Performance Evaluation of Some {FORTRAN} Subroutines for the Solution of Stiff Oscillatory Ordinary Differential Equations", journal = j-TOMS, volume = "10", number = "1", pages = "58--72", month = mar, year = "1984", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65L05 (65-04)", MRnumber = "86f:65117", bibdate = "Sun Sep 04 20:02:26 1994", URL = "http://doi.acm.org/10.1145/356068.356073", acknowledgement = ack-nhfb, } @Article{Kaufman:1984:BES, author = "Linda Kaufman", title = "Banded Eigenvalue Solvers on Vector Machines", journal = j-TOMS, volume = "10", number = "1", pages = "73--85", month = mar, year = "1984", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65W05 (65F15)", MRnumber = "86f:65223", bibdate = "Fri Sep 30 01:11:03 1994", URL = "http://doi.acm.org/10.1145/356068.356074", acknowledgement = ack-nhfb, } @Article{Lenard:1984:RGT, author = "Melanie L. Lenard and Michael Minkoff", title = "Randomly Generated Test Problems for Positive Definite Quadratic Programming", journal = j-TOMS, volume = "10", number = "1", pages = "86--96", month = mar, year = "1984", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65K10 (90C20)", MRnumber = "86e:65088", bibdate = "Sun Sep 04 20:02:26 1994", URL = "http://doi.acm.org/10.1145/356068.356075", acknowledgement = ack-nhfb, } @Article{Jones:1984:SRM, author = "Christopher B. Jones", title = "A Significance Rule for Multiple-Precision Arithmetic", journal = j-TOMS, volume = "10", number = "1", pages = "97--107", month = mar, year = "1984", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65G05 (65G10)", MRnumber = "86e:65063", bibdate = "Sun Sep 04 20:02:26 1994", URL = "http://doi.acm.org/10.1145/356068.356076", acknowledgement = ack-nhfb, } @Article{Haymond:1984:AMS, author = "R. E. Haymond and J. P. Jarvis and D. R. Shier", title = "{Algorithm 613}: Minimum Spanning Tree for Moderate Integer Weights", journal = j-TOMS, volume = "10", number = "1", pages = "108--111", month = mar, year = "1984", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/356068.356077", } @Article{Shapiro:1984:IRG, author = "Henry D. Shapiro", title = "Increasing Robustness in Global Adaptive Quadrature Through Interval Selection Heuristics", journal = j-TOMS, volume = "10", number = "2", pages = "117--139", month = jun, year = "1984", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D32 (65V05)", MRnumber = "87a:65053", bibdate = "Sun Sep 04 20:09:42 1994", URL = "http://doi.acm.org/10.1145/399.400", acknowledgement = ack-nhfb, } @Article{Sikorski:1984:OQS, author = "K. Sikorski and F. Stenger", title = "Optimal Quadratures in {$H_p$} Spaces", journal = j-TOMS, volume = "10", number = "2", pages = "140--151", month = jun, year = "1984", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D32", MRnumber = "87a:65054a", bibdate = "Sun Sep 04 20:09:42 1994", URL = "http://doi.acm.org/10.1145/399.448", acknowledgement = ack-nhfb, reviewer = "J. B. Butler, Jr.", } @Article{Sikorski:1984:AFS, author = "K. Sikorski and F. Stenger and J. Schwing", title = "{Algorithm 614}: {A FORTRAN} Subroutine for Numerical Integration in {$H_p$}", journal = j-TOMS, volume = "10", number = "2", pages = "152--160", month = jun, year = "1984", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D32 (65-04)", MRnumber = "87a:65054b", bibdate = "Sun Sep 4 20:11:27 1994", URL = "http://doi.acm.org/10.1145/399.449", acknowledgement = ack-nhfb, reviewer = "J. B. Butler, Jr.", } @Article{Rall:1984:DPS, author = "L. B. Rall", title = "Differentiation in {Pascal-SC}: Type {GRADIENT}", journal = j-TOMS, volume = "10", number = "2", pages = "161--184", month = jun, year = "1984", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D25 (65-04 65H05)", MRnumber = "86j:65025", bibdate = "Sun Sep 04 20:09:42 1994", URL = "http://doi.acm.org/10.1145/399.418", acknowledgement = ack-nhfb, reviewer = "Stephen W. Brady", } @Article{Lawrie:1984:CCC, author = "D. H. Lawrie and A. H. Sameh", title = "The Computation and Communication Complexity of a Parallel Banded System Solver", journal = j-TOMS, volume = "10", number = "2", pages = "185--195", month = jun, year = "1984", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65W05 (65F05 68Q25)", MRnumber = "86k:65138", bibdate = "Sat Nov 19 13:08:12 1994", note = "See also \cite{Lawrie:1985:CCC}.", URL = "http://doi.acm.org/10.1145/399.401", acknowledgement = ack-nhfb, reviewer = "D. Bini", } @Article{Reid:1984:SAB, author = "J. K. Reid and A. Jennings", title = "On Solving Almost Block Diagonal (Staircase) Linear Systems", journal = j-TOMS, volume = "10", number = "2", pages = "196--201", month = jun, year = "1984", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65F05 (65F50 65L10)", MRnumber = "86g:65063", bibdate = "Sun Sep 04 20:09:42 1994", URL = "http://doi.acm.org/10.1145/399.450", acknowledgement = ack-nhfb, } @Article{Armstrong:1984:ABS, author = "R. D. Armstrong and P. O. Beck and M. T. Kung", title = "{Algorithm 615}: The Best Subset of Parameters in Least Absolute Value Regression", journal = j-TOMS, volume = "10", number = "2", pages = "202--206", month = jun, year = "1984", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D10 (65K05)", MRnumber = "791 987", URL = "http://doi.acm.org/10.1145/399.319410", acknowledgement = ack-nhfb, } @Article{Petkov:1984:RDE, author = "P. {Hr.} Petkov and N. D. Christov and M. M. Konstantinov", title = "Remark on ``{Algorithm} 590: {DSUBSP} and {EXCHQZ}: {FORTRAN} Subroutines for Computing Deflating Subspaces with Specified Spectrum''", journal = j-TOMS, volume = "10", number = "2", pages = "207--207", month = jun, year = "1984", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Oct 24 15:51:05 1998", note = "See \cite{VanDooren:1982:ADE}.", URL = "http://doi.acm.org/10.1145/399.319411", acknowledgement = ack-nhfb, } @Article{Krogh:1984:AAP, author = "Fred T. Krogh", title = "{ACM} Algorithms Policy", journal = j-TOMS, volume = "10", number = "2", pages = "208--211", month = jun, year = "1984", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 20:09:42 1994", URL = "http://doi.acm.org/10.1145/399.319412", acknowledgement = ack-nhfb, } @Article{Dongarra:1984:SMA, author = "Jack J. Dongarra and Stanley C. Eisenstat", title = "Squeezing the Most out of an Algorithm in {CRAY} {FORTRAN}", journal = j-TOMS, volume = "10", number = "3", pages = "219--230", month = sep, year = "1984", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65F99", MRnumber = "791 988", bibdate = "Fri Aug 26 23:38:14 1994", URL = "http://doi.acm.org/10.1145/1271.319413", acknowledgement = ack-nhfb, keywords = "cray; fortran; nla; vect", } @Article{Molchanov:1984:PCS, author = "I. N. Molchanov and V. S. Zubatenko and L. D. Nikolenko and M. F. Yakovlev", title = "A Program Complex for Solving Systems of Linear Algebraic Equations", journal = j-TOMS, volume = "10", number = "3", pages = "231--241", month = sep, year = "1984", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65F05 (65F10 65V05)", MRnumber = "86f:65061", bibdate = "Sun Sep 04 20:18:56 1994", URL = "http://doi.acm.org/10.1145/1271.1273", acknowledgement = ack-nhfb, } @Article{Rivara:1984:DDS, author = "Mar{\'i}a-Cecilia Rivara", title = "Design and Data Structure of Fully Adaptive Multigrid, Finite-Element Software", journal = j-TOMS, volume = "10", number = "3", pages = "242--264", month = sep, year = "1984", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65N50 (65F50 65N30)", MRnumber = "86f:65207", bibdate = "Sat Aug 27 19:10:37 1994", URL = "http://doi.acm.org/10.1145/1271.1274", acknowledgement = ack-nhfb, } @Article{Monahan:1984:AFC, author = "John F. Monahan", title = "{Algorithm 616}: Fast Computation of the {Hodges-Lehman} Location Estimator", journal = j-TOMS, volume = "10", number = "3", pages = "265--270", month = sep, year = "1984", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65U05 (62-04 62G05)", MRnumber = "791 991", bibdate = "Sun Sep 4 20:21:15 1994", note = "This paper reduces the previous complexity bound for the {Hodges-Lehman} location estimator from ${O}(n^2\log{n})$ to ${O}(n\log{n})$.", URL = "http://doi.acm.org/10.1145/1271.319414", acknowledgement = ack-nhfb, } @Article{Kronmal:1984:ACA, author = "Richard A. Kronmal and Arthur V. {Peterson, Jr.}", title = "An Acceptance-Complement Analogue of the Mixture-plus-Acceptance-Rejection Method for Generating Random Variables", journal = j-TOMS, volume = "10", number = "3", pages = "271--281", month = sep, year = "1984", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65C10 (65U05)", MRnumber = "86f:65027", bibdate = "Wed Aug 24 22:43:47 1994", URL = "http://doi.acm.org/10.1145/1271.1272", acknowledgement = ack-nhfb, country = "USA", date = "13/05/93", descriptors = "RVG;", enum = "7548", language = "English", location = "SEL: Wi", references = "0", revision = "16/01/94", } @Article{Gill:1984:POP, author = "Philip E. Gill and Walter Murray and Michael A. Saunders and Margaret H. Wright", title = "Procedures for Optimization Problems with a Mixture of Bounds and General Linear Constraints", journal = j-TOMS, volume = "10", number = "3", pages = "282--298", month = sep, year = "1984", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65K10 (65F30 90C30)", MRnumber = "86h:65091", bibdate = "Sun Sep 04 20:18:56 1994", URL = "http://doi.acm.org/10.1145/1271.1276", acknowledgement = ack-nhfb, } @Article{Aluffi-Pentini:1984:DEA, author = "Filippo Aluffi-Pentini and Valerio Parisi and Francesco Zirilli", title = "A Differential-Equations Algorithm for Nonlinear Equations", journal = j-TOMS, volume = "10", number = "3", pages = "299--316", month = sep, year = "1984", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65H10 (65L05)", MRnumber = "87a:65085", bibdate = "Sun Sep 04 20:18:56 1994", URL = "http://doi.acm.org/10.1145/1271.1631", acknowledgement = ack-nhfb, reviewer = "Hj. Wacker", } @Article{Aluffi-Pentini:1984:ADD, author = "Filippo Aluffi-Pentini and Valerio Parisi and Francesco Zirilli", title = "{Algorithm 617}: {DAFNE}: {A} Differential-Equations Algorithm for Nonlinear Equations", journal = j-TOMS, volume = "10", number = "3", pages = "317--324", month = sep, year = "1984", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65H10 (65-04 65L05)", MRnumber = "87a:65086", bibdate = "Sun Sep 04 20:18:56 1994", URL = "http://doi.acm.org/10.1145/1271.1632", acknowledgement = ack-nhfb, reviewer = "Hj. Wacker", } @Article{Regener:1984:MID, author = "Eric Regener", title = "Multiprecision Integer Division Examples Using Arbitrary Radix", journal = j-TOMS, volume = "10", number = "3", pages = "325--328", month = sep, year = "1984", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65V05", MRnumber = "86g:65241", bibdate = "Sun Sep 04 20:18:56 1994", note = "See also \cite{BrinchHansen:1994:MLD}.", URL = "http://doi.acm.org/10.1145/1271.2738", acknowledgement = ack-nhfb, } @Article{Coleman:1984:SES, author = "Thomas F. Coleman and Burton S. Garbow and Jorge J. Mor{\'e}", title = "Software for Estimating Sparse {Jacobian} Matrices", journal = j-TOMS, volume = "10", number = "3", pages = "329--345", month = sep, year = "1984", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65F50 (65H10)", MRnumber = "86f:65086a", bibdate = "Mon Sep 05 09:48:14 1994", URL = "http://doi.acm.org/10.1145/1271.1610", acknowledgement = ack-nhfb, } @Article{Coleman:1984:AFS, author = "Thomas F. Coleman and Burton S. Garbow and Jorge J. Mor{\'e}", title = "{Algorithm 618}: {Fortran} Subroutines for Estimating Sparse {Jacobian} Matrices", journal = j-TOMS, volume = "10", number = "3", pages = "346--347", month = sep, year = "1984", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65F50 (65-04 65H10)", MRnumber = "86f:65086b", bibdate = "Sun Sep 04 20:28:26 1994", URL = "http://doi.acm.org/10.1145/1271.319415", acknowledgement = ack-nhfb, } @Article{Piessens:1984:AAN, author = "Robert Piessens and Rudi Huysmans", title = "{Algorithm 619}: Automatic Numerical Inversion of the {Laplace} Transform [{D5}]", journal = j-TOMS, volume = "10", number = "3", pages = "348--353", month = sep, year = "1984", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65R10", MRnumber = "791 999", URL = "http://doi.acm.org/10.1145/1271.319416", acknowledgement = ack-nhfb, } @Article{Piessens:1984:RNI, author = "Robert Piessens", title = "Remark on ``{Algorithm} 486: Numerical Inversion of {Laplace} Transform''", journal = j-TOMS, volume = "10", number = "3", pages = "354--354", month = sep, year = "1984", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 20:18:56 1994", note = "See \cite{Veillon:1977:RNI,Koppelaar:1976:RNI}.", URL = "http://doi.acm.org/10.1145/1271.319417", acknowledgement = ack-nhfb, } @Article{Rice:1984:ARK, author = "John R. Rice and Richard J. Hanson", title = "{Algorithm 620}: References and Keywords for {\em {Collected Algorithms} of the {ACM}}", journal = j-TOMS, volume = "10", number = "4", pages = "359--360", month = dec, year = "1984", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Mar 28 11:00:44 2003", note = "See also \cite{Hamilton:1985:RRK,Hopkins:1990:RRK}.", URL = "http://doi.acm.org/10.1145/2701.356100", acknowledgement = ack-nhfb, } @Article{Black:1984:NIS, author = "Cheryl M. Black and Robert P. Burton and Thomas H. Miller", title = "The Need for an Industry Standard of Accuracy for Elementary-Function Programs", journal = j-TOMS, volume = "10", number = "4", pages = "361--366", month = dec, year = "1984", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D20", MRnumber = "792 000", bibdate = "Sun Sep 04 20:32:29 1994", URL = "http://doi.acm.org/10.1145/2701.356101", acknowledgement = ack-nhfb, } @Article{Eiger:1984:BMS, author = "A. Eiger and K. Sikorski and F. Stenger", title = "A Bisection Method for Systems of Nonlinear Equations", journal = j-TOMS, volume = "10", number = "4", pages = "367--377", month = dec, year = "1984", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65H10", MRnumber = "86g:65102", bibdate = "Sun Sep 04 20:32:29 1994", URL = "http://doi.acm.org/10.1145/2701.2705", acknowledgement = ack-nhfb, } @Article{Sommeijer:1984:ASL, author = "B. P. Sommeijer and P. J. {van der Houwen}", title = "{Algorithm 621}: Software with Low Storage Requirements for Two-Dimensional, Nonlinear, Parabolic Differential Equations", journal = j-TOMS, volume = "10", number = "4", pages = "378--396", month = dec, year = "1984", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65M20", MRnumber = "792 002", bibdate = "Sat Oct 24 15:50:58 1998", URL = "http://doi.acm.org/10.1145/2701.356103", acknowledgement = ack-nhfb, } @Article{Bundy:1984:GIP, author = "Alan Bundy", title = "A Generalized Interval Package and Its Use for Semantic Checking", journal = j-TOMS, volume = "10", number = "4", pages = "397--409", month = dec, year = "1984", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65G10", MRnumber = "86g:65088", bibdate = "Sun Sep 04 20:32:29 1994", URL = "http://doi.acm.org/10.1145/2701.2702", acknowledgement = ack-nhfb, } @Article{Rice:1984:ASM, author = "John R. Rice and Calvin Ribbens and William A. Ward", title = "{Algorithm 622}: {A} Simple Macroprocessor", journal = j-TOMS, volume = "10", number = "4", pages = "410--416", month = dec, year = "1984", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Mar 09 10:17:12 1999", note = "See remark \cite{Levin:1998:RAS}.", URL = "http://doi.acm.org/10.1145/2701.356105", acknowledgement = ack-nhfb, } @Article{Renka:1984:IDS, author = "Robert J. Renka", title = "Interpolation of Data on the Surface of a Sphere", journal = j-TOMS, volume = "10", number = "4", pages = "417--436", month = dec, year = "1984", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D05 (65-04)", MRnumber = "86k:65013a", bibdate = "Sat Aug 13 17:26:53 MDT 1994", URL = "http://doi.acm.org/10.1145/2701.2703", acknowledgement = ack-nhfb, keywords = "algorithms", review = "ACM CR 8511-1051", reviewer = "G. P. Bhattacharjee", subject = "G.1 Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation", } @Article{Renka:1984:AIS, author = "Robert J. Renka", title = "{Algorithm 623}: Interpolation on the Surface of a Sphere", journal = j-TOMS, volume = "10", number = "4", pages = "437--439", month = dec, year = "1984", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D05 (65-04)", MRnumber = "86k:65013b", bibdate = "Fri Mar 28 11:02:10 2003", URL = "http://doi.acm.org/10.1145/2701.356107", acknowledgement = ack-nhfb, reviewer = "G. P. Bhattacharjee", } @Article{Renka:1984:ATI, author = "Robert J. Renka", title = "{Algorithm 624}: Triangulation and Interpolation at Arbitrarily Distributed Points in the Plane", journal = j-TOMS, volume = "10", number = "4", pages = "440--442", month = dec, year = "1984", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D05 (65V05)", MRnumber = "792 006", bibdate = "Fri Mar 28 11:02:31 2003", URL = "http://doi.acm.org/10.1145/2701.356108", acknowledgement = ack-nhfb, } @Article{Rice:1984:NCG, author = "John R. Rice", title = "Numerical Computation with General Two-Dimensional Domains", journal = j-TOMS, volume = "10", number = "4", pages = "443--452", month = dec, year = "1984", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65N50", MRnumber = "792 007", bibdate = "Sun Sep 04 20:32:29 1994", URL = "http://doi.acm.org/10.1145/2701.356109", acknowledgement = ack-nhfb, } @Article{Rice:1984:ATD, author = "John R. Rice", title = "{Algorithm 625}: {A} Two-Dimensional Domain Processor", journal = j-TOMS, volume = "10", number = "4", pages = "453--462", month = dec, year = "1984", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65N50", MRnumber = "792 008", bibdate = "Fri Mar 28 11:03:12 2003", URL = "http://doi.acm.org/10.1145/2701.356110", acknowledgement = ack-nhfb, } @Article{Preusser:1984:CCS, author = "Albrecht Preusser", title = "Computing Contours by Successive Solution of Quintic Polynomial Equations", journal = j-TOMS, volume = "10", number = "4", pages = "463--472", month = dec, year = "1984", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D05", MRnumber = "792 009", bibdate = "Sun Sep 04 20:32:29 1994", URL = "http://doi.acm.org/10.1145/2701.2770", acknowledgement = ack-nhfb, } @Article{Preusser:1984:ATE, author = "Albrecht Preusser", title = "{Algorithm 626}: {TRICP}\emdash {A} Contour Plot Program for Triangular Meshes", journal = j-TOMS, volume = "10", number = "4", pages = "473--475", month = dec, year = "1984", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D05 (65N50)", MRnumber = "792 010", URL = "http://doi.acm.org/10.1145/2701.2772", acknowledgement = ack-nhfb, } @Article{Garbow:1984:RQA, author = "B. S. Garbow", title = "Remark on ``{Algorithm} 535: The {QZ} Algorithm to Solve the Generalized Eigenvalue Problem for Complex Matrices [{F2}]''", journal = j-TOMS, volume = "10", number = "4", pages = "476--476", month = dec, year = "1984", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 20:32:29 1994", note = "See \cite{Garbow:1978:AQA,Garbow:1982:RQA}.", URL = "http://doi.acm.org/10.1145/2701.356113", acknowledgement = ack-nhfb, } @Article{Celis:1984:RCE, author = "Pedro Celis", title = "Remark: Corrections and Errors in {John Ivie}'s Some {MACSYMA} Programs for Solving Recurrence Relations", journal = j-TOMS, volume = "10", number = "4", pages = "477--478", month = dec, year = "1984", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 20:32:29 1994", note = "See \cite{Ivie:1978:SMP}.", URL = "http://doi.acm.org/10.1145/2701.356114", acknowledgement = ack-nhfb, } @Article{Tomlin:1985:IPS, author = "J. A. Tomlin and J. S. Welch", title = "Integration of a Primal Simplex Network Algorithm with a Large-Scale Mathematical Programming System", journal = j-TOMS, volume = "11", number = "1", pages = "1--11", month = mar, year = "1985", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65K05 (90C05)", MRnumber = "86h:65087", bibdate = "Sun Sep 04 20:43:27 1994", URL = "http://doi.acm.org/10.1145/3147.3163", acknowledgement = ack-nhfb, keywords = "algorithms; measurement; performance", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Linear programming.", } @Article{Davidon:1985:ESD, author = "William C. Davidon and Jorge Nocedal", title = "Evaluation of Step Directions in Optimization Algorithms", journal = j-TOMS, volume = "11", number = "1", pages = "12--19", month = mar, year = "1985", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65K10 (90C30)", MRnumber = "86h:65089", bibdate = "Sun Sep 04 20:43:27 1994", URL = "http://doi.acm.org/10.1145/3147.3164", acknowledgement = ack-nhfb, keywords = "algorithms; measurement; performance", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Gradient methods.", } @Article{Cuyt:1985:CIM, author = "Annie A. M. Cuyt and L. B. Rall", title = "Computational Implementation of the Multivariate {Halley} Method for Solving Nonlinear Systems of Equations", journal = j-TOMS, volume = "11", number = "1", pages = "20--36", month = mar, year = "1985", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65H05 (65-04)", MRnumber = "86g:65092", bibdate = "Sun Sep 04 20:43:27 1994", URL = "http://doi.acm.org/10.1145/3147.3162", acknowledgement = ack-nhfb, keywords = "algorithms; languages", subject = "{\bf G.1.5}: Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Iterative methods. {\bf G.1.5}: Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Systems of equations. {\bf G.1.m}: Mathematics of Computing, NUMERICAL ANALYSIS, Miscellaneous. {\bf I.1.m}: Computing Methodologies, ALGEBRAIC MANIPULATION, Miscellaneous.", } @Article{Vitter:1985:RSR, author = "Jeffrey Scott Vitter", title = "Random Sampling with a Reservoir", journal = j-TOMS, volume = "11", number = "1", pages = "37--57", month = mar, year = "1985", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65C10 (62-04)", MRnumber = "87b:65007", bibdate = "Sun Sep 04 20:43:27 1994", URL = "http://doi.acm.org/10.1145/3147.3165", acknowledgement = ack-nhfb, keywords = "algorithms; design; performance; theory; verification", reviewer = "Brian Conolly", subject = "{\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Probabilistic algorithms (including Monte Carlo). {\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Random number generation. {\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Statistical software. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf D.4.3}: Software, OPERATING SYSTEMS, File Systems Management, Access methods.", } @Article{Bownds:1985:AFS, author = "John M. Bownds and Lee Appelbaum", title = "{Algorithm 627}: {A} {FORTRAN} Subroutine for Solving {Volterra} Integral Equations", journal = j-TOMS, volume = "11", number = "1", pages = "58--65", month = mar, year = "1985", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65R20", MRnumber = "793 057", URL = "http://doi.acm.org/10.1145/3147.214314", acknowledgement = ack-nhfb, keywords = "documentation; economics; performance", subject = "{\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Chebyshev approximation and theory. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Portability.", } @Article{Winkler:1985:AAC, author = "F. Winkler and B. Buchberger and F. Lichtenberger and H. Rolletschek", title = "{Algorithm 628}: An Algorithm for Constructing Canonical Bases of Polynomial Ideals", journal = j-TOMS, volume = "11", number = "1", pages = "66--78", month = mar, year = "1985", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "68Q40 (13-04)", MRnumber = "793 058", URL = "http://doi.acm.org/10.1145/3147.214316", acknowledgement = ack-nhfb, keywords = "algorithms; theory", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf I.1.1}: Computing Methodologies, ALGEBRAIC MANIPULATION, Expressions and Their Representation. {\bf I.1.2}: Computing Methodologies, ALGEBRAIC MANIPULATION, Algorithms. {\bf J.2}: Computer Applications, PHYSICAL SCIENCES AND ENGINEERING.", } @Article{Atkinson:1985:AIE, author = "Kendall E. Atkinson", title = "{Algorithm 629}: An Integral Equation Program for {Laplace}'s Equation in Three Dimensions", journal = j-TOMS, volume = "11", number = "2", pages = "85--96", month = jun, year = "1985", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65N30 (65R20)", MRnumber = "86m:65137", URL = "http://doi.acm.org/10.1145/214392.214393", acknowledgement = ack-nhfb, keywords = "algorithms; theory", reviewer = "H. Kersten", subject = "{\bf G.1.9}: Mathematics of Computing, NUMERICAL ANALYSIS, Integral Equations. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Dembo:1985:TPG, author = "R. S. Dembo and T. Steihaug", title = "A Test Problem Generator for Large-Scale Unconstrained Optimization", journal = j-TOMS, volume = "11", number = "2", pages = "97--102", month = jun, year = "1985", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65K10 (90C30)", MRnumber = "86h:65090", bibdate = "Sun Sep 04 20:43:27 1994", URL = "http://doi.acm.org/10.1145/214392.214394", abstract = "A test problem generator for large-scale unconstrained optimization is described. It permits the generation of a poorly or well-conditioned problems of arbitrary size, derived from nonlinear network flow models. An eigenvalue analysis provides bounds on the condition number of the Hessian of the objective function and an example of an efficient preconditioner, using these bounds, is outlined.", acknowledgement = ack-nhfb, keywords = "algorithms; experimentation; measurement", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Nonlinear programming. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing. {\bf D.2.5}: Software, SOFTWARE ENGINEERING, Testing and Debugging, Test data generators.", } @Article{Buckley:1985:ABE, author = "A. Buckley and A. LeNir", title = "{Algorithm 630}: {BBVSCG}\emdash {A} Variable Storage Algorithm for Function Minimization", journal = j-TOMS, volume = "11", number = "2", pages = "103--119", month = jun, year = "1985", CODEN = "ACMSCU", ISSN = "0098-3500", note = "See remark \cite{Buckley:1989:RA}.", URL = "http://doi.acm.org/10.1145/214392.214395", keywords = "algorithms", subject = "{\bf G.1}: Mathematics of Computing, NUMERICAL ANALYSIS. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Gradient methods.", } @Article{Norton:1985:AFB, author = "Victor Norton", title = "{Algorithm 631}: Finding a Bracketed Zero by {Larkin}'s Method of Rational Interpolation", journal = j-TOMS, volume = "11", number = "2", pages = "120--134", month = jun, year = "1985", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65H05 (65D05)", MRnumber = "797 616", note = "See \cite{Norton:1986:RFB}.", URL = "http://doi.acm.org/10.1145/214392.214396", acknowledgement = ack-nhfb, keywords = "algorithms; theory", subject = "{\bf G.1.5}: Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Iterative methods. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation.", } @Article{Martello:1985:APM, author = "Silvano Martello and Paolo Toth", title = "{Algorithm 632}: {A} Program for the $0-1$ Multiple Knapsack Problem", journal = j-TOMS, volume = "11", number = "2", pages = "135--140", month = jun, year = "1985", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Sep 30 01:12:05 1994", URL = "http://doi.acm.org/10.1145/214392.214397", keywords = "algorithms", subject = "{\bf G.2.1}: Mathematics of Computing, DISCRETE MATHEMATICS, Combinatorics, Combinatorial algorithms. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization.", } @Article{Liu:1985:MMD, author = "Joseph W. H. Liu", title = "Modification of the Minimum-Degree Algorithm by Multiple Elimination", journal = j-TOMS, volume = "11", number = "2", pages = "141--153", month = jun, year = "1985", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65F50 (65F05)", MRnumber = "86m:65040", bibdate = "Sun Sep 04 20:43:27 1994", URL = "http://doi.acm.org/10.1145/214392.214398", abstract = "The most widely used ordering scheme to reduce fills and operations in sparse matrix computation is the minimum-degree algorithm. The notion of {\em multiple elimination} is introduced here as a modification to the conventional scheme. The motivation is discussed using the $k$-by-$k$ grid model problem. Experimental results indicate that the modified version retains the fill-reducing property of (and is often better than) the original ordering algorithm and yet requires less computer time. The reduction in ordering time is problem dependent, and for some problems the modified algorithm can run a few times faster than existing implementations of the minimum-degree algorithm. The use of {\em external degree} in the algorithm is also introduced.", acknowledgement = ack-nhfb, keywords = "algorithms", reviewer = "David R. Kincaid", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse and very large systems. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Gan:1985:NCG, author = "C. T. Gan", title = "A Note on Combination Generators", journal = j-TOMS, volume = "11", number = "2", pages = "154--156", month = jun, year = "1985", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 20:43:27 1994", URL = "http://doi.acm.org/10.1145/214392.214401", abstract = "A recent study by Akl indicates that Mifsud's algorithm, which involves unnecessary searching operations, is the fastest existing combination generator. A modified Page and Wilson's algorithm, which is essentially similar to Mifsud's algorithm, is presented. A theoretical analysis of the modified algorithm is also given.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.2.1}: Mathematics of Computing, DISCRETE MATHEMATICS, Combinatorics, Combinatorial algorithms. {\bf F.2.2}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Computations on discrete structures.", } @Article{Ahrens:1985:SRS, author = "J. H. Ahrens and U. Dieter", title = "Sequential Random Sampling", journal = j-TOMS, volume = "11", number = "2", pages = "157--169", month = jun, year = "1985", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 20:43:27 1994", URL = "http://doi.acm.org/10.1145/214392.214402", abstract = "Fast algorithms for selecting a random set of exactly $k$ records from a file of $n$ records are constructed. Selection is sequential: the sample records are chosen in the same order in which they occur in the file. All procedures run in $O(k)$ time. The ``geometric'' method has two versions: with or without $O(k)$ auxiliary space. A further procedure uses hashing techniques and requires $O(k)$ space.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Random number generation. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Ward:1985:AAL, author = "R. C. Ward and G. J. Davis and V. E. Kane", title = "{Algorithm 633}: An Algorithm for Linear Dependency Analysis of Multivariate Data", journal = j-TOMS, volume = "11", number = "2", pages = "170--182", month = jun, year = "1985", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65U05 (62-04)", MRnumber = "86j:65187", bibdate = "Fri Sep 30 01:12:58 1994", URL = "http://doi.acm.org/10.1145/214392.214403", acknowledgement = ack-nhfb, keywords = "measurement; performance", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra. {\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Statistical computing.", } @Article{Novotny:1985:RNS, author = "Milan Novotny", title = "Remark on ``{Algorithm} 30: Numerical Solution of the Polynomial Equation''", journal = j-TOMS, volume = "11", number = "2", pages = "183--184", month = jun, year = "1985", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 20:43:27 1994", note = "See \cite{Ellenberger:1960:NSP}.", URL = "http://doi.acm.org/10.1145/214392.214404", acknowledgement = ack-nhfb, keywords = "algorithms; theory", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Hill:1985:RCS, author = "I. D. Hill and M. C. Pike", title = "Remark on ``{Algorithm} 299: Chi-Squared Integral''", journal = j-TOMS, volume = "11", number = "2", pages = "185--185", month = jun, year = "1985", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Thu Apr 29 15:20:54 1999", note = "See \cite{Hill:1967:CSI,elLozy:1976:RAC,elLozy:1979:RAS}.", URL = "http://doi.acm.org/10.1145/214392.214405", acknowledgement = ack-nhfb, keywords = "algorithms; theory", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Preusser:1985:RBI, author = "Albrect Preusser", title = "Remark on ``{Algorithm} 526: Bivariate Interpolation and Smooth Surface Fitting for Irregularly Distributed Data Points [{E1}]''", journal = j-TOMS, volume = "11", number = "2", pages = "186--187", month = jun, year = "1985", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 20:43:27 1994", note = "See \cite{Akima:1978:ABI,Akima:1979:RBI}.", URL = "http://doi.acm.org/10.1145/214392.214407", acknowledgement = ack-nhfb, keywords = "algorithms; theory", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Lawrie:1985:CCC, author = "D. H. Lawrie and A. H. Sameh", title = "Corrections to ``{The} Computation and Communication Complexity of a Parallel Banded System Solver''", journal = j-TOMS, volume = "11", number = "2", pages = "188--188", month = jun, year = "1985", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 20:43:27 1994", note = "See \cite{Lawrie:1984:CCC}.", URL = "http://doi.acm.org/10.1145/214392.356133", acknowledgement = ack-nhfb, } @Article{Krogh:1985:AAP, author = "Fred T. Krogh", title = "{ACM} Algorithms Policy", journal = j-TOMS, volume = "11", number = "2", pages = "193--196", month = jun, year = "1985", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 20:43:27 1994", URL = "http://doi.acm.org/10.1145/214392.356134", acknowledgement = ack-nhfb, } @Article{Bartels:1985:LSF, author = "Richard H. Bartels and John J. Jezioranski", title = "Least-Squares Fitting Using Orthogonal Multinomials", journal = j-TOMS, volume = "11", number = "3", pages = "201--217", month = sep, year = "1985", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D10", MRnumber = "87f:65016", bibdate = "Sun Sep 04 20:57:44 1994", URL = "http://doi.acm.org/10.1145/214408.214410", abstract = "Forsythe has given a method for generating basis polynomials in a single variable that are orthogonal with respect to a given inner product. Weisfeld later demonstrated that Forsythe's approach could be extended to polynomials in an arbitrary number of variables. In this paper we sharpen Weisfeld's results and present a method for computing weighted, multinomial, least-squares approximations to given data.", acknowledgement = ack-nhfb, keywords = "algorithms", reviewer = "Wolfgang Boehm", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Least squares methods. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials.", } @Article{Bartels:1985:ACE, author = "Richard H. Bartels and John J. Jezioranski", title = "{Algorithm 634}: {CONSTR} and {EVAL}: Routines for Fitting Multinomials in a Least-Squares Sense", journal = j-TOMS, volume = "11", number = "3", pages = "218--228", month = sep, year = "1985", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D10", MRnumber = "87f:65017", bibdate = "Sun Sep 4 20:58:40 1994", URL = "http://doi.acm.org/10.1145/214408.214412", acknowledgement = ack-nhfb, keywords = "algorithms", reviewer = "Wolfgang Boehm", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Least squares methods. {\bf F.1.2}: Theory of Computation, COMPUTATION BY ABSTRACT DEVICES, Modes of Computation.", } @Article{Hull:1985:PRV, author = "T. E. Hull and A. Abrham", title = "Properly Rounded Variable Precision Square Root", journal = j-TOMS, volume = "11", number = "3", pages = "229--237", month = sep, year = "1985", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D15 (65G05)", MRnumber = "87a:65041", bibdate = "Mon Dec 08 12:36:56 1997", URL = "http://doi.acm.org/10.1145/214408.214413", abstract = "The square root function presented here returns a properly rounded approximation to the square root of its argument, or it raises an error condition if the argument is negative. {\em Properly rounded} means rounded to the nearest, or to nearest even in case of a tie. It is {\em variable precision} in that it is designed to return a $p$-digit approximation to a $p$-digit argument, for any $p>0$. (Precision $p$ means $p$ decimal digits.) The program and the analysis are valid for all $p>0$, but current implementations place some restrictions on $p$.", acknowledgement = ack-nhfb, keywords = "algorithms; verification", subject = "{\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Verification. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Error analysis. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms.", } @Article{Stewart:1985:NCD, author = "G. W. Stewart", title = "A Note on Complex Division", journal = j-TOMS, volume = "11", number = "3", pages = "238--241", month = sep, year = "1985", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Aug 26 23:38:15 1994", note = "See also \cite{Stewart:1986:CNC}.", URL = "http://doi.acm.org/10.1145/214408.214414", abstract = "An algorithm for computing the quotient of two complex numbers is modified to make it more robust in the presence of underflows.", acknowledgement = ack-nhfb, keywords = "algorithms; complex arithmetic; computer arithmetic; na", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Reliability and robustness.", } @Article{Streit:1985:AAS, author = "Roy L. Streit", title = "{Algorithm 635}: An Algorithm for the Solution of Systems of Complex Linear Equations in the ${L}_\infty$ Norm with Constraints on the Unknowns", journal = j-TOMS, volume = "11", number = "3", pages = "242--249", month = sep, year = "1985", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 20:59:33 1994", URL = "http://doi.acm.org/10.1145/214408.214415", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Minimax approximation and algorithms. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Linear programming.", } @Article{Le:1985:EDF, author = "D. Le", title = "An Efficient Derivative-Free Method for Solving Nonlinear Equations", journal = j-TOMS, volume = "11", number = "3", pages = "250--262", month = sep, year = "1985", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65H05", MRnumber = "87d:65057", bibdate = "Sat Nov 19 13:08:37 1994", note = "See also \cite{Le:1989:CED}.", URL = "http://doi.acm.org/10.1145/214408.214416", abstract = "An algorithm is presented for finding a root of a real function. The algorithm combines bisection with second and third order methods using derivatives estimated from objective function values. Global convergence is ensured and the number of function evaluations is bounded by four times the number needed by bisection. Numerical comparisons with existing algorithms indicate the superiority of the new algorithm in all classes of problems.", acknowledgement = ack-nhfb, keywords = "algorithms", reviewer = "T. Feagin", subject = "{\bf G.1.5}: Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Convergence.", } @Article{Tischer:1985:ESN, author = "P. E. Tischer and G. K. Gupta", title = "An Evaluation of Some New Cyclic Linear Multistep Formulas for Stiff {ODEs}", journal = j-TOMS, volume = "11", number = "3", pages = "263--270", month = sep, year = "1985", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65L05 (65-04)", MRnumber = "87d:65078", bibdate = "Sun Sep 04 20:57:44 1994", URL = "http://doi.acm.org/10.1145/214408.214417", abstract = "We evaluate several sets of cyclic linear multistep formulas (CLMFs). One of these sets was derived by Tischer and Sacks-Davis. Three new sets of formulas have been derived and we present their characteristics.\par The formulas have been evaluated by comparing the performance of four versions of a code which implements CLMFs. The four versions are very similar and each version implements one of the sets of CLMFs being studied. We compare the performance of these codes with that of a widely used code, LSODE. One of the new sets of CLMFs is not only much more efficient in solving stiff problems that have a Jacobian with eigenvalues close to the imaginary axis but is almost as efficient as LSODE in solving other problems. This is a significant improvement over the only other CLMF code available, STINT from Tendler, Bickart, and Picel.", acknowledgement = ack-nhfb, keywords = "algorithms; performance", reviewer = "W. H. Enright", subject = "{\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations.", } @Article{Johnsson:1985:SNB, author = "S. Lennart Johnsson", title = "Solving Narrow Banded Systems on Ensemble Architectures", journal = j-TOMS, volume = "11", number = "3", pages = "271--288", month = sep, year = "1985", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65W05 (65F05)", MRnumber = "86m:65170", bibdate = "Sun Sep 04 21:01:13 1994", URL = "http://doi.acm.org/10.1145/214408.214418", abstract = "We present concurrent algorithms for the solution of narrow banded systems on ensemble architectures, and analyze the communication and arithmetic complexities of the algorithms. The algorithms consist of three phases. In phase 1, a block tridiagonal system of reduced size is produced through largely local operations. Diagonal dominance is preserved. If the original system is positive, definite, and symmetric, so is the reduced system. It is solved in a second phase, and the remaining variables obtained through local back substitution in a third phase. With a sufficient number of processing elements, there is no first and third phase. We investigate the arithmetic and communication complexity of Gaussian elimination and block cyclic reduction for the solution of the reduced system on boolean cubes, perfect shuffle and shuffle-exchange networks, binary trees, and linear arrays.\par With an optimum number of processors, the minimum solution time on a linear array is of an order that ranges from $O(m^{2}Nm)$ to $O(m^{3} + m^{3}\log_{2}(N/m))$ depending on the bandwidth, the dimension of the problem, and the times for communication and arithmetic. For boolean cubes, cube-connected cycles, prefect shuffle and shuffle-exchange networks, and binary trees, the minimum time is $O(m^{3}+m^{3}\log_2(N/m))$ including the communication complexity", acknowledgement = ack-nhfb, keywords = "algorithms; band matrix; linear system; nla; performance; prll", subject = "{\bf C.1.2}: Computer Systems Organization, PROCESSOR ARCHITECTURES, Multiple Data Stream Architectures (Multiprocessors), Multiple-instruction-stream, multiple-data-stream processors (MIMD). {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf I.1.2}: Computing Methodologies, ALGEBRAIC MANIPULATION, Algorithms, Analysis of algorithms.", } @Article{Hall:1985:ESR, author = "George Hall", title = "Equilibrium States of {Runge Kutta} Schemes", journal = j-TOMS, volume = "11", number = "3", pages = "289--301", month = sep, year = "1985", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65L05", MRnumber = "87c:65082", bibdate = "Sun Sep 04 20:57:44 1994", URL = "http://doi.acm.org/10.1145/214408.214424", abstract = "Understanding the behavior of Runge-Kutta codes when stability considerations restrict the stepsize provides useful information for stiffness detection and other implementation details. Analysis of equilibrium states on test problems is presented which provides predictions and insights into this behavior. The implications for global error are also discussed.", acknowledgement = ack-nhfb, keywords = "algorithms", reviewer = "Henning Esser", subject = "{\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Initial value problems. {\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Single step methods. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Ericksen:1985:IPT, author = "Wilhelm S. Ericksen", title = "Inverse Pairs of Test Matrices", journal = j-TOMS, volume = "11", number = "3", pages = "302--304", month = sep, year = "1985", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "15A09 (65F35)", MRnumber = "87f:15002", bibdate = "Sun Sep 04 20:57:44 1994", URL = "http://doi.acm.org/10.1145/214408.214425", abstract = "Algorithms that are readily programmable are provided for constructing inverse pairs of matrices with elements in a field, a division ring, or a ring.", acknowledgement = ack-nhfb, keywords = "algorithms", reviewer = "R. Kala", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Condition (and ill-condition). {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Conditioning. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Matrix inversion.", } @Article{Hamilton:1985:RRK, author = "Dennis E. Hamilton", title = "Remark on ``{Algorithm} 620: References and Keywords for {\em {Collected Algorithms} of the {ACM}}''", journal = j-TOMS, volume = "11", number = "3", pages = "305--307", month = sep, year = "1985", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 20:57:44 1994", note = "See \cite{Rice:1984:ARK,Hopkins:1990:RRK}.", URL = "http://doi.acm.org/10.1145/214408.214426", acknowledgement = ack-nhfb, keywords = "algorithms; theory", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Boisvert:1985:GFM, author = "Ronald F. Boisvert and Sally E. Howe and David K. Kahaner", title = "{GAMS}: {A} Framework for the Management of Scientific Software", journal = j-TOMS, volume = "11", number = "4", pages = "313--355", month = dec, year = "1985", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 21:06:30 1994", URL = "http://doi.acm.org/10.1145/6187.6188", acknowledgement = ack-nhfb, keywords = "documentation; human factors; management", review = "ACM CR 8702-0100", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, GAMS. {\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Statistical software. {\bf H.3.5}: Information Systems, INFORMATION STORAGE AND RETRIEVAL, Online Information Services. {\bf D.2.7}: Software, SOFTWARE ENGINEERING, Distribution and Maintenance, Documentation.", } @Article{Davenport:1985:PRA, author = "J. H. Davenport and B. M. Trager", title = "On the Parallel {Risch} Algorithm ({II})", journal = j-TOMS, volume = "11", number = "4", pages = "356--362", month = dec, year = "1985", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "12H05 (68Q40)", MRnumber = "87d:12010", bibdate = "Sun Sep 04 21:06:32 1994", URL = "http://doi.acm.org/10.1145/6187.6189", acknowledgement = ack-nhfb, keywords = "algorithms; theory; verification", reviewer = "Michael F. Singer", subject = "{\bf I.1.2}: Computing Methodologies, ALGEBRAIC MANIPULATION, Algorithms.", } @Article{Coleman:1985:SES, author = "Thomas F. Coleman and Burton S. Garbow and Jorge J. Mor{\'e}", title = "Software for Estimating Sparse {Hessian} Matrices", journal = j-TOMS, volume = "11", number = "4", pages = "363--377", month = dec, year = "1985", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65F50 (65K10)", MRnumber = "828 562", bibdate = "Sat Aug 13 17:26:53 MDT 1994", URL = "http://doi.acm.org/10.1145/6187.6190", acknowledgement = ack-nhfb, keywords = "algorithms", review = "ACM CR 8710-0876", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse and very large systems. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Nonlinear programming. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Coleman:1985:AFS, author = "Thomas F. Coleman and Burton S. Garbow and Jorge J. Mor{\'e}", title = "{Algorithm 636}: {FORTRAN} subroutines for estimating sparse {Hessian} matrices", journal = j-TOMS, volume = "11", number = "4", pages = "378--378", month = dec, year = "1985", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "378. 65F50 (65-04)", MRnumber = "828 563", bibdate = "Sat Aug 27 14:55:36 1994", note = "The title of this paper incorrectly said Algorithm 649; it should be {Algorithm 636}.", URL = "http://doi.acm.org/10.1145/6187.6193", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf E.1}: Data, DATA STRUCTURES, Graphs. {\bf E.2}: Data, DATA STORAGE REPRESENTATIONS, Linked representations. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra. {\bf G.m}: Mathematics of Computing, MISCELLANEOUS. {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN.", } @Article{Houstis:1985:CSS, author = "E. N. Houstis and W. F. Mitchell and J. R. Rice", title = "Collocation Software for Second-Order Elliptic Partial Differential Equations", journal = j-TOMS, volume = "11", number = "4", pages = "379--412", month = dec, year = "1985", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65N35 (65-04)", MRnumber = "87e:65081a", bibdate = "Sun Sep 04 21:07:32 1994", URL = "http://doi.acm.org/10.1145/6187.6191", acknowledgement = ack-nhfb, keywords = "algorithms; design; measurement; performance", review = "ACM CR 8702-0097", reviewer = "John Stephenson", subject = "{\bf G.1.8}: Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Elliptic equations. {\bf G.1.8}: Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Finite element methods.", } @Article{Houstis:1985:AGC, author = "E. N. Houstis and W. F. Mitchell and J. R. Rice", title = "{Algorithm 637}: {GENCOL}: Collocation of General Domains with Bicubic {Hermite} Polynomials", journal = j-TOMS, volume = "11", number = "4", pages = "413--415", month = dec, year = "1985", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65N35 (65-04)", MRnumber = "87e:65081b", bibdate = "Sat Aug 27 14:56:32 1994", URL = "http://doi.acm.org/10.1145/6187.6194", acknowledgement = ack-nhfb, reviewer = "John Stephenson", subject = "G.1.8 Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Elliptic equations \\ G.1.8 Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Finite element methods \\ G.m Mathematics of Computing, MISCELLANEOUS \\ D.3.2 Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN", } @Article{Houstis:1985:AIH, author = "E. N. Houstis and W. F. Mitchell and J. R. Rice", title = "{Algorithm 638}: {INTCOL} and {HERMCOL}: Collocation on Rectangular Domains with Bicubic {Hermite} Polynomials", journal = j-TOMS, volume = "11", number = "4", pages = "416--418", month = dec, year = "1985", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65N35 (65-04)", MRnumber = "87e:65081c", bibdate = "Sun Sep 04 21:08:06 1994", URL = "http://doi.acm.org/10.1145/6187.6195", acknowledgement = ack-nhfb, keywords = "algorithms", reviewer = "John Stephenson", subject = "{\bf G.1.8}: Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Elliptic equations. {\bf G.1.8}: Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Finite element methods. {\bf G.m}: Mathematics of Computing, MISCELLANEOUS. {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN.", } @Article{Schnabel:1985:MSA, author = "Robert B. Schnabel and John E. Koontz and Barry E. Weiss", title = "A Modular System of Algorithms for Unconstrained Minimization", journal = j-TOMS, volume = "11", number = "4", pages = "419--440", month = dec, year = "1985", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65K10 (65-04 90-04 90C30)", MRnumber = "828 567", bibdate = "Sat Aug 13 17:26:53 MDT 1994", URL = "http://doi.acm.org/10.1145/6187.6192", acknowledgement = ack-nhfb, keywords = "algorithms", review = "ACM CR 8702-0093", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Unconstrained optimization. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, UNCMIN.", } @Article{Er:1985:RG, author = "M. C. Er", title = "Remark on ``{Algorithm} 246: {Graycode} [{Z}]''", journal = j-TOMS, volume = "11", number = "4", pages = "441--443", month = dec, year = "1985", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Sep 05 20:42:44 1994", note = "See \cite{Boothroyd:1964:G,Misra:1975:RG}.", URL = "http://doi.acm.org/10.1145/6187.356154", acknowledgement = ack-nhfb, } @Article{Shampine:1986:FVV, author = "L. F. Shampine and L. S. Baca", title = "Fixed versus Variable Order {Runge-Kutta}", journal = j-TOMS, volume = "12", number = "1", pages = "1--23", month = mar, year = "1986", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 21:09:54 1994", URL = "http://doi.acm.org/10.1145/5960.5964", acknowledgement = ack-nhfb, keywords = "algorithms; measurement; performance", review = "ACM CR 8702-0096", subject = "{\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Initial value problems. {\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Single step methods. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Lyness:1986:AIS, author = "James Lyness and Gwendolen Hines", title = "{Algorithm 639}: To Integrate Some Infinite Oscillating Tails", journal = j-TOMS, volume = "12", number = "1", pages = "24--25", month = mar, year = "1986", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D30 (65D32)", MRnumber = "868 093", URL = "http://doi.acm.org/10.1145/5960.214318", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.1.4}: Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation.", } @Article{Laub:1986:AEC, author = "Alan J. Laub", title = "{Algorithm 640}: Efficient Calculation of Frequency Response Matrices from State Space Models", journal = j-TOMS, volume = "12", number = "1", pages = "26--33", month = mar, year = "1986", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/5960.214319", keywords = "algorithms", subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Matrix inversion. {\bf J.2}: Computer Applications, PHYSICAL SCIENCES AND ENGINEERING, Engineering.", } @Article{Deak:1986:EMG, author = "I. Deak", title = "The Economical Method for Generating Random Samples from Discrete Distributions", journal = j-TOMS, volume = "12", number = "1", pages = "34--36", month = mar, year = "1986", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 21:11:10 1994", URL = "http://doi.acm.org/10.1145/5960.214321", abstract = "The idea of the economical method is applied for generating samples from any discrete distribution. In the resulting procedure, the expected number of uniformly distributed random numbers is less than in the alias method (practically 1). A refinement gives a version where in limit just one uniformly distributed number is required at the expense of some storage space.", acknowledgement = ack-nhfb, country = "USA", date = "13/05/93", descriptors = "RVG;", enum = "7183", keywords = "algorithms", language = "English", location = "SEL: Wi", references = "0", revision = "16/01/94", subject = "{\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS. {\bf I.6.1}: Computing Methodologies, SIMULATION AND MODELING, Simulation Theory.", } @Article{Law:1986:NAM, author = "Kincho H. Law and Steven J. Fenives", title = "A Node-Addition Model for Symbolic Factorization", journal = j-TOMS, volume = "12", number = "1", pages = "37--50", month = mar, year = "1986", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65F30", MRnumber = "87m:65068", bibdate = "Sun Sep 04 21:11:23 1994", URL = "http://doi.acm.org/10.1145/5960.5963", acknowledgement = ack-nhfb, keywords = "algorithms; measurement; performance; theory; verification", review = "ACM CR 8704-0290", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf G.2.2}: Mathematics of Computing, DISCRETE MATHEMATICS, Graph Theory, Graph algorithms. {\bf E.1}: Data, DATA STRUCTURES.", } @Article{Springer:1986:ESG, author = "J{\"o}rn Springer", title = "Exact Solution of General Integer Systems of Linear Equations", journal = j-TOMS, volume = "12", number = "1", pages = "51--61", month = mar, year = "1986", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65F20", MRnumber = "868 095", bibdate = "Sat Aug 13 17:26:53 MDT 1994", URL = "http://doi.acm.org/10.1145/5960.5961", acknowledgement = ack-nhfb, keywords = "algorithms; theory", review = "ACM CR 8703-0190", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Least squares approximation. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations in finite fields.", } @Article{Jansen:1986:HAA, author = "Paul Jansen and Peter Weidner", title = "High-Accuracy Arithmetic Software\emdash Some Tests of the {ACRITH} Problem-Solving Routines", journal = j-TOMS, volume = "12", number = "1", pages = "62--70", month = mar, year = "1986", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65Dxx", MRnumber = "868 096", bibdate = "Sat Aug 13 17:26:53 MDT 1994", URL = "http://doi.acm.org/10.1145/5960.5962", acknowledgement = ack-nhfb, keywords = "algorithms", review = "ACM CR 8612-1110", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, ACRITH. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf I.1.3}: Computing Methodologies, ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE. {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Reliability and robustness.", } @Article{Hanson:1986:RCA, author = "Richard J. Hanson", title = "Remark on ``{Algorithm} 584: {CUBTRI}: Automatic Cubature over a Triangle''", journal = j-TOMS, volume = "12", number = "1", pages = "71--71", month = mar, year = "1986", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 20:57:44 1994", note = "See \cite{Laurie:1982:ACA}.", URL = "http://doi.acm.org/10.1145/5960.356162", acknowledgement = ack-nhfb, } @Article{Norton:1986:RFB, author = "Victor Norton", title = "Remark on ``{Algorithm} 631: Finding a Bracketed Zero by {Larkin}'s Method of Rational Interpolation''", journal = j-TOMS, volume = "12", number = "1", pages = "72--72", month = mar, year = "1986", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "72. 65H05 (65D05)", MRnumber = "868 097", bibdate = "Mon Sep 05 20:41:38 1994", note = "See \cite{Norton:1985:AFB}.", URL = "http://doi.acm.org/10.1145/5960.356163", acknowledgement = ack-nhfb, } @Article{Hull:1986:VPE, author = "T. E. Hull and A. Abrham", title = "Variable Precision Exponential Function", journal = j-TOMS, volume = "12", number = "2", pages = "79--91", month = jun, year = "1986", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D15 (65D20)", MRnumber = "863 786", bibdate = "Sun Sep 04 21:17:51 1994", URL = "http://doi.acm.org/10.1145/6497.6498", acknowledgement = ack-nhfb, keywords = "algorithms; theory; verification", review = "ACM CR 8702-0091", subject = "{\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Verification.", } @Article{Dolk:1986:GMM, author = "Daniel R. Dolk", title = "A Generalized Model Management System for Mathematical Programming", journal = j-TOMS, volume = "12", number = "2", pages = "92--126", month = jun, year = "1986", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 21:18:01 1994", URL = "http://doi.acm.org/10.1145/6497.6501", acknowledgement = ack-nhfb, keywords = "human factors; languages; management", review = "ACM CR 8705-0407", subject = "{\bf H.4.2}: Information Systems, INFORMATION SYSTEMS APPLICATIONS, Types of Systems, Decision support. {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, Applicative languages. {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, Nonprocedural languages. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Linear programming. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Nonlinear programming. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Integer programming. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, XMP. {\bf H.2.3}: Information Systems, DATABASE MANAGEMENT, Languages, Query languages. {\bf H.2.4}: Information Systems, DATABASE MANAGEMENT, Systems, Query processing. {\bf D.2.2}: Software, SOFTWARE ENGINEERING, Tools and Techniques, User interfaces. {\bf I.2.1}: Computing Methodologies, ARTIFICIAL INTELLIGENCE, Applications and Expert Systems, GXMP. {\bf I.2.4}: Computing Methodologies, ARTIFICIAL INTELLIGENCE, Knowledge Representation Formalisms and Methods.", } @Article{Liu:1986:CRS, author = "Joseph W. H. Liu", title = "A Compact Row Storage Scheme for {Cholesky} Factors Using Elimination Trees", journal = j-TOMS, volume = "12", number = "2", pages = "127--148", month = jun, year = "1986", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65F05 (65F50)", MRnumber = "863 787", bibdate = "Sun Sep 04 21:18:32 1994", URL = "http://doi.acm.org/10.1145/6497.6499", acknowledgement = ack-nhfb, keywords = "algorithms; experimentation; measurement; performance; theory; verification", review = "ACM CR 8703-0191", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse and very large systems. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.2.2}: Mathematics of Computing, DISCRETE MATHEMATICS, Graph Theory.", } @Article{Springer:1986:AES, author = "J{\"o}rn Springer", title = "{Algorithm 641}: Exact Solution of General Systems of Linear Equations", journal = j-TOMS, volume = "12", number = "2", pages = "149--149", month = jun, year = "1986", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 4 21:19:01 1994", URL = "http://doi.acm.org/10.1145/6497.356167", acknowledgement = ack-nhfb, } @Article{Hutchinson:1986:AFP, author = "M. F. Hutchinson", title = "{Algorithm 642}: {A} Fast Procedure for Calculating Minimum Cross-Validation Cubic Smoothing Splines", journal = j-TOMS, volume = "12", number = "2", pages = "150--153", month = jun, year = "1986", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D10 (65D07)", MRnumber = "863 788", URL = "http://doi.acm.org/10.1145/6497.214322", abstract = "The procedure CUBGCV is an implementation of a recently developed algorithm for fast $O(n)$ calculation of a cubic smoothing spline fitted to $n$ noisy data points, with the degree of smoothing chosen to minimize the expected mean square error at the data points when the variance of the error associated with the data is known, or, to minimize the generalized cross validation (GCV) when the variance of the error associated with the data is unknown. The data may be unequally spaced and nonuniformly weighted. The algorithm exploits the banded structure of the matrices associated with the cubic smoothing spline problem. Bayesian point error estimates are also calculated in $O(n)$ operations.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation, Smoothing. {\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation, Spline and piecewise polynomial interpolation. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Spline and piecewise polynomial approximation. {\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Statistical software.", } @Article{Mehta:1986:AFF, author = "Cyrus R. Mehta and Nitin R. Patel", title = "{Algorithm 643}: {FEXACT}: {A FORTRAN} Subroutine for {Fisher}'s Exact Test on Unordered $r\times c$ Contingency Tables", journal = j-TOMS, volume = "12", number = "2", pages = "154--161", month = jun, year = "1986", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65U05", MRnumber = "863 789", bibdate = "Tue Mar 9 10:27:54 1999", note = "See remark \cite{Clarkson:1993:RAF}.", URL = "http://doi.acm.org/10.1145/6497.214326", abstract = "The computer code for Mehta and Patel's (1983) network algorithm for Fisher's exact test on unordered $r\times c$ contingency tables is provided. The code is written in double precision FORTRAN 77. This code provides the fastest currently available method for executing Fisher's exact test, and is shown to be orders of magnitude superior to any other available algorithm. Many important details of data structures and implementation that have contributed crucially to the success of the network algorithm are recorded here.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Nonlinear programming. {\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Statistical computing. {\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Statistical software.", } @Article{McKeown:1986:IIU, author = "G. P. McKeown", title = "Iterated Interpolation Using a Systolic Array", journal = j-TOMS, volume = "12", number = "2", pages = "162--170", month = jun, year = "1986", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 13 17:26:53 MDT 1994", URL = "http://doi.acm.org/10.1145/6497.6500", acknowledgement = ack-nhfb, keywords = "algorithms; design", review = "ACM CR 8703-0161", subject = "{\bf B.6.1}: Hardware, LOGIC DESIGN, Design Styles, Cellular arrays and automata. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Parallel algorithms. {\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation.", } @Article{Krogh:1986:AAP, author = "Fred T. Krogh", title = "{ACM} Algorithms Policy", journal = j-TOMS, volume = "12", number = "2", pages = "171--174", month = jun, year = "1986", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 21:20:12 1994", URL = "http://doi.acm.org/10.1145/6497.356171", acknowledgement = ack-nhfb, } @Article{Hall:1986:ESR, author = "George Hall", title = "Equilibrium States of {Runge-Kutta} Schemes: Part {II}", journal = j-TOMS, volume = "12", number = "3", pages = "183--192", month = sep, year = "1986", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65L05", MRnumber = "88e:65087", bibdate = "Sun Sep 04 21:21:39 1994", URL = "http://doi.acm.org/10.1145/7921.7922", acknowledgement = ack-nhfb, keywords = "algorithms", reviewer = "Henning Esser", subject = "{\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Initial value problems. {\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Single step methods. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Enright:1986:IRK, author = "W. H. Enright and K. R. Jackson and S. P. N{\o}rsett and P. G. Thomsen", title = "Interpolants for {Runge-Kutta} Formulas", journal = j-TOMS, volume = "12", number = "3", pages = "193--218", month = sep, year = "1986", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D07 (65L05)", MRnumber = "889 066", bibdate = "Sun Sep 04 21:21:52 1994", URL = "http://doi.acm.org/10.1145/7921.7923", acknowledgement = ack-nhfb, keywords = "algorithms; theory", review = "ACM CR 8707-0591", subject = "{\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Single step methods. {\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Error analysis. {\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Initial value problems. {\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation, Interpolation formulas.", } @Article{Kallay:1986:PCM, author = "Michael Kallay", title = "Plane Curves of Minimal Energy", journal = j-TOMS, volume = "12", number = "3", pages = "219--222", month = sep, year = "1986", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "53A04 (58E10 73K05)", MRnumber = "89c:53002", bibdate = "Sun Sep 04 21:22:21 1994", URL = "http://doi.acm.org/10.1145/7921.7924", acknowledgement = ack-nhfb, keywords = "algorithms; theory", review = "ACM CR 8706-0499", subject = "{\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation, Spline and piecewise polynomial interpolation. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Spline and piecewise polynomial approximation. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Constrained optimization. {\bf I.3.5}: Computing Methodologies, COMPUTER GRAPHICS, Computational Geometry and Object Modeling, Curve, surface, solid, and object representations.", } @Article{Skeel:1986:NBL, author = "Robert D. Skeel and Thu V. Vu", title = "Note on Blended Linear Multistep Formulas", journal = j-TOMS, volume = "12", number = "3", pages = "223--224", month = sep, year = "1986", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 13 17:26:53 MDT 1994", URL = "http://doi.acm.org/10.1145/7921.7925", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Initial value problems. {\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Stiff equations. {\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Single step methods.", } @Article{Sagie:1986:CAM, author = "Ike Sagie", title = "Computer-Aided Modeling and Planning ({CAMP})", journal = j-TOMS, volume = "12", number = "3", pages = "225--248", month = sep, year = "1986", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 13 17:26:53 MDT 1994", URL = "http://doi.acm.org/10.1145/7921.15667", acknowledgement = ack-nhfb, keywords = "economics; languages; management", review = "ACM CR 8710-0893", subject = "{\bf J.6}: Computer Applications, COMPUTER-AIDED ENGINEERING, Computer-aided design (CAD). {\bf H.2.3}: Information Systems, DATABASE MANAGEMENT, Languages. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Linear programming. {\bf H.1.2}: Information Systems, MODELS AND PRINCIPLES, User/Machine Systems, Human factors. {\bf I.6.2}: Computing Methodologies, SIMULATION AND MODELING, Simulation Languages. {\bf I.2.7}: Computing Methodologies, ARTIFICIAL INTELLIGENCE, Natural Language Processing.", } @Article{Liu:1986:SRC, author = "Joseph W. H. Liu", title = "On the Storage Requirement in the Out-of-Core Multifrontal Method for Sparse Factorization", journal = j-TOMS, volume = "12", number = "3", pages = "249--264", month = sep, year = "1986", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65F50", MRnumber = "889 068", bibdate = "Sun Sep 04 21:23:42 1994", URL = "http://doi.acm.org/10.1145/7921.11325", acknowledgement = ack-nhfb, keywords = "algorithms; performance", review = "ACM CR 8709-0776", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse and very large systems. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Amos:1986:APP, author = "D. E. Amos", title = "{Algorithm 644}: {A} Portable Package for {Bessel} Functions of a Complex Argument and Nonnegative Order", journal = j-TOMS, volume = "12", number = "3", pages = "265--273", month = sep, year = "1986", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D20", MRnumber = "889 069", bibdate = "Tue Mar 09 10:26:27 1999", note = "See also \cite{Amos:1990:RPP,Amos:1995:RAP}.", URL = "http://doi.acm.org/10.1145/7921.214331", abstract = "This algorithm is a package of subroutines for Computing Bessel functions $H_{v}^{(1)}(z)$, $H_{v}^{(2)}(z)$, $I_{v}(z)$, $J_{v}(z)$, $K_{v}(z)$, $Y_{v}(z)$ and Airy functions $\mbox{Ai}(z)$, $\mbox{Ai}'(z)$, $\mbox{Bi}(z)$, $\mbox{Bi}'(z)$ for orders $v>=0$ and complex $z$ in $-\pi< \mbox{arg} z <= \pi$. Eight callable subroutines and their double-precision counterparts are provided. Exponential scaling and sequence generation are auxiliary options.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf G.1.m}: Mathematics of Computing, NUMERICAL ANALYSIS, Miscellaneous. {\bf G.m}: Mathematics of Computing, MISCELLANEOUS.", } @Article{Nash:1986:AST, author = "J. C. Nash and R. L. C. Wang", title = "{Algorithm 645}: Subroutines for Testing Programs that Compute the Generalized Inverse of a Matrix", journal = j-TOMS, volume = "12", number = "3", pages = "274--277", month = sep, year = "1986", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65F20", MRnumber = "889 070", URL = "http://doi.acm.org/10.1145/7921.214334", acknowledgement = ack-nhfb, keywords = "algorithms; performance", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods).", } @Article{Crawford:1986:APR, author = "Charles R. Crawford", title = "{Algorithm 646}: {PDFIND}: {A} Routine to Find a Positive Definite Linear Combination of Two Real Symmetric Matrices", journal = j-TOMS, volume = "12", number = "3", pages = "278--282", month = sep, year = "1986", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65F30", MRnumber = "889 071", bibdate = "Sun Sep 04 21:24:35 1994", URL = "http://doi.acm.org/10.1145/7921.214335", abstract = "PDFIND is a FORTRAN-77 implementation of an algorithm that finds a positive definite linear combination of two symmetric matrices, or determines that such a combination does not exist. The algorithm is designed to be independent of the data structures used to store the matrices. The user must provide a subroutine, CHLSKY, which acts as an interface between PDFIND and the matrix data structures. CHLSKY also provides the user control over the number of iterations of the algorithm. Implementations of CHLSKY are included which call LINPAC routines for full matrices as well as symmetric banded matrices.", acknowledgement = ack-nhfb, keywords = "algorithms; geig; nla; symmetric matrix", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra.", } @Article{Hake:1986:RCC, author = "J.-Fr. Hake", title = "Remark on ``{Algorithm} 569: {COLSYS}: Collocation Software for Boundary-Value {ODEs} [{D2}]''", journal = j-TOMS, volume = "12", number = "3", pages = "283--284", month = sep, year = "1986", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Sep 30 01:16:18 1994", note = "See \cite{Ascher:1981:ACC}.", URL = "http://doi.acm.org/10.1145/7921.356181", acknowledgement = ack-nhfb, } @Article{Stewart:1986:CNC, author = "G. W. Stewart", title = "Corrigendum: ``{A} Note on Complex Division''", journal = j-TOMS, volume = "12", number = "3", pages = "285--285", month = sep, year = "1986", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Sep 30 01:17:25 1994", note = "See \cite{Stewart:1985:NCD}.", URL = "http://doi.acm.org/10.1145/7921.356182", acknowledgement = ack-nhfb, } @Article{Milovanovic:1986:CEI, author = "G. V. Milovanovi{\'c} and M. S. Petkovi{\'c}", title = "On Computational Efficiency of the Iterative Methods for the Simultaneous Approximation of Polynomial Zeros", journal = j-TOMS, volume = "12", number = "4", pages = "295--306", month = dec, year = "1986", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Sep 30 01:39:24 1994", URL = "http://doi.acm.org/10.1145/22721.8932", acknowledgement = ack-nhfb, keywords = "measurement; performance", review = "ACM CR 8707-0590", subject = "{\bf G.1.5}: Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Iterative methods.", } @Article{Nazareth:1986:IAO, author = "J. L. Nazareth", title = "Implementation Aids for Optimization Algorithms that Solve Sequences of Linear Programs", journal = j-TOMS, volume = "12", number = "4", pages = "307--323", month = dec, year = "1986", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 21:29:30 1994", URL = "http://doi.acm.org/10.1145/22721.22959", acknowledgement = ack-nhfb, keywords = "algorithms; experimentation; languages", review = "ACM CR 8708-0686", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Linear programming. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Constrained optimization. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Nonlinear programming. {\bf D.2.2}: Software, SOFTWARE ENGINEERING, Tools and Techniques, Modules and interfaces. {\bf D.2.2}: Software, SOFTWARE ENGINEERING, Tools and Techniques, Software libraries. {\bf D.3.3}: Software, PROGRAMMING LANGUAGES, Language Constructs and Features, Modules, packages.", } @Article{Cowell:1986:TFD, author = "Wayne R. Cowell and Christopher P. Thompson", title = "Transforming {Fortran DO} Loops to Improve Performance on Vector Architectures", journal = j-TOMS, volume = "12", number = "4", pages = "324--353", month = dec, year = "1986", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 21:30:12 1994", URL = "http://doi.acm.org/10.1145/22721.24035", acknowledgement = ack-nhfb, keywords = "algorithms; languages; performance", review = "ACM CR 8712-0989", subject = "{\bf D.2.2}: Software, SOFTWARE ENGINEERING, Tools and Techniques. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra. {\bf C.1.2}: Computer Systems Organization, PROCESSOR ARCHITECTURES, Multiple Data Stream Architectures (Multiprocessors), Array and vector processors.", } @Article{Ostermann:1986:SCP, author = "A. Ostermann and P. Kaps and T. D. Bui", title = "The Solution of a Combustion Problem with {Rosenbrock} Methods", journal = j-TOMS, volume = "12", number = "4", pages = "354--361", month = dec, year = "1986", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 21:30:24 1994", URL = "http://doi.acm.org/10.1145/22721.22722", acknowledgement = ack-nhfb, keywords = "performance", subject = "{\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Initial value problems. {\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Stiff equations. {\bf G.1.8}: Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Method of lines.", } @Article{Fox:1986:AIR, author = "Bennett L. Fox", title = "{Algorithm 647}: Implementation and Relative Efficiency of Quasirandom Sequence Generators", journal = j-TOMS, volume = "12", number = "4", pages = "362--376", month = dec, year = "1986", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Mar 28 10:43:26 2003", URL = "http://doi.acm.org/10.1145/22721.356187", } @Article{Didonato:1986:CIG, author = "Armido R. DiDonato and Alfred H. {Morris, Jr.}", title = "Computation of the Incomplete Gamma Function Ratios and Their Inverse", journal = j-TOMS, volume = "12", number = "4", pages = "377--393", month = dec, year = "1986", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 21:31:03 1994", URL = "http://doi.acm.org/10.1145/22721.23109", acknowledgement = ack-nhfb, keywords = "algorithms", review = "ACM CR 8709-0775", subject = "{\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation.", } @Article{Enright:1987:TFP, author = "W. H. Enright and J. D. Pryce", title = "Two {FORTRAN} Packages for Assessing Initial Value Methods", journal = j-TOMS, volume = "13", number = "1", pages = "1--27", month = mar, year = "1987", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Nov 19 13:08:36 1994", note = "See also \cite{Enright:1989:CFP}.", URL = "http://doi.acm.org/10.1145/23002.27645", acknowledgement = ack-nhfb, keywords = "algorithms; performance; reliability", review = "ACM CR 8803-0208", subject = "{\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Initial value problems. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing.", } @Article{Enright:1987:ANS, author = "W. H. Enright and J. D. Pryce", title = "{Algorithm 648}: {NSDTST} and {STDTST}: Routines for Assessing the Performance of {IV} Solvers", journal = j-TOMS, volume = "13", number = "1", pages = "28--34", month = mar, year = "1987", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 4 21:32:17 1994", URL = "http://doi.acm.org/10.1145/23002.214338", acknowledgement = ack-nhfb, keywords = "algorithms; performance; reliability", subject = "{\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Initial value problems. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing.", } @Article{Alagar:1987:FLS, author = "Vangalur S. Alagar and David K. Probst", title = "A Fast, Low-Space Algorithm for Multiplying Dense Multivariate Polynomials", journal = j-TOMS, volume = "13", number = "1", pages = "35--57", month = mar, year = "1987", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 21:32:38 1994", URL = "http://doi.acm.org/10.1145/23002.27646", acknowledgement = ack-nhfb, keywords = "algorithms; design", review = "ACM CR 8802-0114", subject = "{\bf I.1.2}: Computing Methodologies, ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. {\bf I.1.2}: Computing Methodologies, ALGEBRAIC MANIPULATION, Algorithms, Analysis of algorithms.", } @Article{Vitter:1987:EAS, author = "Jeffrey Scott Vitter", title = "An Efficient Algorithm for Sequential Random Sampling", journal = j-TOMS, volume = "13", number = "1", pages = "58--67", month = mar, year = "1987", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 21:32:58 1994", URL = "http://doi.acm.org/10.1145/23002.23003", acknowledgement = ack-nhfb, keywords = "algorithms; design; performance", review = "ACM CR 8808-0614", subject = "{\bf F.2.m}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Miscellaneous. {\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Statistical software.", } @Article{Foley:1987:IIP, author = "Thomas A. Foley", title = "Interpolation with Interval and Point Tension Controls Using Cubic Weighted $v$-Splines", journal = j-TOMS, volume = "13", number = "1", pages = "68--96", month = mar, year = "1987", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D07 (65D05 65D10)", MRnumber = "88h:65023", bibdate = "Sat Nov 19 13:08:26 1994", note = "See also \cite{Foley:1988:CIP}.", URL = "http://doi.acm.org/10.1145/23002.23004", acknowledgement = ack-nhfb, keywords = "algorithms; theory", review = "ACM CR 8802-0098", reviewer = "K. Jetter", subject = "{\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation, Spline and piecewise polynomial interpolation. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Constrained optimization. {\bf I.3.5}: Computing Methodologies, COMPUTER GRAPHICS, Computational Geometry and Object Modeling, Curve, surface, solid, and object representations.", } @Article{Giunta:1987:APC, author = "G. Giunta and A. Murli", title = "{Algorithm 649}: {A} Package for Computing Trigonometric {Fourier} Coefficients Based on {Lyness}'s Algorithm", journal = j-TOMS, volume = "13", number = "1", pages = "97--107", month = mar, year = "1987", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/23002.214339", abstract = "We present a package that allows the computation of the trigonometric Fourier coefficients of a smooth function. The function can be provided as a subprogram or as a data list of function values at equally spaced points.\par The computational cost of the algorithm does not depend on the required number of Fourier coefficients. Numerical results of comparative tests with a standard integrator for oscillatory functions are also reported.", keywords = "algorithms", subject = "{\bf G.1.4}: Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation.", } @Article{Dyksen:1987:IEI, author = "Wayne R. Dyksen and Calvin J. Ribbens", title = "Interactive {ELLPACK}: An Interactive Problem-Solving Environment for Elliptic Partial Differential Equations", journal = j-TOMS, volume = "13", number = "2", pages = "113--132", month = jun, year = "1987", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65N99 (65V05)", MRnumber = "88g:65127", bibdate = "Sun Sep 04 21:35:01 1994", URL = "http://doi.acm.org/10.1145/328512.328515", acknowledgement = ack-nhfb, reviewer = "W. C. Rheinboldt", } @Article{Pardalos:1987:GLS, author = "Panos M. Pardalos", title = "Generation of Large-Scale Quadratic Programs for Use as Global Optimization Test Problems", journal = j-TOMS, volume = "13", number = "2", pages = "133--137", month = jun, year = "1987", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "49D40 (90C30 93A15)", MRnumber = "88h:49057", bibdate = "Sun Sep 04 21:35:01 1994", URL = "http://doi.acm.org/10.1145/328512.328516", acknowledgement = ack-nhfb, reviewer = "G. Di Pillo", } @Article{Johnson:1987:AES, author = "Kenneth C. Johnson", title = "{Algorithm 650}: Efficient Square Root Implementation on the 68000", journal = j-TOMS, volume = "13", number = "2", pages = "138--151", month = jun, year = "1987", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D15", MRnumber = "898 489", bibdate = "Sun Sep 4 21:36:32 1994", note = "See also \cite{Johnson:1987:CES}.", URL = "http://doi.acm.org/10.1145/328512.328520", acknowledgement = ack-nhfb, } @Article{Morgan:1987:BBS, author = "Alexander Morgan and Vadim Shapiro", title = "Box-Bisection for Solving Second-Degree Systems and the Problem of Clustering", journal = j-TOMS, volume = "13", number = "2", pages = "152--167", month = jun, year = "1987", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65H10", MRnumber = "88e:65063", bibdate = "Sat Nov 19 13:08:20 1994", note = "See also \cite{Morgan:1987:CBS}.", URL = "http://doi.acm.org/10.1145/328512.328521", acknowledgement = ack-nhfb, } @Article{Monahan:1987:AGC, author = "John F. Monahan", title = "An Algorithm for Generating Chi Random Variables", journal = j-TOMS, volume = "13", number = "2", pages = "168--172", month = jun, year = "1987", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65C10", MRnumber = "88d:65013", bibdate = "Sat Nov 19 13:08:24 1994", note = "See also \cite{Johnson:1987:CES,Monahan:1988:CAG}.", URL = "http://doi.acm.org/10.1145/328512.328522", acknowledgement = ack-nhfb, } @Article{Liu:1987:PPS, author = "Joseph W. H. Liu", title = "A Partial Pivoting Strategy for Sparse Symmetric Matrix Decomposition", journal = j-TOMS, volume = "13", number = "2", pages = "173--182", month = jun, year = "1987", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65F05 (65F50)", MRnumber = "88f:65046", bibdate = "Sun Sep 04 21:35:01 1994", URL = "http://doi.acm.org/10.1145/328512.328525", acknowledgement = ack-nhfb, reviewer = "R. P. Tewarson", } @Article{Krogh:1987:AAP, author = "Fred T. Krogh", title = "{ACM} Algorithms Policy", journal = j-TOMS, volume = "13", number = "2", pages = "183--186", month = jun, year = "1987", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 21:35:01 1994", URL = "http://doi.acm.org/10.1145/328512.328526", acknowledgement = ack-nhfb, } @Article{Kearfott:1987:STG, author = "R. Baker Kearfott", title = "Some Tests of Generalized Bisection", journal = j-TOMS, volume = "13", number = "3", pages = "197--220", month = sep, year = "1987", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65H10", MRnumber = "88m:65081", bibdate = "Sat Nov 19 13:08:33 1994", note = "See also \cite{Kearfott:1988:CTG}.", URL = "http://doi.acm.org/10.1145/29380.29862", acknowledgement = ack-nhfb, keywords = "algorithms; performance; theory", subject = "{\bf G.1.5}: Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Systems of equations. {\bf G.1.5}: Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Polynomials, methods for.", } @Article{Boisvert:1987:FOA, author = "Ronald F. Boisvert", title = "A Fourth-Order-Accurate {Fourier} Method for the {Helmholtz} Equation in Three Dimensions", journal = j-TOMS, volume = "13", number = "3", pages = "221--234", month = sep, year = "1987", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65N05", MRnumber = "88m:65149", bibdate = "Sun Sep 04 21:39:43 1994", URL = "http://doi.acm.org/10.1145/29380.29863", acknowledgement = ack-nhfb, keywords = "algorithms; theory; verification", review = "ACM CR 8808-0622", reviewer = "Ian Gladwell", subject = "G.1.8 Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Elliptic equations \\ G.4 Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis", } @Article{Boisvert:1987:AAH, author = "Ronald F. Boisvert", title = "{Algorithm 651}: Algorithm {HFFT}\emdash High-Order Fast-Direct Solution of the {Helmholtz} Equation", journal = j-TOMS, volume = "13", number = "3", pages = "235--249", month = sep, year = "1987", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65V05", MRnumber = "918 578", bibdate = "Sun Sep 4 21:40:33 1994", note = "See also \cite{Johnson:1987:CES}.", URL = "http://doi.acm.org/10.1145/29380.214342", abstract = "HFFT is a software package for solving the Helmholtz equation on bounded two- and three-dimensional rectangular domains with Dirichlet, Neumann, or periodic boundary conditions. The software is the result of combining new fourth-order accurate compact finite difference (HODIE) discretizations and a fast-direct solution technique (the Fourier method). In this paper we briefly describe the user interface to HFFT and present an example of its usage and several details of its implementation.", acknowledgement = ack-nhfb, keywords = "algorithms; theory; verification", subject = "{\bf G.1.8}: Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Elliptic equations. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Liu:1987:TPM, author = "Joseph W. H. Liu", title = "On Threshold Pivoting in the Multifrontal Method for Sparse Indefinite Systems", journal = j-TOMS, volume = "13", number = "3", pages = "250--261", month = sep, year = "1987", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65F50 (65F05)", MRnumber = "88j:65089", bibdate = "Sun Sep 04 21:40:49 1994", URL = "http://doi.acm.org/10.1145/29380.31331", acknowledgement = ack-nhfb, keywords = "algorithms; measurement; performance; theory", review = "ACM CR 8804-0281", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse and very large systems. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Corana:1987:MMF, author = "A. Corana and M. Marchesi and C. Martini and S. Ridella", title = "Minimizing Multimodal Functions of Continuous Variables with the {``Simulated Annealing''} Algorithm", journal = j-TOMS, volume = "13", number = "3", pages = "262--280", month = sep, year = "1987", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "90C30 (65K05)", MRnumber = "88m:90121", bibdate = "Sat Nov 19 13:08:34 1994", note = "See also \cite{Corana:1989:CMF}.", URL = "http://doi.acm.org/10.1145/29380.29864", acknowledgement = ack-nhfb, keywords = "algorithms; performance", review = "ACM CR 8804-0282", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Nonlinear programming. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing. {\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Probabilistic algorithms (including Monte Carlo). {\bf F.2.2}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Sorting and searching.", } @Article{Watson:1987:AHS, author = "Layne T. Watson and Stephen C. Billups and Alexander P. Morgan", title = "{Algorithm 652}: {HOMPACK}: {A} Suite of Codes for Globally Convergent Homotopy Algorithms", journal = j-TOMS, volume = "13", number = "3", pages = "281--310", month = sep, year = "1987", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65V05 (58C30 65H10 90C30)", MRnumber = "918 581", bibdate = "Sun Sep 4 21:41:46 1994", URL = "http://doi.acm.org/10.1145/29380.214343", abstract = "There are algorithms for finding zeros or fixed points of nonlinear systems of equations that are globally convergent for almost all starting points, i.e., with probability one. The essence of all such algorithms is the construction of an appropriate homotopy map and then tracking some smooth curve in the zero set of this homotopy map. HOMPACK provides three qualitatively different algorithms for tracking the homotopy zero curve: ordinary differential equation-based, normal flow, and augmented Jacobian matrix. Separate routines are also provided for dense and sparse Jacobian matrices. A high-level driver is included for the special case of polynomial systems.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.1.5}: Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Systems of equations. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Hanson:1987:ATA, author = "R. J. Hanson and F. T. Krogh", title = "{Algorithm 653}: Translation of {Algorithm} 539: {PC-BLAS Basic Linear Algebra Subprograms} for {FORTRAN} Usage with the {INTEL} 8087, 80287 Numeric Data Processor", journal = j-TOMS, volume = "13", number = "3", pages = "311--317", month = sep, year = "1987", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Sep 05 23:07:52 1994", note = "See \cite{Lawson:1979:ABL,Dodson:1982:RBL,Dodson:1983:CRB,Louter-Nool:1988:ATA}.", URL = "http://doi.acm.org/10.1145/29380.214346", acknowledgement = ack-nhfb, } @Article{DiDonato:1987:AFS, author = "Armido R. {DiDonato} and Alfred H. {Morris Jr.}", title = "{Algorithm 654}: {FORTRAN} Subroutines for Computing the Incomplete Gamma Function Ratios and their Inverse", journal = j-TOMS, volume = "13", number = "3", pages = "318--319", month = sep, year = "1987", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 4 21:43:08 1994", URL = "http://doi.acm.org/10.1145/29380.214348", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation. {\bf G.m}: Mathematics of Computing, MISCELLANEOUS.", } @Article{Johnson:1987:CES, author = "Kenneth C. Johnson", title = "Corrigendum: {``Algorithm 650: efficient square root implementation on the 68000'' [{ACM} Trans. Math. Software {\bf 13} (1987), no. 2, 138--151]}", journal = j-TOMS, volume = "13", number = "3", pages = "320--320", month = sep, year = "1987", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "320. 65D15", MRnumber = "918 582", note = "See \cite{Johnson:1987:AES,Monahan:1987:AGC,Boisvert:1987:AAH}.", URL = "http://doi.acm.org/10.1145/29380.356210", acknowledgement = ack-nhfb, } @Article{Bar-On:1987:PPA, author = "Ilan Bar-On", title = "A Practical Parallel Algorithm for Solving Band Symmetric Positive Definite Systems of Linear Equations", journal = j-TOMS, volume = "13", number = "4", pages = "323--332", month = dec, year = "1987", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65F05 (65W05)", MRnumber = "88m:65048", bibdate = "Sun Sep 04 21:45:57 1994", URL = "http://doi.acm.org/10.1145/35078.35079", acknowledgement = ack-nhfb, keywords = "algorithms; performance; theory", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Parallel algorithms. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Matrix inversion.", } @Article{Schoenauer:1987:SCB, author = "Willi Sch{\"o}nauer and Eric Schnepf", title = "Software Considerations for the ``Black Box'' Solver {FIDISOL} for Partial Differential Equations", journal = j-TOMS, volume = "13", number = "4", pages = "333--349", month = dec, year = "1987", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Nov 19 13:08:16 1994", URL = "http://doi.acm.org/10.1145/35078.35080", acknowledgement = ack-nhfb, keywords = "algorithms; design", review = "ACM CR 8809-0699", subject = "{\bf G.1.8}: Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Difference methods. {\bf G.1.8}: Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Elliptic equations. {\bf G.1.8}: Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Parabolic equations. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, FIDOSOL.", } @Article{Ahlfeld:1987:NPG, author = "David P. Ahlfeld and John M. Mulvey and Ron S. Dembo and Stavros A. Zenios", title = "Nonlinear Programming on Generalized Networks", journal = j-TOMS, volume = "13", number = "4", pages = "350--367", month = dec, year = "1987", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "90C35 (90C30)", MRnumber = "89b:90218", bibdate = "Sun Sep 04 21:47:23 1994", URL = "http://doi.acm.org/10.1145/35078.42181", acknowledgement = ack-nhfb, keywords = "algorithms; theory", review = "ACM CR 8810-0796", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Constrained optimization. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Gradient methods. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Nonlinear programming. {\bf G.2.2}: Mathematics of Computing, DISCRETE MATHEMATICS, Graph Theory, Network problems.", } @Article{Haas:1987:MPR, author = "Alexander Haas", title = "The Multiple Prime Random Number Generator", journal = j-TOMS, volume = "13", number = "4", pages = "368--381", month = dec, year = "1987", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65C10", MRnumber = "89h:65018", bibdate = "Sun Sep 04 21:45:57 1994", URL = "http://doi.acm.org/10.1145/35078.214349", abstract = "A new pseudorandom number generator, the Multiple Prime Random Number Generator, has been developed; it is efficient, conceptually simple, flexible, and easy to program. The generator utilizes cycles around prime numbers to guarantee the length of the period, which can easily be programmed to surpass the maximum period of any other presently available random number generator. There are minimum limits placed on the seed values of the variables because the period of the generator is not a function of the initial values of the variables. The generator passes thirteen standard random number generator tests. It requires only about fifteen lines of FORTRAN code to program and utilizes programming language constructs found in most major languages. Finally, it compares very favorably to the fastest of the other available generators.", acknowledgement = ack-nhfb, keywords = "algorithms; economics; experimentation; performance; reliability", reviewer = "Brian Conolly", subject = "{\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Probabilistic algorithms (including Monte Carlo). {\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Random number generation. {\bf I.6.3}: Computing Methodologies, SIMULATION AND MODELING, Applications. {\bf I.6.4}: Computing Methodologies, SIMULATION AND MODELING, Model Validation and Analysis. {\bf J.2}: Computer Applications, PHYSICAL SCIENCES AND ENGINEERING, Mathematics and statistics. {\bf J.4}: Computer Applications, SOCIAL AND BEHAVIORAL SCIENCES, Economics. {\bf J.4}: Computer Applications, SOCIAL AND BEHAVIORAL SCIENCES, Sociology.", } @Article{Schneider:1987:EEA, author = "Michael H. Schneider", title = "The Expanding Equilibrium Algorithm", journal = j-TOMS, volume = "13", number = "4", pages = "382--398", month = dec, year = "1987", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 21:48:37 1994", URL = "http://doi.acm.org/10.1145/35078.42322", acknowledgement = ack-nhfb, keywords = "algorithms; economics; performance", review = "ACM CR 8812-0937", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Nonlinear programming. {\bf J.4}: Computer Applications, SOCIAL AND BEHAVIORAL SCIENCES, Economics.", } @Article{Elhay:1987:AIF, author = "Sylvan Elhay and Jaroslav Kautsky", title = "{Algorithm 655}: {IQPACK}: {FORTRAN} Subroutines for the Weights of Interpolatory Quadratures", journal = j-TOMS, volume = "13", number = "4", pages = "399--415", month = dec, year = "1987", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 4 21:49:00 1994", URL = "http://doi.acm.org/10.1145/35078.214351", abstract = "We present FORTRAN subroutines that implement the method described in [3] for the stable evaluation of the weights of interpolatory quadratures with prescribed simple or multiple knots. Given a set of knots and their multiplicities, the package generates the weights by using the zeroth moment $\mu_{0}$ of $w$, the weight function in the integrand, and the (symmetric tridiagonal) Jacobi matrix $J$ associated with the polynomials orthogonal on $(a, b)$ with respect to $w$. There are utility routines that generate $\mu_{0}$ and $J$ for classical weight functions, but quadratures can be generated for any $\mu_{0}$ and $J$ supplied by the user. Utility routines are also provided that (1) evaluate a computed quadrature, applied to a user-supplied integrand, (2) check the polynomial order of precision of a quadrature formula, and (3) compute the knots and weights of simple Gaussian quadrature formula.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf G.1.4}: Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation, Gaussian quadrature.", } @Article{Morgan:1987:CBS, author = "Alexander Morgan and Vadim Shapiro", title = "Corrigendum: ``{Box-Bisection} for Solving Second-Degree Systems and the Problem of Clustering''", journal = j-TOMS, volume = "13", number = "4", pages = "416--416", month = dec, year = "1987", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65H10", MRnumber = "89a:65088, 88e:65063", bibdate = "Sun Sep 04 21:45:57 1994", note = "See \cite{Morgan:1987:BBS}.", URL = "http://doi.acm.org/10.1145/35078.356217", acknowledgement = ack-nhfb, } @Article{Dongarra:1988:ESF, author = "Jack J. Dongarra and Jeremy Du Croz and Sven Hammarling and Richard J. Hanson", title = "An Extended Set of {FORTRAN Basic Linear Algebra Subprograms}", journal = j-TOMS, volume = "14", number = "1", pages = "1--17", month = mar, year = "1988", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Nov 19 13:08:30 1994", note = "See also \cite{Dongarra:1988:CES}.", URL = "http://doi.acm.org/10.1145/42288.42291", acknowledgement = ack-nhfb, keywords = "algorithms; standardization", review = "ACM CR 8812-0940", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Portability. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra.", } @Article{Dongarra:1988:AES, author = "Jack J. Dongarra and Jeremy Du Croz and Sven Hammarling and Richard J. Hanson", title = "{Algorithm 656}: An Extended Set of {Basic Linear Algebra Subprograms}: Model Implementation and Test Programs", journal = j-TOMS, volume = "14", number = "1", pages = "18--32", month = mar, year = "1988", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 21:52:44 1994", URL = "http://doi.acm.org/10.1145/42288.42292", acknowledgement = ack-nhfb, keywords = "algorithms; blas; nla; software; theory; vect", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Sewell:1988:PCS, author = "Granville Sewell", title = "Plotting Contour Surfaces of a Function of Three Variables", journal = j-TOMS, volume = "14", number = "1", pages = "33--41", month = mar, year = "1988", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65S05", MRnumber = "89c:65140", bibdate = "Sun Sep 04 21:53:18 1994", URL = "http://doi.acm.org/10.1145/42288.42289", acknowledgement = ack-nhfb, keywords = "algorithms; design", review = "ACM CR 8810-0795", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Sewell:1988:ASP, author = "Granville Sewell", title = "{Algorithm 657}: Software for Plotting Contour Surfaces of a Function of Three Variables", journal = j-TOMS, volume = "14", number = "1", pages = "42--44", month = mar, year = "1988", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 15:08:25 1994", note = "See also \cite{Sewell:1990:RSP}.", URL = "http://doi.acm.org/10.1145/42288.42290", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Leis:1988:SSS, author = "Jorge R. Leis and Mark A. Kramer", title = "The Simultaneous Solution and Sensitivity Analysis of Systems Described by Ordinary Differential Equations", journal = j-TOMS, volume = "14", number = "1", pages = "45--60", month = mar, year = "1988", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65L05 (65V05)", MRnumber = "89b:65176", bibdate = "Sun Sep 04 21:54:22 1994", URL = "http://doi.acm.org/10.1145/42288.46156", acknowledgement = ack-nhfb, keywords = "algorithms; experimentation; performance; reliability; theory", review = "ACM CR 8903-0152", subject = "{\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations. {\bf I.6.4}: Computing Methodologies, SIMULATION AND MODELING, Model Validation and Analysis. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency.", } @Article{Leis:1988:AOO, author = "Jorge R. Leis and Mark A. Kramer", title = "{Algorithm 658}: {ODESSA}: An Ordinary Differential Equation Solver with Explicit Simultaneous Sensitivity Analysis", journal = j-TOMS, volume = "14", number = "1", pages = "61--67", month = mar, year = "1988", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/42288.214371", abstract = "ODESSA is a package of FORTRAN routines for simultaneous solution of ordinary differential equations and the associated first-order parametric sensitivity equations, yielding the ODE solution vector $\underline{y}(t)$ and the first-order sensitivity coefficients with respect to equation parameters $\underline{p}$, $\partial \underline{y}(t)/\partial \underline{p}$. ODESSA is a modification of the widely disseminated initial-value solver LSODE, and retains many of the same operational features. Standard program usage and optional capabilities, installation, and verification considerations are addressed herein.", keywords = "algorithms; measurement; performance", subject = "{\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Initial value problems. {\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Error analysis. {\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Stiff equations. {\bf I.6.4}: Computing Methodologies, SIMULATION AND MODELING, Model Validation and Analysis. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency.", } @Article{Butcher:1988:TEI, author = "J. C. Butcher", title = "Towards Efficient Implementation of Singly-Implicit Methods", journal = j-TOMS, volume = "14", number = "1", pages = "68--75", month = mar, year = "1988", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65L05", MRnumber = "89b:65167", bibdate = "Sat Aug 13 17:26:53 MDT 1994", URL = "http://doi.acm.org/10.1145/42288.42341", acknowledgement = ack-nhfb, keywords = "algorithms; performance", review = "ACM CR 8812-0938", subject = "{\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Initial value problems. {\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Single step methods. {\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Stiff equations. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency.", } @Article{Ammann:1988:RCR, author = "Larry Ammann and John {Van Ness}", title = "A Routine for Converting Regression Algorithms into Corresponding Orthogonal Regression Algorithms", journal = j-TOMS, volume = "14", number = "1", pages = "76--87", month = mar, year = "1988", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65U05", MRnumber = "944 765", bibdate = "Sat Aug 13 17:26:53 MDT 1994", URL = "http://doi.acm.org/10.1145/42288.42342", acknowledgement = ack-nhfb, keywords = "algorithms; reliability", review = "ACM CR 8903-0155", subject = "{\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf J.2}: Computer Applications, PHYSICAL SCIENCES AND ENGINEERING.", } @Article{Bratley:1988:AIS, author = "Paul Bratley and Bennett L. Fox", title = "{Algorithm 659}: Implementing {Sobol}'s Quasirandom Sequence Generator", journal = j-TOMS, volume = "14", number = "1", pages = "88--100", month = mar, year = "1988", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/42288.214372", abstract = "We compare empirically accuracy and speed of low-discrepancy sequence generators of Sobol' and Faure. These generators are useful for multidimensional integration and global optimization. We discuss our implementation of the Sobol' generator.", keywords = "algorithms; measurement; performance", subject = "{\bf G.1.4}: Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency.", } @Article{Robertazzi:1988:BFP, author = "T. G. Robertazzi and S. C. Schwartz", title = "Best ``Ordering'' for Floating-Point Addition", journal = j-TOMS, volume = "14", number = "1", pages = "101--110", month = mar, year = "1988", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65G99 (65V05)", MRnumber = "89b:65117", bibdate = "Sat Nov 19 13:08:22 1994", URL = "http://doi.acm.org/10.1145/42288.42343", acknowledgement = ack-nhfb, keywords = "algorithms; performance", review = "ACM CR 8810-0794", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic.", } @Article{Monahan:1988:CAG, author = "John F. Monahan", title = "Corrigendum: ``{An} Algorithm for Generating Chi Random Variables''", journal = j-TOMS, volume = "14", number = "1", pages = "111--111", month = mar, year = "1988", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "111. 65C10", MRnumber = "89d:65006, 88d:65013", bibdate = "Fri Mar 28 10:45:16 2003", note = "See \cite{Monahan:1987:AGC}.", URL = "http://doi.acm.org/10.1145/42288.356228", acknowledgement = ack-nhfb, } @Article{Melhem:1988:MRS, author = "Rami G. Melhem and K. V. S. Ramarao", title = "Multicolor Reordering of Sparse Matrices Resulting from Irregular Grids", journal = j-TOMS, volume = "14", number = "2", pages = "117--138", month = jun, year = "1988", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65F50 (65D30)", MRnumber = "90b:65084", bibdate = "Mon Dec 08 12:15:02 1997", URL = "http://doi.acm.org/10.1145/45054.214373", abstract = "Many iterative algorithms for the solution of large linear systems may be effectively vectorized if the diagonal of the matrix is surrounded by a large band of zeroes, whose width is called the zero stretch. In this paper, a multicolor numbering technique is suggested for maximizing the zero stretch of irregularly sparse matrices. The technique, which is a generalization of a known multicoloring algorithm for regularly sparse matrices, executes in linear time, and produces a zero stretch approximately equal to $n/2\sigma$, where $2\sigma$ is the number of colors used in the algorithm. For triangular meshes, it is shown that $\sigma \leq 3$, and that it is possible to obtain $\sigma=2$ by applying a simple backtracking scheme.", acknowledgement = ack-nhfb, keywords = "algorithms; performance; theory", reviewer = "Stephen W. Brady", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse and very large systems. {\bf G.1.4}: Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation, Iterative methods. {\bf G.2.2}: Mathematics of Computing, DISCRETE MATHEMATICS, Graph Theory, Graph algorithms. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Renka:1988:MIL, author = "Robert J. Renka", title = "Multivariate Interpolation of Large Sets of Scattered Data", journal = j-TOMS, volume = "14", number = "2", pages = "139--148", month = jun, year = "1988", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D05 (41A05)", MRnumber = "89d:65009", bibdate = "Sun Sep 04 22:00:07 1994", URL = "http://doi.acm.org/10.1145/45054.45055", acknowledgement = ack-nhfb, keywords = "algorithms", review = "ACM CR 8903-0148", subject = "{\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Renka:1988:AQQa, author = "Robert J. Renka", title = "{Algorithm 660}: {QSHEP2D}: Quadratic {Shepard} Method for Bivariate Interpolation of Scattered Data", journal = j-TOMS, volume = "14", number = "2", pages = "149--150", month = jun, year = "1988", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Mar 28 10:45:50 2003", URL = "http://doi.acm.org/10.1145/45054.356231", acknowledgement = ack-nhfb, } @Article{Renka:1988:AQQb, author = "Robert J. Renka", title = "{Algorithm 661}: {QSHEP3D}; Quadratic {Shepard} Method for Trivariate Interpolation of Scattered Data", journal = j-TOMS, volume = "14", number = "2", pages = "151--152", month = jun, year = "1988", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/45054.214374", keywords = "algorithms", subject = "{\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Wan:1988:AMD, author = "S. J. Wan and S. K. M. Wong and P. Prusinkiewicz", title = "An Algorithm for Multidimensional Data Clustering", journal = j-TOMS, volume = "14", number = "2", pages = "153--162", month = jun, year = "1988", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 22:00:57 1994", URL = "http://doi.acm.org/10.1145/45054.45056", acknowledgement = ack-nhfb, keywords = "algorithms; performance", review = "ACM CR 8912-0911", subject = "{\bf I.5.3}: Computing Methodologies, PATTERN RECOGNITION, Clustering, Algorithms.", } @Article{Garbow:1988:SIW, author = "B. S. Garbow and G. Giunta and J. N. Lyness and A. Murli", title = "Software for an Implementation of {Weeks}' Method for the Inverse {Laplace} Transform", journal = j-TOMS, volume = "14", number = "2", pages = "163--170", month = jun, year = "1988", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65R10 (65V05)", MRnumber = "89d:65107", bibdate = "Sun Sep 04 22:01:52 1994", URL = "http://doi.acm.org/10.1145/45054.45057", acknowledgement = ack-nhfb, keywords = "algorithms", review = "ACM CR 8903-0153", subject = "{\bf G.1.9}: Mathematics of Computing, NUMERICAL ANALYSIS, Integral Equations, Fredholm equations. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Nonlinear approximation. {\bf G.1.4}: Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation, Finite difference methods.", } @Article{Garbow:1988:AFS, author = "B. S. Garbow and G. Giunta and J. N. Lyness and A. Murli", title = "{Algorithm 662}: {A FORTRAN} Software Package for the Numerical Inversion of the {Laplace} Transform Based on {Weeks}' Method", journal = j-TOMS, volume = "14", number = "2", pages = "171--176", month = jun, year = "1988", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 4 23:29:03 1994", note = "See also \cite{Garbow:1990:RFS}.", URL = "http://doi.acm.org/10.1145/45054.214375", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.m}: Mathematics of Computing, MISCELLANEOUS.", } @Article{Louter-Nool:1988:ATA, author = "Margreet Louter-Nool", title = "{Algorithm 663}: Translation of {Algorithm} 539: {Basic Linear Algebra Subprograms} for {FORTRAN} Usage in {FORTRAN} 200 for the {Cyber} 205", journal = j-TOMS, volume = "14", number = "2", pages = "177--195", month = jun, year = "1988", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Sep 05 23:08:05 1994", note = "See \cite{Lawson:1979:ABL,Dodson:1982:RBL,Dodson:1983:CRB,Hanson:1987:ATA}.", URL = "http://doi.acm.org/10.1145/45054.45058", acknowledgement = ack-nhfb, keywords = "algorithms; measurement; performance", review = "ACM CR 8904-0243", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency. {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN.", } @Article{Diaz:1988:RCA, author = "J. C. Diaz and G. Fairweather and P. Keast", title = "Remark on ``{Algorithm} 603: {COLROW} and {ARCECO}: {FORTRAN} Packages for Solving Certain Almost Block Diagonal Linear Systems by Modified Alternate Row and Column Elimination''", journal = j-TOMS, volume = "14", number = "2", pages = "196--196", month = jun, year = "1988", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 21:59:18 1994", note = "See \cite{Diaz:1983:ACA}.", URL = "http://doi.acm.org/10.1145/45054.356237", acknowledgement = ack-nhfb, } @Article{Hull:1988:EHS, author = "T. E. Hull and M. S. Cohen and J. T. M. Sawshuk and D. B. Wortman", title = "Exception Handling in Scientific Computing", journal = j-TOMS, volume = "14", number = "3", pages = "201--217", month = sep, year = "1988", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 22:27:23 1994", URL = "http://doi.acm.org/10.1145/44128.44129", acknowledgement = ack-nhfb, keywords = "design; languages", subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, Specialized application languages. {\bf D.3.3}: Software, PROGRAMMING LANGUAGES, Language Constructs and Features, Control structures. {\bf D.3.4}: Software, PROGRAMMING LANGUAGES, Processors, Compilers. {\bf D.3.4}: Software, PROGRAMMING LANGUAGES, Processors, Run-time environments. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Freeman:1988:DSM, author = "Timothy S. Freeman and Gregory M. Imirzian and Erich Kaltofen and Lakshman Yagati", title = "{Dagwood}: {A} System for Manipulating Polynomials Given by Straight-Line Programs", journal = j-TOMS, volume = "14", number = "3", pages = "218--240", month = sep, year = "1988", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 22:27:49 1994", URL = "http://doi.acm.org/10.1145/44128.214376", abstract = "We discuss the design, implementation, and benchmarking of a system that can manipulate symbolic expressions represented by their straight-line computations. Our system is capable of performing rational arithmetic on, evaluating, differentiating, taking greatest common divisors of, and factoring polynomials in straight-line format. The straight-line results can also be converted to standard, sparse format. We show by example that our system can handle problems for which conventional methods lead to excessive intermediate expression swell.", acknowledgement = ack-nhfb, keywords = "algorithms; design; measurement; performance", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency. {\bf I.1.1}: Computing Methodologies, ALGEBRAIC MANIPULATION, Expressions and Their Representation, Representations (general and polynomial). {\bf I.1.3}: Computing Methodologies, ALGEBRAIC MANIPULATION, Languages and Systems, Special-purpose algebraic systems.", } @Article{Grimes:1988:SLD, author = "Roger G. Grimes and Horst D. Simon", title = "Solution of Large, Dense Symmetric Generalized Eigenvalue Problems Using Secondary Storage", journal = j-TOMS, volume = "14", number = "3", pages = "241--256", month = sep, year = "1988", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65-04 (65F15)", MRnumber = "1 062 476", bibdate = "Sun Sep 04 22:29:30 1994", URL = "http://doi.acm.org/10.1145/44128.44130", acknowledgement = ack-nhfb, keywords = "algorithms; performance", review = "ACM CR 8903-0149", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Eigenvalues. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse and very large systems. {\bf D.4.2}: Software, OPERATING SYSTEMS, Storage Management, Secondary storage.", } @Article{Schrauf:1988:AGA, author = "G{\'e}za Schrauf", title = "{Algorithm 664}: {A Gauss} Algorithm to Solve Systems with Large Banded Matrices Using Random-Access Disk Storage", journal = j-TOMS, volume = "14", number = "3", pages = "257--260", month = sep, year = "1988", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/44128.214379", abstract = "A FORTRAN 77 implementation of a Gauss algorithm with partial pivoting for banded matrices is described. The algorithm keeps only part of the matrix that is necessary for the actual computation in memory. This allows large systems to be solved on machine without virtual memory, or if the virtual memory is too small for the problem.", keywords = "algorithms", subject = "{\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse and very large systems.", } @Article{Minh:1988:GGV, author = "Do Le Minh", title = "Generating Gamma Variates", journal = j-TOMS, volume = "14", number = "3", pages = "261--266", month = sep, year = "1988", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65-04 (65U05)", MRnumber = "1 062 477", bibdate = "Sun Sep 04 22:30:10 1994", URL = "http://doi.acm.org/10.1145/44128.214382", abstract = "An algorithm to generate variates having a gamma distribution with shape parameter greater than one is presented in this paper. This algorithm is faster than Schmeiser and Lal's G4PE, which is the fastest one currently available, yet is equally simple and easy to implement.", acknowledgement = ack-nhfb, country = "USA", date = "13/05/93", descriptors = "RVG;", enum = "7672", keywords = "algorithms; theory", language = "English", location = "SEL: Wi", references = "0", revision = "16/01/94", subject = "{\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS. {\bf I.6.1}: Computing Methodologies, SIMULATION AND MODELING, Simulation Theory.", } @Article{Duff:1988:RIN, author = "Iain S. Duff and Torbj{\"o}rn Wiberg", title = "Remarks on Implementation of ${O}(n^{1/2}\tau)$ Assignment Algorithms", journal = j-TOMS, volume = "14", number = "3", pages = "267--287", month = sep, year = "1988", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65-04 (65F50)", MRnumber = "1 062 478", bibdate = "Sat Aug 13 17:26:53 MDT 1994", URL = "http://doi.acm.org/10.1145/44128.44131", acknowledgement = ack-nhfb, keywords = "algorithms; theory", review = "ACM CR 8904-0244", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse and very large systems. {\bf G.2.2}: Mathematics of Computing, DISCRETE MATHEMATICS, Graph Theory, Graph algorithms. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Cormack:1988:RTP, author = "R. S. Cormack and I. D. Hill", title = "Remark on ``{Algorithm} 346: ${F}$-Test Probabilities''", journal = j-TOMS, volume = "14", number = "3", pages = "288--289", month = sep, year = "1988", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 22:27:49 1994", note = "See \cite{Morris:1969:TP}.", URL = "http://doi.acm.org/10.1145/44128.356244", acknowledgement = ack-nhfb, } @Article{Krogh:1988:AAP, author = "Fred T. Krogh", title = "{ACM} Algorithms Policy", journal = j-TOMS, volume = "14", number = "3", pages = "290--293", month = sep, year = "1988", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 22:27:49 1994", URL = "http://doi.acm.org/10.1145/44128.356245", acknowledgement = ack-nhfb, } @Article{Foley:1988:CIP, author = "Thomas A. Foley", title = "Corrigendum: ``{Interpolation} with Interval and Point Tension Controls Using Cubic Weighted $v$-Splines''", journal = j-TOMS, volume = "14", number = "3", pages = "297--297", month = sep, year = "1988", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Nov 19 13:26:45 1994", note = "See \cite{Foley:1987:IIP}.", URL = "http://doi.acm.org/10.1145/44128.356246", acknowledgement = ack-nhfb, } @Article{Cody:1988:AMS, author = "W. J. Cody", title = "{Algorithm 665}: {MACHAR}: {A} Subroutine to Dynamically Determine Machine Parameters", journal = j-TOMS, volume = "14", number = "4", pages = "303--311", month = dec, year = "1988", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 22:33:58 1994", URL = "http://doi.acm.org/10.1145/50063.51907", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Portability. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic.", } @Article{Vrahatis:1988:SSN, author = "Michael N. Vrahatis", title = "Solving Systems of Nonlinear Equations Using the Nonzero Value of the Topological Degree", journal = j-TOMS, volume = "14", number = "4", pages = "312--329", month = dec, year = "1988", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65-04 (65H10 90C30)", MRnumber = "91g:65006", bibdate = "Sun Sep 04 22:34:19 1994", URL = "http://doi.acm.org/10.1145/50063.214384", abstract = "Two algorithms are described here for the numerical solution of a system of nonlinear equations $F(X) = \Theta, Q=(0,0,\ldots,0)$ in $R$, and $F$ is a given continuous mapping of a region $D$ in $R^{n}$ into $R^{n}$. The first algorithm locates at least one root of the sy stem within $n$-dimensional polyhedron, using the nonzero value of the topological degree of $F$ at [theta] relative to the polyhedron; the second algorithm applies a new generalized bisection method in order to compute an approximate solution to the system. The size of the original $n$-dimensional polyhedron is arbitrary, and the method is globally convergent in a residual sense.\par These algorithms, in the various function evaluations, only make use of the algebraic sign of $F$ and do not require computations of the topological degree. Moreover, they can be applied to nondifferentiable continuous functions $F$ and do not involve derivatives of $F$ or approximations of such derivatives.", acknowledgement = ack-nhfb, keywords = "algorithms; theory", subject = "{\bf G.1.5}: Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Systems of equations. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Vrahatis:1988:ACM, author = "Michael N. Vrahatis", title = "{Algorithm 666}: {CHABIS}: {A} Mathematical Software Package for Locating and Evaluating Roots of Systems of Nonlinear Equations", journal = j-TOMS, volume = "14", number = "4", pages = "330--336", month = dec, year = "1988", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65-04 (90C30)", MRnumber = "91g:65007", bibdate = "Sat Aug 27 15:08:54 1994", URL = "http://doi.acm.org/10.1145/50063.51906", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Portability. {\bf G.1.5}: Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Systems of equations.", } @Article{Garavelli:1988:AMS, author = "John S. Garavelli", title = "An Algorithm for the Multiplication of Symmetric Polynomials", journal = j-TOMS, volume = "14", number = "4", pages = "337--344", month = dec, year = "1988", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "05-04 (68Q40)", MRnumber = "91f:05002", bibdate = "Sun Sep 04 22:34:19 1994", URL = "http://doi.acm.org/10.1145/50063.214385", abstract = "Although the cycle index polynomial for a permutation group can often be easily determined, expansion of the figure counting series in a P{\'o}lya enumeration presents computational difficulties for object sets with higher degrees of symmetry and more than modest size. An algorithm that does not require algebraic symbol manipulation is derived for multiplying symmetric polynomials represented by partitions. Because the repetitive identification and collection of common terms are eliminated and storage requirements reduced, this algorithm is useful in rapidly expanding the figure counting series in such P{\'o}lya enumeration problems as the counting of chemical isomers.", acknowledgement = ack-nhfb, keywords = "algorithms; theory", reviewer = "Kevin Lawrence McAvaney", subject = "{\bf G.2.1}: Mathematics of Computing, DISCRETE MATHEMATICS, Combinatorics, Combinatorial algorithms. {\bf I.1.1}: Computing Methodologies, ALGEBRAIC MANIPULATION, Expressions and Their Representation, Representations (general and polynomial). {\bf I.1.2}: Computing Methodologies, ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms.", } @Article{Aluffi-Pentini:1988:GOA, author = "Filippo Aluffi-Pentini and Valerio Parisi and Francesco Zirilli", title = "A Global Optimization Algorithm Using Stochastic Differential Equations", journal = j-TOMS, volume = "14", number = "4", pages = "345--365", month = dec, year = "1988", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65-04 (65K05 90C30)", MRnumber = "1 062 482", bibdate = "Sun Sep 04 22:36:23 1994", URL = "http://doi.acm.org/10.1145/50063.50064", acknowledgement = ack-nhfb, keywords = "algorithms; languages; theory; verification", review = "ACM CR 8907-0480", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing.", } @Article{Aluffi-Pentini:1988:ASE, author = "Filippo Aluffi-Pentini and Valerio Parisi and Francesco Zirilli", title = "{Algorithm 667}: {SIGMA}\emdash {A} Stochastic-Integration Global Minimization Algorithm", journal = j-TOMS, volume = "14", number = "4", pages = "366--380", month = dec, year = "1988", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65-04 (90C30)", MRnumber = "1 062 483", bibdate = "Sat Aug 13 17:26:53 MDT 1994", URL = "http://doi.acm.org/10.1145/50063.51908", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Portability. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization.", } @Article{Higham:1988:AFC, author = "Nicholas J. Higham", title = "{Algorithm 674}: {FORTRAN} Codes for Estimating the One-Norm of a Real or Complex Matrix, with Applications to Condition Estimation", journal = j-TOMS, volume = "14", number = "4", pages = "381--396", month = dec, year = "1988", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65-04 (65F35)", MRnumber = "1 062 484", bibdate = "Sat Aug 27 15:05:32 1994", note = "See also \cite{Higham:1989:CFC}.", URL = "http://doi.acm.org/10.1145/50063.214386", abstract = "FORTRAN 77 codes SONEST and CONEST are presented for estimating the 1-norm ( or the infinity-norm) of a real or complex matrix, respectively. The codes are of wide applicability in condition estimation since explicit access to the matrix, $A$, is not required; instead, matrix-vector products $Ax$ and $A^Tx$ are computed by the calling program via a reverse communication interface. The algorithms are based on a convex optimization method for estimating the 1-norm of a real matrix devised by Hager. We derive new results concerning the behavior of Hager's method, extend it to complex matrices, and make several algorithmic modifications in order to improve the reliability and efficiency.", acknowledgement = ack-nhfb, keywords = "algorithms; condition estimation; nla; software", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra.", } @Article{Kachitvichyanukul:1988:AHS, author = "Voratas Kachitvichyanukul and Bruce W. Schmeiser", title = "{Algorithm 668}: {H2PEC}: Sampling from the Hypergeometric Distribution", journal = j-TOMS, volume = "14", number = "4", pages = "397--398", month = dec, year = "1988", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 4 22:37:31 1994", URL = "http://doi.acm.org/10.1145/50063.214387", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Random number generation. {\bf G.m}: Mathematics of Computing, MISCELLANEOUS.", } @Article{Dongarra:1988:CES, author = "Jack J. Dongarra and Jeremy Du Croz and Sven Hammarling and Richard J. Hanson", title = "Corrigenda: ``{An} Extended Set of {FORTRAN Basic Linear Algebra Subprograms}''", journal = j-TOMS, volume = "14", number = "4", pages = "399--399", month = dec, year = "1988", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Mar 28 10:48:38 2003", note = "See \cite{Dongarra:1988:ESF}.", URL = "http://doi.acm.org/10.1145/50063.356256", acknowledgement = ack-nhfb, } @Article{Kearfott:1988:CTG, author = "R. Baker Kearfott", title = "Corrigenda: ``{Some} Tests of Generalized Bisection''", journal = j-TOMS, volume = "14", number = "4", pages = "399--399", month = dec, year = "1988", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "399 (1989). 65H10", MRnumber = "1 062 485, 88m:65081", bibdate = "Sat Nov 19 13:04:08 1994", note = "See \cite{Kearfott:1987:STG}.", URL = "http://doi.acm.org/10.1145/50063.356257", acknowledgement = ack-nhfb, } @Article{Anonymous:1988:FCA, author = "Anonymous", title = "Five-Year Cumulative Author Index (Vol. 10--14. 1984--1988)", journal = j-TOMS, volume = "14", number = "4", pages = "403--411", month = dec, year = "1988", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "00A15", MRnumber = "1 062 486", bibdate = "Fri Mar 28 10:56:10 2003", URL = "http://doi.acm.org/10.1145/50063.356247", acknowledgement = ack-nhfb, } @Article{Duff:1989:SMT, author = "Iain S. Duff and Roger G. Grimes and John G. Lewis", title = "Sparse Matrix Test Problems", journal = j-TOMS, volume = "15", number = "1", pages = "1--14", month = mar, year = "1989", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 22:42:25 1994", URL = "http://doi.acm.org/10.1145/62038.62043", acknowledgement = ack-nhfb, keywords = "measurement; performance", review = "ACM CR 9002-0143", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse and very large systems. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Cash:1989:BRK, author = "J. R. Cash", title = "A Block 6(4) {Runge-Kutta} Formula for Nonstiff Initial Value Problems", journal = j-TOMS, volume = "15", number = "1", pages = "15--28", month = mar, year = "1989", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 22:42:48 1994", URL = "http://doi.acm.org/10.1145/62038.62042", acknowledgement = ack-nhfb, keywords = "algorithms; performance; theory", review = "ACM CR 8909-0672", subject = "{\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Initial value problems. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation, Interpolation formulas.", } @Article{Cash:1989:ABF, author = "J. R. Cash", title = "{Algorithm 669}: {BRKF45}: {A FORTRAN} Subroutine for Solving First-Order Systems of Nonstiff Initial Value Problems for Ordinary Differential Equations", journal = j-TOMS, volume = "15", number = "1", pages = "29--30", month = mar, year = "1989", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 22:44:52 1994", note = "See also \cite{Higham:1991:RBF}.", URL = "http://doi.acm.org/10.1145/62038.214388", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation, Interpolation formulas. {\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Initial value problems. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Brankin:1989:ARK, author = "R. W. Brankin and I. Gladwell and J. R. Dormand and P. J. Prince and W. L. Seward", title = "{Algorithm 670}: a {Runge-Kutta-Nystr{\"o}m} code", journal = j-TOMS, volume = "15", number = "1", pages = "31--40", month = mar, year = "1989", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 13 17:26:53 MDT 1994", URL = "http://doi.acm.org/10.1145/62038.69650", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Reliability and robustness.", } @Article{Cody:1989:PEP, author = "W. J. Cody and L. Stoltz", title = "Performance Evaluation of Programs for Certain {Bessel} Functions", journal = j-TOMS, volume = "15", number = "1", pages = "41--48", month = mar, year = "1989", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 22:43:58 1994", URL = "http://doi.acm.org/10.1145/62038.62039", acknowledgement = ack-nhfb, keywords = "algorithms; performance; reliability; verification", review = "ACM CR 8911-0825", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Reliability and robustness. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms.", } @Article{Shanno:1989:NES, author = "David F. Shanno and Kang Hoh Phua", title = "Numerical Experience with Sequential Quadratic Programming Algorithms for Equality Constrained Nonlinear Programming", journal = j-TOMS, volume = "15", number = "1", pages = "49--63", month = mar, year = "1989", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "90C30 (90B20)", MRnumber = "91c:90104", bibdate = "Sun Sep 04 22:44:29 1994", URL = "http://doi.acm.org/10.1145/62038.62040", acknowledgement = ack-nhfb, keywords = "algorithms", review = "ACM CR 8909-0670", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Nonlinear programming. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Constrained optimization.", } @Article{Chang:1989:IPS, author = "Michael D. Chang and Chou-Hong J. Chen and Michael Engquist", title = "An Improved Primal Simplex Variant for Pure Processing Networks", journal = j-TOMS, volume = "15", number = "1", pages = "64--78", month = mar, year = "1989", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 13 17:26:53 MDT 1994", URL = "http://doi.acm.org/10.1145/62038.62041", acknowledgement = ack-nhfb, keywords = "algorithms; design; performance; theory", review = "ACM CR 8909-0669", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Linear programming. {\bf G.2.2}: Mathematics of Computing, DISCRETE MATHEMATICS, Graph Theory, Network problems. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency.", } @Article{Preusser:1989:AFF, author = "Albrecht Preusser", title = "{Algorithm 671}: {FARB-E-2D}: Fill Area with Bicubics on Rectangles\emdash {A} Contour Plot Program", journal = j-TOMS, volume = "15", number = "1", pages = "79--89", month = mar, year = "1989", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 22:46:19 1994", URL = "http://doi.acm.org/10.1145/62038.69651", acknowledgement = ack-nhfb, keywords = "algorithms; design", subject = "{\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation, Spline and piecewise polynomial interpolation. {\bf I.3.5}: Computing Methodologies, COMPUTER GRAPHICS, Computational Geometry and Object Modeling, Curve, surface, solid, and object representations.", } @Article{Morgan:1989:FAI, author = "Alexander P. Morgan and Andrew J. Sommese and Layne T. Watson", title = "Finding All Isolated Solutions to Polynomial Systems Using {HOMPACK}", journal = j-TOMS, volume = "15", number = "2", pages = "93--122", month = jun, year = "1989", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65-04 (58C30 65H10)", MRnumber = "91g:65003", bibdate = "Sun Sep 04 22:46:37 1994", URL = "http://doi.acm.org/10.1145/63522.64124", acknowledgement = ack-nhfb, keywords = "algorithms; theory", review = "ACM CR 8912-0895", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, HOMPACK. {\bf G.1.5}: Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Systems of equations. {\bf G.1.5}: Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Polynomials, methods for.", } @Article{Patterson:1989:AGIa, author = "T. N. L. Patterson", title = "An Algorithm for Generating Interpolatory Quadrature Rules of the Highest Degree of Precision with Preassigned Nodes for General Weight Functions", journal = j-TOMS, volume = "15", number = "2", pages = "123--136", month = jun, year = "1989", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65-04 (65D32)", MRnumber = "91g:65004", bibdate = "Sun Sep 04 22:46:58 1994", URL = "http://doi.acm.org/10.1145/63522.63523", acknowledgement = ack-nhfb, keywords = "algorithms", review = "ACM CR 9006-0500", subject = "{\bf G.1.4}: Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation, Gaussian quadrature. {\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials.", } @Article{Patterson:1989:AGIb, author = "T. N. L. Patterson", title = "{Algorithm 672}: Generation of Interpolatory Quadrature Rules of the Highest Degree of Precision with Preassigned Nodes for General Weight Functions", journal = j-TOMS, volume = "15", number = "2", pages = "137--143", month = jun, year = "1989", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65-04", MRnumber = "91g:65005", bibdate = "Sat Aug 13 17:26:53 MDT 1994", URL = "http://doi.acm.org/10.1145/63522.69649", acknowledgement = ack-nhfb, keywords = "algorithms; languages; performance", subject = "{\bf G.1.4}: Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation. {\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Tang:1989:TDI, author = "Ping Tak Peter Tang", title = "Table-Driven Implementation of the Exponential Function in {IEEE} Floating-Point Arithmetic", journal = j-TOMS, volume = "15", number = "2", pages = "144--157", month = jun, year = "1989", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 22:47:40 1994", bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", URL = "http://doi.acm.org/10.1145/63522.214389", abstract = "Algorithms and implementation details for the exponential function in both single- and double-precision of IEEE 754 arithmetic are presented here. With a table of moderate size, the implementations need only working-precision arithmetic and are provably accurate to within 0.54 ulp as long as the final result does not underflow. When the final result suffers gradual underflow, the error is still no worse than 0.77 ulp.", acknowledgement = ack-nj, keywords = "algorithms", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Error analysis. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Vitter:1989:ADH, author = "Jeffrey Scott Vitter", title = "{Algorithm 673}: Dynamic {Huffman} Coding", journal = j-TOMS, volume = "15", number = "2", pages = "158--167", month = jun, year = "1989", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 22:47:58 1994", URL = "http://doi.acm.org/10.1145/63522.214390", abstract = "We present a Pascal implementation of the one-pass algorithm for constructing dynamic Huffman codes that is described and analyzed in a companion paper. The program runs in real time; that is, the processing time for each letter of the message is proportional to the length of its codeword. The number of bits used to encode a message of $t$ letters is less than $t$ bits more than that used by the well-known two-pass algorithm. This is best possible for any one-pass Huffman scheme. In practice, it uses fewer bits than all other Huffman schemes. The algorithm has applications in file compression and network transmission.", acknowledgement = ack-nhfb, keywords = "algorithms; design; performance; theory", subject = "{\bf C.2.0}: Computer Systems Organization, COMPUTER-COMMUNICATION NETWORKS, General, Data communications. {\bf E.1}: Data, DATA STRUCTURES, Trees. {\bf E.4}: Data, CODING AND INFORMATION THEORY, Data compaction and compression. {\bf E.4}: Data, CODING AND INFORMATION THEORY, Nonsecret encoding schemes. {\bf F.2.2}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems. {\bf G.2.2}: Mathematics of Computing, DISCRETE MATHEMATICS, Graph Theory, Trees. {\bf H.1.1}: Information Systems, MODELS AND PRINCIPLES, Systems and Information Theory, Value of information.", } @Article{Higham:1989:CFC, author = "Nicholas J. Higham", title = "Corrigendum: ``{Algorithm} 674: {FORTRAN} Codes for Estimating the One-Norm of a Real or Complex Matrix, with Applications to Condition Estimation''", journal = j-TOMS, volume = "15", number = "2", pages = "168--168", month = jun, year = "1989", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Sep 30 01:18:49 1994", note = "See \cite{Higham:1988:AFC}.", URL = "http://doi.acm.org/10.1145/63522.214391", abstract = "We omitted giving this article an ACM algorithm number when it was first published in its entirety in the December 1988 issue of {\em TOMS}, Vol. 14, No. 4, pp. 381-396. To correct this, we do so here, and reprint the title as a pointer to the original article.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra.", } @Article{Krogh:1989:AAP, author = "Fred T. Krogh", title = "{ACM} Algorithms Policy", journal = j-TOMS, volume = "15", number = "2", pages = "169--172", month = jun, year = "1989", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Mar 28 10:56:42 2003", URL = "http://doi.acm.org/10.1145/63522.356273", acknowledgement = ack-nhfb, } @Article{Ribbens:1989:FAG, author = "Calvin J. Ribbens", title = "A Fast Adaptive Grid Scheme for Elliptic Partial Differential Equations", journal = j-TOMS, volume = "15", number = "3", pages = "179--197", month = sep, year = "1989", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 22:50:47 1994", URL = "http://doi.acm.org/10.1145/66888.66889", acknowledgement = ack-nhfb, keywords = "algorithms", review = "ACM CR 9006-0506", subject = "{\bf G.1.8}: Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Elliptic equations. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Parallel algorithms.", } @Article{Liu:1989:GPA, author = "Joseph W. H. Liu", title = "A Graph Partitioning Algorithm by Node Separators", journal = j-TOMS, volume = "15", number = "3", pages = "198--219", month = sep, year = "1989", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65-04 (05-04 05C70 65F50)", MRnumber = "1 062 491", bibdate = "Sun Sep 04 22:51:08 1994", URL = "http://doi.acm.org/10.1145/66888.66890", acknowledgement = ack-nhfb, keywords = "algorithms", review = "ACM CR 9003-0235", subject = "{\bf G.2.2}: Mathematics of Computing, DISCRETE MATHEMATICS, Graph Theory, Graph algorithms. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse and very large systems. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices.", } @Article{Mahdavi-Amiri:1989:CNL, author = "Nezam Mahdavi-Amiri and Richard H. Bartels", title = "Constrained Nonlinear Least Squares: An Exact Penalty Approach with Projected Structured Quasi-{Newton} Updates", journal = j-TOMS, volume = "15", number = "3", pages = "220--242", month = sep, year = "1989", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65-04 (65K05)", MRnumber = "1 062 492", bibdate = "Sun Sep 04 22:51:35 1994", URL = "http://doi.acm.org/10.1145/66888.66891", acknowledgement = ack-nhfb, keywords = "algorithms", review = "ACM CR 9004-0320", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization. {\bf G.1.5}: Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations.", } @Article{Vanbegin:1989:AFS, author = "Michel Vanbegin and Paul {Van Dooren} and Michel Verhaegen", title = "{Algorithm 675}: {FORTRAN} Subroutines for Computing the Square Root Covariance Filter and Square Root Information Filter in Dense or {Hessenberg} Forms", journal = j-TOMS, volume = "15", number = "3", pages = "243--256", month = sep, year = "1989", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 22:52:41 1994", URL = "http://doi.acm.org/10.1145/66888.69647", acknowledgement = ack-nhfb, keywords = "algorithms; measurement", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices.", } @Article{Dadurkevicius:1989:RA, author = "Virgis Dadurkevi{\v{c}}ius", title = "Remark on ``{Algorithm} 587: Two Algorithms for the Linearly Constrained Least Squares Problem''", journal = j-TOMS, volume = "15", number = "3", pages = "257--261", month = sep, year = "1989", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Sep 05 20:52:30 1994", note = "See \cite{Hanson:1982:ATA}.", URL = "http://doi.acm.org/10.1145/66888.77344", acknowledgement = ack-nhfb, keywords = "algorithms; theory", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Constrained optimization. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Least squares approximation. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Least squares methods.", } @Article{Buckley:1989:RA, author = "A. Buckley", title = "Remark on {Algorithm 630}", journal = j-TOMS, volume = "15", number = "3", pages = "262--274", month = sep, year = "1989", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 22:53:33 1994", note = "See \cite{Buckley:1985:ABE}.", URL = "http://doi.acm.org/10.1145/66888.69648", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Gradient methods.", } @Article{Domich:1989:RHN, author = "Paul D. Domich", title = "Residual {Hermite} Normal Form Computations", journal = j-TOMS, volume = "15", number = "3", pages = "275--286", month = sep, year = "1989", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "15A21 (15-04 15A36 65-04 65F05)", MRnumber = "91d:15020", bibdate = "Sun Sep 04 22:53:52 1994", URL = "http://doi.acm.org/10.1145/66888.66892", acknowledgement = ack-nhfb, keywords = "algorithms; theory", review = "ACM CR 9007-0597", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices.", } @Article{Corana:1989:CMF, author = "A. Corana and M. Marchesi and C. Martini and S. Ridella", title = "Corrigenda: ``{Minimizing} Multimodal Functions of Continuous Variables with the `Simulated Annealing' Algorithm''", journal = j-TOMS, volume = "15", number = "3", pages = "287--287", month = sep, year = "1989", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "287. 90C30 (65K05)", MRnumber = "1 062 494, 88m:90121", bibdate = "Sat Feb 24 09:58:06 1996", note = "See \cite{Corana:1987:MMF}.", URL = "http://doi.acm.org/10.1145/66888.356281", acknowledgement = ack-nhfb, } @Article{Enright:1989:CFP, author = "W. H. Enright and J. D. Pryce", title = "Corrigenda: ``{Two FORTRAN} Packages for Assessing Initial Value Methods''", journal = j-TOMS, volume = "15", number = "3", pages = "287--287", month = sep, year = "1989", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Mar 28 10:57:50 2003", note = "See \cite{Enright:1987:TFP}.", URL = "http://doi.acm.org/10.1145/66888.356282", acknowledgement = ack-nhfb, } @Article{Le:1989:CED, author = "D. Le", title = "Corrigenda: ``{An} Efficient Derivative-Free Method for Solving Nonlinear Equations''", journal = j-TOMS, volume = "15", number = "3", pages = "287--287", month = sep, year = "1989", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "287. 65H05", MRnumber = "1 062 495, 87d:65057", bibdate = "Fri Mar 28 10:57:46 2003", note = "See \cite{Le:1985:EDF}.", URL = "http://doi.acm.org/10.1145/66888.356283", acknowledgement = ack-nhfb, } @Article{Ashcraft:1989:IRS, author = "Cleve Ashcraft and Roger Grimes", title = "The Influence of Relaxed Supernode Partitions on the Multifrontal Method", journal = j-TOMS, volume = "15", number = "4", pages = "291--309", month = dec, year = "1989", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 22:58:46 1994", URL = "http://doi.acm.org/10.1145/76909.76910", acknowledgement = ack-nhfb, keywords = "algorithms; design; performance", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse and very large systems. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices. {\bf G.2.2}: Mathematics of Computing, DISCRETE MATHEMATICS, Graph Theory. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods).", } @Article{Liu:1989:MMP, author = "Joseph W. H. Liu", title = "The Multifrontal Method and Paging in Sparse {Cholesky} Factorization", journal = j-TOMS, volume = "15", number = "4", pages = "310--325", month = dec, year = "1989", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 22:59:06 1994", URL = "http://doi.acm.org/10.1145/76909.76911", acknowledgement = ack-nhfb, keywords = "algorithms; design; experimentation; performance", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse and very large systems. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Matrix inversion. {\bf D.4.2}: Software, OPERATING SYSTEMS, Storage Management, Virtual memory. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices.", } @Article{Mitchell:1989:CAR, author = "William F. Mitchell", title = "A Comparison of Adaptive Refinement Techniques for Elliptic Problems", journal = j-TOMS, volume = "15", number = "4", pages = "326--347", month = dec, year = "1989", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65N99 (65-04)", MRnumber = "1 062 496", bibdate = "Sun Sep 04 22:59:21 1994", URL = "http://doi.acm.org/10.1145/76909.76912", acknowledgement = ack-nhfb, keywords = "experimentation", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf G.1.8}: Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Finite element methods. {\bf G.1.8}: Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Elliptic equations. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation.", } @Article{Boggs:1989:AOS, author = "Paul T. Boggs and Janet R. Donaldson and Richard h. Byrd and Robert B. Schnabel", title = "{Algorithm 676}: {ODRPACK}: Software for Weighted Orthogonal Distance Regression", journal = j-TOMS, volume = "15", number = "4", pages = "348--364", month = dec, year = "1989", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 15:09:23 1994", URL = "http://doi.acm.org/10.1145/76909.76913", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Statistical computing. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Least squares methods.", } @Article{Montefusco:1989:ASI, author = "Laura Bacchelli Montefusco and Giulio Casciola", title = "{Algorithm 677}: ${C}^1$ Surface Interpolation", journal = j-TOMS, volume = "15", number = "4", pages = "365--374", month = dec, year = "1989", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Sep 30 01:22:34 1994", URL = "http://doi.acm.org/10.1145/76909.76914", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization.", } @Article{Corliss:1989:IIV, author = "George Corliss and Gary Krenz", title = "Indefinite Integration with Validation", journal = j-TOMS, volume = "15", number = "4", pages = "375--393", month = dec, year = "1989", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D30 (65-04)", MRnumber = "1 062 497", bibdate = "Sun Sep 04 23:01:02 1994", URL = "http://doi.acm.org/10.1145/76909.76915", acknowledgement = ack-nhfb, keywords = "algorithms; theory", review = "ACM CR 9007-0598", subject = "{\bf G.1.4}: Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Chebyshev approximation and theory.", } @Article{Kachitvichyanukul:1989:ABS, author = "Voratas Kachitvichyanukul and Bruce W. Schmeiser", title = "{Algorithm 678}: {BTPEC}: Sampling from the Binomial Distribution", journal = j-TOMS, volume = "15", number = "4", pages = "394--397", month = dec, year = "1989", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 13 17:26:53 MDT 1994", URL = "http://doi.acm.org/10.1145/76909.76916", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Random number generation.", } @Article{Dongarra:1990:SLB, author = "Jack J. Dongarra and Jeremy Du Croz and Sven Hammarling and Iain Duff", title = "A Set of Level 3 {Basic Linear Algebra Subprograms}", journal = j-TOMS, volume = "16", number = "1", pages = "1--17", month = mar, year = "1990", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 19:10:43 1994", URL = "http://doi.acm.org/10.1145/77626.79170", acknowledgement = ack-nhfb, keywords = "algorithms; measurement; performance; reliability; verification", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms.", } @Article{Dongarra:1990:ASL, author = "Jack J. Dongarra and Jeremy Du Croz and Sven Hammarling and Iain Duff", title = "{Algorithm 679}: {A} Set of Level 3 {Basic Linear Algebra Subprograms}: Model Implementation and Test Programs", journal = j-TOMS, volume = "16", number = "1", pages = "18--28", month = mar, year = "1990", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 27 17:29:49 1994", note = "See also \cite{Higham:1990:EFM,Demmel:1992:SBA,Dayde:1994:PBI}.", URL = "http://doi.acm.org/10.1145/77626.77627", acknowledgement = ack-nhfb, keywords = "algorithms; measurement; performance; reliability; verification", subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN 8X. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Cody:1990:PEP, author = "W. J. Cody", title = "Performance Evaluation of Programs for the Error and Complementary Error Functions", journal = j-TOMS, volume = "16", number = "1", pages = "29--37", month = mar, year = "1990", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65-04 (65G05)", MRnumber = "1 073 407", bibdate = "Sun Sep 04 23:03:20 1994", URL = "http://doi.acm.org/10.1145/77626.77628", acknowledgement = ack-nhfb, keywords = "algorithms; performance; reliability", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Reliability and robustness. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms.", } @Article{Poppe:1990:MEC, author = "G. P. M. Poppe and C. M. J. Wijers", title = "More Efficient Computation of the Complex Error Function", journal = j-TOMS, volume = "16", number = "1", pages = "38--46", month = mar, year = "1990", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65G05 (65D20)", MRnumber = "91h:65068a", bibdate = "Sun Sep 04 23:03:20 1994", URL = "http://doi.acm.org/10.1145/77626.77629", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Rational approximation.", } @Article{Poppe:1990:AEC, author = "G. P. M. Poppe and C. M. J. Wijers", title = "{Algorithm 680}: Evaluation of the Complex Error Function", journal = j-TOMS, volume = "16", number = "1", pages = "47--47", month = mar, year = "1990", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "47. 65G05 (65-04)", MRnumber = "91h:65068b", bibdate = "Sun Sep 04 23:03:20 1994", URL = "http://doi.acm.org/10.1145/77626.77630", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Rational approximation.", } @Article{Arney:1990:AMM, author = "David C. Arney and Joseph E. Flaherty", title = "An Adaptive Mesh-Moving and Local Refinement Method for Time-Dependent Partial Differential Equations", journal = j-TOMS, volume = "16", number = "1", pages = "48--71", month = mar, year = "1990", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65M50", MRnumber = "91f:65154", bibdate = "Sun Sep 04 23:03:20 1994", URL = "http://doi.acm.org/10.1145/77626.77631", acknowledgement = ack-nhfb, keywords = "algorithms; design; performance", subject = "{\bf G.1.8}: Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Finite element methods. {\bf G.1.8}: Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Difference methods. {\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Boundary value problems. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency.", } @Article{Schryer:1990:DSO, author = "N. L. Schryer", title = "Designing Software for One-Dimensional Partial Differential Equations", journal = j-TOMS, volume = "16", number = "1", pages = "72--85", month = mar, year = "1990", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65-04 (65P05)", MRnumber = "1 073 411", bibdate = "Sun Sep 04 23:03:20 1994", URL = "http://doi.acm.org/10.1145/77626.77632", acknowledgement = ack-nhfb, keywords = "algorithms; design", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf G.1.8}: Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations. {\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Boundary value problems.", } @Article{Hansen:1990:PES, author = "Eldon R. Hansen and Merell L. Patrick and Richard L. C. Wang", title = "Polynomial Evaluation with Scaling", journal = j-TOMS, volume = "16", number = "1", pages = "86--93", month = mar, year = "1990", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65Y10", MRnumber = "1 073 412", bibdate = "Fri Aug 26 23:38:17 1994", URL = "http://doi.acm.org/10.1145/77626.77633", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials.", } @Article{Snow:1990:WGO, author = "Dennis M. Snow", title = "{Weyl} Group Orbits", journal = j-TOMS, volume = "16", number = "1", pages = "94--108", month = mar, year = "1990", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "20G99 (22E15)", MRnumber = "91j:20115", bibdate = "Sun Sep 04 23:03:20 1994", URL = "http://doi.acm.org/10.1145/77626.77634", acknowledgement = ack-nhfb, keywords = "algorithms; performance; theory", reviewer = "V. L. Popov", subject = "{\bf F.2.2}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Computations on discrete structures. {\bf I.1.2}: Computing Methodologies, ALGEBRAIC MANIPULATION, Algorithms. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency.", } @Article{Sewell:1990:RSP, author = "Granville Sewell", title = "Remark on ``{Algorithm 657}: Software for Plotting Contour Surfaces of a Function of Three Variables''", journal = j-TOMS, volume = "16", number = "1", pages = "109--109", month = mar, year = "1990", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 23:03:20 1994", note = "See \cite{Sewell:1988:ASP}.", URL = "http://doi.acm.org/10.1145/77626.356300", acknowledgement = ack-nhfb, } @Article{Zenios:1990:INO, author = "Stavros A. Zenios", title = "Integrating Network Optimization Capabilities into a High-Level Modeling Language", journal = j-TOMS, volume = "16", number = "2", pages = "113--142", month = jun, year = "1990", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 23:09:48 1994", URL = "http://doi.acm.org/10.1145/78928.78929", acknowledgement = ack-nhfb, keywords = "algorithms; design; experimentation; languages; performance; theory", subject = "{\bf G.2.2}: Mathematics of Computing, DISCRETE MATHEMATICS, Graph Theory, Network problems. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Constrained optimization. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Nonlinear programming. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Linear programming. {\bf C.2.1}: Computer Systems Organization, COMPUTER-COMMUNICATION NETWORKS, Network Architecture and Design. {\bf C.4}: Computer Systems Organization, PERFORMANCE OF SYSTEMS, Modeling techniques.", } @Article{Meintjes:1990:CES, author = "Keith Meintjes and Alexander P. Morgan", title = "Chemical Equilibrium Systems as Numerical Test Problems", journal = j-TOMS, volume = "16", number = "2", pages = "143--151", month = jun, year = "1990", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 23:09:48 1994", URL = "http://doi.acm.org/10.1145/78928.78930", acknowledgement = ack-nhfb, keywords = "algorithms; theory", subject = "{\bf G.1.5}: Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Systems of equations. {\bf G.1.5}: Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Polynomials, methods for. {\bf J.2}: Computer Applications, PHYSICAL SCIENCES AND ENGINEERING, Chemistry.", } @Article{Kearfott:1990:AIP, author = "R. Baker Kearfott and Manuel {Novoa III}", title = "{Algorithm 681}: {INTBIS}, a Portable Interval {Newton}\slash Bisection Package", journal = j-TOMS, volume = "16", number = "2", pages = "152--157", month = jun, year = "1990", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 23:09:48 1994", URL = "http://doi.acm.org/10.1145/78928.78931", acknowledgement = ack-nhfb, keywords = "algorithms; theory", subject = "{\bf G.1.5}: Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Systems of equations. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation.", } @Article{Murli:1990:ATM, author = "A. Murli and M. Rizzardi", title = "{Algorithm 682}: {Talbot}'s Method for the {Laplace} Inversion Problem", journal = j-TOMS, volume = "16", number = "2", pages = "158--168", month = jun, year = "1990", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 23:09:48 1994", URL = "http://doi.acm.org/10.1145/78928.78932", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computation of transforms. {\bf G.1.4}: Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation, Equal interval integration. {\bf G.1.9}: Mathematics of Computing, NUMERICAL ANALYSIS, Integral Equations, Fredholm equations.", } @Article{Amos:1990:CEI, author = "Donald E. Amos", title = "Computation of Exponential Integrals of a Complex Argument", journal = j-TOMS, volume = "16", number = "2", pages = "169--177", month = jun, year = "1990", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D20", MRnumber = "92k:65025", bibdate = "Sun Sep 04 23:09:48 1994", URL = "http://doi.acm.org/10.1145/78928.78933", acknowledgement = ack-nhfb, keywords = "algorithms; theory", subject = "{\bf G.1.9}: Mathematics of Computing, NUMERICAL ANALYSIS, Integral Equations. {\bf G.1.m}: Mathematics of Computing, NUMERICAL ANALYSIS, Miscellaneous.", } @Article{Amos:1990:APF, author = "Donald E. Amos", title = "{Algorithm 683}: {A} Portable {FORTRAN} Subroutine for Exponential Integrals of a Complex Argument", journal = j-TOMS, volume = "16", number = "2", pages = "178--182", month = jun, year = "1990", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D20 (65Y10)", MRnumber = "92k:65026", bibdate = "Sun Sep 04 23:09:48 1994", URL = "http://doi.acm.org/10.1145/78928.78934", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN.", } @Article{Tang:1990:AET, author = "Ping Tak Peter Tang", title = "Accurate and Efficient Testing of the Exponential and Logarithm Functions", journal = j-TOMS, volume = "16", number = "3", pages = "185--200", month = sep, year = "1990", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65-04 (65G99)", MRnumber = "1 070 797", bibdate = "Sun Sep 04 23:14:59 1994", URL = "http://doi.acm.org/10.1145/79505.79506", abstract = "Table-driven techniques can be used to test highly accurate implementation of EXP LOG. The largest error observed in EXP and LOG accurately to within 1/500 unit in the last place are reported in our tests. Methods to verify the tests' reliability are discussed. Results of applying the tests to our own as well as to a number of other implementations of EXP and LOG are presented.", acknowledgement = ack-nhfb, keywords = "algorithms; languages; verification", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Error analysis. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Portability.", } @Article{Cash:1990:VOR, author = "J. R. Cash and Alan H. Karp", title = "A Variable Order {Runge-Kutta} Method for Initial Value Problems with Rapidly Varying Right-Hand Sides", journal = j-TOMS, volume = "16", number = "3", pages = "201--222", month = sep, year = "1990", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65L05 (65-04)", MRnumber = "1 070 798", bibdate = "Sun Sep 04 23:14:59 1994", URL = "http://doi.acm.org/10.1145/79505.79507", abstract = "Explicit Runge-Kutta methods (RKMs) are among the most popular classes of formulas for the approximate numerical integration of nonstiff, initial value problems. However, high-order Runge-Kutta methods require more function evaluations per integration step than, for example, Adams methods used in PECE mode, and so, with RKMs, it is especially important to avoid rejected steps. Steps are often rejected when certain derivatives of the solutions are very large for part of the region of integration. This corresponds, for example, to regions where the solution has a sharp front or, in the limit, some derivative of the solution is discontinuous. In these circumstances the assumption that the local truncation error is changing slowly is invalid, and so any step-choosing algorithm is likely to produce an unacceptable step. In this paper we derive a family of explicit Runge-Kutta formulas. Each formula is very efficient for problems with smooth solution as well as problems having rapidly varying solutions. Each member of this family consists of a fifty-order formula that contains imbedded formulas of all orders 1 through 4. By computing solutions at several different orders, it is possible to detect sharp fronts or discontinuities before all the function evaluations defining the full Runge-Kutta step have been computed. We can then either accept a lower order solution or abort the step, depending on which course of action seems appropriate. The efficiency of the new algorithm is demonstrated on the DETEST test set as well as on some difficult test problems with sharp fronts or discontinuities.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Initial value problems. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation.", } @Article{Weiss:1990:SSC, author = "Shlomo Weiss and James E. Smith", title = "A Study of Scalar Compilation Techniques for Pipelined Supercomputers", journal = j-TOMS, volume = "16", number = "3", pages = "223--245", month = sep, year = "1990", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 23:14:59 1994", URL = "http://doi.acm.org/10.1145/79505.79508", abstract = "This paper studies two compilation techniques for enhancing scalar performance in high-speed scientific processors: software pipelining and loop unrolling. We study the impact of the architecture (size of the register file) and of the hardware (size of instruction buffer) on the efficiency of loop unrolling. We also develop a methodology for classifying software pipelining techniques. For loop unrolling, a straightforward scheduling algorithm is shown to produce near-optimal results when not inhibited by recurrences or memory hazards. Our study indicates that the performance produced with a modified CRAY-1S scalar architecture and a code scheduler utilizing loop unrolling is comparable to the performance achieved by the CRAY-1S with a vector unit and the CFT vectorizing compiler.\par Finally, we show that the combination of loop unrolling and dynamic software pipelining, as implemented by a decoupled computer, substantially outperforms the vector CRAY-1S.", acknowledgement = ack-nhfb, keywords = "design; experimentation; performance", subject = "{\bf C.1.1}: Computer Systems Organization, PROCESSOR ARCHITECTURES, Single Data Stream Architectures, Pipeline processors. {\bf C.4}: Computer Systems Organization, PERFORMANCE OF SYSTEMS, Performance attributes. {\bf D.3.4}: Software, PROGRAMMING LANGUAGES, Processors, Compilers. {\bf C.5.1}: Computer Systems Organization, COMPUTER SYSTEM IMPLEMENTATION, Large and Medium (``Mainframe'') Computers.", } @Article{Preusser:1990:EFB, author = "Albrecht Preusser", title = "Efficient Formulation of a Bivariate Nonic ${C}^2$-{Hermite} Polynomial on Triangles", journal = j-TOMS, volume = "16", number = "3", pages = "246--252", month = sep, year = "1990", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D05 (65-04)", MRnumber = "1 070 799", bibdate = "Sun Sep 04 23:14:59 1994", URL = "http://doi.acm.org/10.1145/79505.79509", abstract = "Bivariate polynomials over triangular domains are widely in use for the definition of surfaces that are continuously differentiable across a set of triangles. A description is given of how explicit formulas for the coefficients of bivariate nonic polynomials can be found with the help of a computer algebra system. A linear system with 55 equations and 45 nonzero right hand sides must be solved algebraically. The interpolant is twice differentiable across triangle sides and based on function values and partial derivatives up to fourth order at the nodes. Horner's scheme for evaluating polynomials can be applied directly, leading to optimal efficiency during the evaluation phase (54 additions and multiplications for one point). Starting with transformed nodal data, the calculation of one set of coefficients takes about 350 additions, the same number of multiplications, and 30 divisions.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation, Spline and piecewise polynomial interpolation. {\bf I.3.5}: Computing Methodologies, COMPUTER GRAPHICS, Computational Geometry and Object Modeling, Curve, surface, solid, and object representations. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods).", } @Article{Preusser:1990:AIT, author = "Albrecht Preusser", title = "{Algorithm 684}: ${C}^1$- and ${C}^2$-Interpolation on Triangles with Quintic and Nonic Bivariate Polynomials", journal = j-TOMS, volume = "16", number = "3", pages = "253--257", month = sep, year = "1990", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65-04 (65D05)", MRnumber = "1 070 800", bibdate = "Sun Sep 04 23:14:59 1994", URL = "http://doi.acm.org/10.1145/79505.79510", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation, Spline and piecewise polynomial interpolation. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Shacham:1990:FBD, author = "Orit Shacham and Mordechai Shacham", title = "Finding Boundaries of the Domain of Definition for Functions Along a One-Dimensional Ray", journal = j-TOMS, volume = "16", number = "3", pages = "258--268", month = sep, year = "1990", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65-04 (65D99)", MRnumber = "1 070 801", bibdate = "Sun Sep 04 23:14:59 1994", URL = "http://doi.acm.org/10.1145/79505.79511", abstract = "A program for finding boundaries of function domains along a one-dimensional ray has been developed. The program decomposes the function into subexpressions which are recursively tested for intervals where they are undefined, negative, or fractional, or points where they equal zero. The intervals in which the subexpressions are undefined are then united to create the boundaries of the domain of definition of the whole function. The advantages of the use of such a program in solution of systems of nonlinear algebraic equations and nonlinear optimization are demonstrated.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf G.1.5}: Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization.", } @Article{Nair:1990:IAO, author = "K. Aiyappan Nair", title = "An Improved Algorithm for Ordered Sequential Random Sampling", journal = j-TOMS, volume = "16", number = "3", pages = "269--274", month = sep, year = "1990", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65C10", MRnumber = "1 070 802", bibdate = "Sat Aug 27 15:57:03 1994", URL = "http://doi.acm.org/10.1145/79505.356313", acknowledgement = ack-nhfb, } @Article{Palacios-Velez:1990:DHS, author = "Oscar Palacios-V{\'e}lez and Baltazar Cuevas Renaud", title = "A Dynamic Hierarchical Subdivision Algorithm for Computing {Delaunay} Triangulations and Other Closest-Point Problems", journal = j-TOMS, volume = "16", number = "3", pages = "275--292", month = sep, year = "1990", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65-04", MRnumber = "1 070 803", bibdate = "Sat Aug 27 15:57:45 1994", URL = "http://doi.acm.org/10.1145/79505.79512", abstract = "A new, dynamic, hierarchical subdivision and recursive algorithm for computing Delaunay triangulations is presented. The algorithm has four main steps: (1) location of the already formed triangle that contains the point (2) identification of other adjoining triangles whose circumcircle contains the point (3) formation of the new triangles, and (4) database update. Different search procedures are analyzed. It is shown that the ``oriented walk'' search, when the total number of points is less than 417 or when the points are presorted by distance or coordinates. The algorithm has point-deletion capabilities which are discussed in detail.", acknowledgement = ack-nhfb, keywords = "algorithms; design", subject = "{\bf F.2.2}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Geometrical problems and computations. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf I.3.5}: Computing Methodologies, COMPUTER GRAPHICS, Computational Geometry and Object Modeling, Geometric algorithms, languages, and systems. {\bf I.3.5}: Computing Methodologies, COMPUTER GRAPHICS, Computational Geometry and Object Modeling, Hierarchy and geometric transformations. {\bf F.2.2}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Sorting and searching.", } @Article{Krogh:1990:AAP, author = "Fred T. Krogh", title = "{ACM} Algorithms Policy", journal = j-TOMS, volume = "16", number = "3", pages = "293--296", month = sep, year = "1990", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 23:14:59 1994", URL = "http://doi.acm.org/10.1145/79505.356315", acknowledgement = ack-nhfb, } @Article{Pothen:1990:CBT, author = "Alex Pothen and Chin-Ju Fan", title = "Computing the Block Triangular Form of a Sparse Matrix", journal = j-TOMS, volume = "16", number = "4", pages = "303--324", month = dec, year = "1990", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65F50", MRnumber = "91k:65075", bibdate = "Sat Aug 27 15:58:44 1994", URL = "http://doi.acm.org/10.1145/98267.98287", abstract = "We consider the problem of permuting the rows and columns of a rectangular or square, unsymmetric sparse matrix to compute its block triangular form. This block triangular form is based on a canonical decomposition of bipartite graphs induced by a maximum matching and was discovered by Dulmage and Mendelsohn. We describe implementations of algorithms to compute the block triangular form and provide computational results on sparse matrices from test collections. Several applications of the block triangular form are also included.", acknowledgement = ack-nhfb, keywords = "algorithms; perm; sparse", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse and very large systems. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.2.1}: Mathematics of Computing, DISCRETE MATHEMATICS, Combinatorics, Permutations and combinations. {\bf G.2.2}: Mathematics of Computing, DISCRETE MATHEMATICS, Graph Theory.", } @Article{Kaufman:1990:APS, author = "Linda Kaufman and Daniel D. Warner", title = "{Algorithm 685}: {A} Program for Solving Separable Elliptic Equations", journal = j-TOMS, volume = "16", number = "4", pages = "325--351", month = dec, year = "1990", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 23:21:57 1994", URL = "http://doi.acm.org/10.1145/98267.98289", abstract = "This paper presents a program SERRG2 that solves separable elliptic equations on a rectangle. The program uses a matrix decomposition technique to directly solve the linear system arising from a Rayleigh-Ritz-Galerkin approach with tensor product B-splines to solve the separable partial differential equation. This approach permits high-order discretizations, variable meshes, and multiple knots.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.1.8}: Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Higham:1990:EFM, author = "Nicholas J. Higham", title = "Exploiting Fast Matrix Multiplication Within the Level 3 {BLAS}", journal = j-TOMS, volume = "16", number = "4", pages = "352--368", month = dec, year = "1990", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65-04 (65F99)", MRnumber = "1 095 133", bibdate = "Sun Sep 04 23:21:57 1994", note = "Describes algorithms based on Strassen's method which are asymptotically faster than the standard ${N}^3$ algorithm, and in practice, faster for ${N}\approx100$, and examines their numerical stability. See \cite{Dongarra:1990:ASL,Demmel:1992:SBA,Dayde:1994:PBI}.", URL = "http://doi.acm.org/10.1145/98267.98290", abstract = "The Level 3 BLAS (BLAS3) are a set of specifications of FORTRAN 77 subprograms for carrying out matrix multiplications and the solution of triangular systems with multiple right-hand sides. They are intended to provide efficient and portable building blocks for linear algebra algorithms on high-performance computers. We describe algorithms for the BLAS3 operations that are asymptotically faster than the conventional ones. These algorithms are based on Strassen's method for fast matrix multiplication, which is now recognized to be a practically useful technique once matrix dimensions exceed about 100. We pay particular attention to the numerical stability of these ``fast BLAS3.'' Error bounds are given and their significance is explained and illustrated with the aid of numerical experiments. Our conclusion is that the fast BLAS3, although not as strongly stable as conventional implementations, are stable enough to merit careful consideration in many applications.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra. {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN 77.", } @Article{Reichel:1990:AFS, author = "L. Reichel and W. B. Gragg", title = "{Algorithm 686}: {FORTRAN} Subroutines for Updating the {QR} Decomposition", journal = j-TOMS, volume = "16", number = "4", pages = "369--377", month = dec, year = "1990", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 23:25:40 1994", URL = "http://doi.acm.org/10.1145/98267.98291", acknowledgement = ack-nhfb, keywords = "algorithms; Gram-Schmidt algorithm; nla; qrd; software; updating", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Tang:1990:TDI, author = "Ping Tak Peter Tang", title = "Table-Driven Implementation of the Logarithm Function in {IEEE} Floating-Point Arithmetic", journal = j-TOMS, volume = "16", number = "4", pages = "378--400", month = dec, year = "1990", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 23:26:09 1994", bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", URL = "http://doi.acm.org/10.1145/98267.98294", abstract = "Algorithms and implementation details for the logarithm functions in both single and double precision of IEEE 754 arithmetic are presented here. With a table of moderate size, the implementation need only working- precision arithmetic and are provably accurate to within 0.57 ulp.", acknowledgement = ack-nj, keywords = "algorithms; design; performance; reliability; standardization; theory; verification", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Error analysis. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Hopkins:1990:RRK, author = "Tim Hopkins and David Morse", title = "Remark on ``{Algorithm 620}: References and Keywords for {\em {Collected Algorithms} of the {ACM}}''", journal = j-TOMS, volume = "16", number = "4", pages = "401--403", month = dec, year = "1990", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Feb 24 09:58:26 1996", note = "See \cite{Rice:1984:ARK,Hamilton:1985:RRK}.", URL = "http://doi.acm.org/10.1145/98267.98297", abstract = "The authors report on an enhanced version of the database originally reported in `Algorithm 620: references and keywords for collected algorithms from ACM', J. R. Rice and R. J. Hanson, ACM Trans Math. Soft. vol. 10, no. 4, p. 359-360 (1984). In this new version they have included all the information necessary to generate full bibliographic references. Extra information includes the author's name (including any accents), the page range of the original reference (rather than just the starting page), the month and year of publication and an abbreviated journal name. The programming language used to code the algorithm is also given. Any mathematical notation used within the algorithm title and accents in the author's name have been defined using {\TeX}. Following the practice used with Bib{\TeX}, all letters within the title that need to remain capitalized in a printed version of the reference (e.g. Fortran, Bessel) are enclosed in braces. (3 Refs.)", acknowledgement = ack-nhfb, affiliation = "Kent Univ., UK", classification = "C7250C (Bibliographic systems); C7310 (Mathematics); C4100 (Numerical analysis)", keywords = "Abbreviated journal name; Algorithm title; algorithms; Bibliographic references; BibTeX; Mathematical notation; TeX", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", thesaurus = "Bibliographic systems; Mathematics computing; Numerical methods", } @Article{Amos:1990:RPP, author = "D. E. Amos", title = "Remark on ``{Algorithm 644}: {A} Portable Package for {Bessel} Functions of a Complex Argument and Nonnegative Order''", journal = j-TOMS, volume = "16", number = "4", pages = "404--404", month = dec, year = "1990", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Mar 09 10:26:24 1999", note = "See \cite{Amos:1986:APP,Amos:1995:RAP}.", URL = "http://doi.acm.org/10.1145/98267.98299", acknowledgement = ack-nhfb, keywords = "algorithms; theory", subject = "{\bf F.2.2}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems.", } @Article{Garbow:1990:RFS, author = "B. S. Garbow and J. N. Lyness", title = "Remark on ``{Algorithm 662}: {A FORTRAN} Software Package for the Numerical Inversion of the {Laplace} Transform Based on {Weeks}' Method''", journal = j-TOMS, volume = "16", number = "4", pages = "405--406", month = dec, year = "1990", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 23:21:57 1994", note = "See \cite{Garbow:1988:AFS}.", URL = "http://doi.acm.org/10.1145/98267.98302", acknowledgement = ack-nhfb, keywords = "algorithms; theory", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf F.2.2}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems.", } @Article{Addison:1991:ADT, author = "C. A. Addison and W. H. Enright and P. W. Gaffney and I. Gladwell and P. M. Hanson", title = "{Algorithm 687}: {A} Decision Tree for the Numerical Solution of Initial Value Ordinary Differential Equations", journal = j-TOMS, volume = "17", number = "1", pages = "1--10", month = mar, year = "1991", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 23:33:02 1994", URL = "http://doi.acm.org/10.1145/103147.103148", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Initial value problems.", } @Article{Shampine:1991:RSS, author = "L. F. Shampine and I. Gladwell and R. W. Brankin", title = "Reliable Solutions of Special Event Location Problems for {ODEs}", journal = j-TOMS, volume = "17", number = "1", pages = "11--25", month = mar, year = "1991", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65L05", MRnumber = "92e:65093", bibdate = "Sun Sep 04 23:33:02 1994", URL = "http://doi.acm.org/10.1145/103147.103149", abstract = "Computing the solution of the initial value problem in ordinary differential equations (ODEs) may be only part of a larger task. One such task is finding where an algebraic function of the solution (an event function) has a root (an event occurs). This is a task which is difficult both in theory and in software practice. For certain useful kinds of event functions, it is possible to avoid two fundamental difficulties. It is described how to achieve the reliable solutions of such problems in a way that allows the capability to be grafted onto popular codes for the initial value problem.", acknowledgement = ack-nhfb, keywords = "algorithms; design; theory", reviewer = "H. Shintani", subject = "{\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Initial value problems.", } @Article{Gal:1991:AEM, author = "Shmuel Gal and Boris Bachelis", title = "An Accurate Elementary Mathematical Library for the {IEEE} Floating Point Standard", journal = j-TOMS, volume = "17", number = "1", pages = "26--45", month = mar, year = "1991", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D20 (65-04 65D15)", MRnumber = "92a:65069", bibdate = "Sun Sep 04 23:33:02 1994", URL = "http://doi.acm.org/10.1145/103147.103151", abstract = "The algorithms used by the IBM Israel Scientific Center for the elementary mathematical library using the IEEE standard for binary floating point arithmetic are described. The algorithms are based on the ``accurate tables method.'' This methodology achieves high performance and produces very accurate results. It overcomes one of the main problems encountered in elementary mathematical functions computations: achieving last bit accuracy. The results obtained are correctly rounded for almost all argument values.\par Our main idea in the accurate tables method is to use ``nonstandard tables,'' which are different from the natural tables of equally spaced points in which the rounding error prevents obtaining last bit accuracy. In order to achieve a small error we use the following idea: Perturb the original, equally spaced, points in such a way that the table value (or tables values in case we need several tables) will be very close to numbers which can be exactly represented by the computer (much closer than the usual double precision representation). Thus we were able to control the error introduced by the computer representation of real numbers and extended the accuracy without actually using extended precision arithmetic.", acknowledgement = ack-nhfb, keywords = "algorithms; theory", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation.", } @Article{Cody:1991:PEP, author = "W. J. Cody", title = "Performance Evaluation of Programs Related to the Real Gamma Function", journal = j-TOMS, volume = "17", number = "1", pages = "46--54", month = mar, year = "1991", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D20 (65Y20)", MRnumber = "91m:65052", bibdate = "Sun Sep 04 23:33:02 1994", URL = "http://doi.acm.org/10.1145/103147.103153", abstract = "Methods are presented for evaluating the performance of programs for the functions $\Gamma(x)$, $\ln \Gamma(x)$, and $\psi(x)$. Accuracy estimates are based on comparisons using the manipulation theorem. Ideas for checking robustness are also given, and details on specific implementations of test programs are included.", acknowledgement = ack-nhfb, keywords = "measurement; performance; reliability", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing.", } @Article{Cody:1991:UTS, author = "W. J. Cody and L. Stoltz", title = "The Use of {Taylor} Series to Test Accuracy of Function Programs", journal = j-TOMS, volume = "17", number = "1", pages = "55--63", month = mar, year = "1991", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D20 (65Y20)", MRnumber = "91m:65053", bibdate = "Sun Sep 04 23:36:36 1994", bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", URL = "http://doi.acm.org/10.1145/103147.103154", abstract = "This paper discusses the use of local Taylor series expansions for determining the accuracy of computer programs for special functions. The main example is testing of programs for exponential integrals. Additional applications include testing of programs for certain Bessel functions, Dawson's integral, and error functions.", acknowledgement = ack-nhfb, keywords = "algorithms; measurement; performance; verification", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms.", } @Article{Dax:1991:CAB, author = "Achiya Dax", title = "On Computational Aspects of Bounded Linear Least Squares Problems", journal = j-TOMS, volume = "17", number = "1", pages = "64--73", month = mar, year = "1991", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65K10", MRnumber = "91m:65179", bibdate = "Sun Sep 04 23:33:02 1994", URL = "http://doi.acm.org/10.1145/103147.103155", abstract = "The paper describes numerical experiments with active set methods for solving bounded linear least squares problems. It concentrates on two problems that arise in the implementation of the active set method. One problem is the choice of a good starting point. The second problem is how to move out of a ``{\em dead point}.'' The paper investigates the use of simple iterative methods to solve these problems. The results of our experiments indicate that the use of Gauss-Seidel iterations to obtain a starting point is likely to provide large gains in efficiency. Another interesting conclusion is that dropping one constraint at a time is advantageous to dropping several constraints at a time.", acknowledgement = ack-nhfb, keywords = "algorithms; experimentation; performance; theory", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Least squares methods.", } @Article{Pardalos:1991:CTP, author = "Panos M. Pardalos", title = "Construction of Test Problems in Quadratic Bivalent Programming", journal = j-TOMS, volume = "17", number = "1", pages = "74--87", month = mar, year = "1991", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65K05", MRnumber = "92c:65075", bibdate = "Sun Sep 04 23:33:02 1994", URL = "http://doi.acm.org/10.1145/103147.103156", abstract = "A method of constructing test problems for constrained bivalent quadratic programming is presented. For any feasible integer point for a given domain, the method generates quadratic functions whose minimum over the given domain occurs at the selected point.\par Certain properties of unconstrained quadratic zero-one programs that determine the difficulty of the test problems are also discussed. In addition, a standardized random test problem generator for unconstrained quadratic zero-one programming is given.", acknowledgement = ack-nhfb, keywords = "algorithms; experimentation; performance", reviewer = "P. K. Subramanian", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Integer programming. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Nonlinear programming. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Klier:1991:FCB, author = "Peter Klier and Richard J. Fateman", title = "On Finding the Closest Bitwise Matches in a Fixed Set", journal = j-TOMS, volume = "17", number = "1", pages = "88--97", month = mar, year = "1991", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "68Q20", MRnumber = "1 103 630", bibdate = "Sun Sep 04 23:33:02 1994", URL = "http://doi.acm.org/10.1145/103147.103157", abstract = "In a given large fixed table of bit-vectors, we would like to find, as rapidly as possible, those bit-vectors which have the least Hamming distances from a newly-presented arbitrary bit-vector.", acknowledgement = ack-nhfb, keywords = "algorithms; performance", subject = "{\bf F.2.2}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Pattern matching. {\bf E.2}: Data, DATA STORAGE REPRESENTATIONS. {\bf F.2.2}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Sorting and searching. {\bf H.3.3}: Information Systems, INFORMATION STORAGE AND RETRIEVAL, Information Search and Retrieval, Search process.", } @Article{LEcuyer:1991:IRN, author = "Pierre L'Ecuyer and Serge C{\^o}t{\'e}", title = "Implementing a Random Number Package with Splitting Facilities", journal = j-TOMS, volume = "17", number = "1", pages = "98--111", month = mar, year = "1991", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65C10", MRnumber = "91m:65016", bibdate = "Sun Sep 04 23:33:02 1994", URL = "http://doi.acm.org/10.1145/103147.103158", abstract = "A portable set of software tools is described for uniform random variates generation. It provides for multiple generators running simultaneously, and each generator has its sequence of numbers partitioned into many long (disjoint) substreams. Simple procedure calls allow the user to make any generator ``jump'' ahead to the beginning of its next substream, back to the beginning of its current substream, or back to the beginning of its first substream\ldots. Implementation issues are discussed\ldots. A Pascal implementation for 32-bit computers is described.", acknowledgement = ack-nhfb, keywords = "algorithms; performance", subject = "{\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Random number generation. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Liu:1991:GEM, author = "Joseph W. H. Liu", title = "A Generalized Envelope Method for Sparse Factorization by Rows", journal = j-TOMS, volume = "17", number = "1", pages = "112--129", month = mar, year = "1991", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65F50", MRnumber = "92b:65037", bibdate = "Sun Sep 04 23:43:02 1994", URL = "http://doi.acm.org/10.1145/103147.103159", abstract = "A generalized form of the envelope method is proposed for the solution of large sparse symmetric and positive definite matrices by rows. The method is demonstrated to have practical advantages over the conventional column-oriented factorization using compressed column storage or the multifrontal method using full frontal submatrices.", acknowledgement = ack-nhfb, keywords = "algorithms; functional algorithm", reviewer = "R. P. Tewarson", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse and very large systems. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Mohideen:1991:RCG, author = "Saleem Mohideen and Vladimir Cherkassky", title = "On Recursive Calculation of the Generalized Inverse of a Matrix", journal = j-TOMS, volume = "17", number = "1", pages = "130--147", month = mar, year = "1991", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65F10 (65F20)", MRnumber = "92c:65042", bibdate = "Sun Sep 04 23:33:02 1994", URL = "http://doi.acm.org/10.1145/103147.103160", abstract = "The generalized inverse of a matrix is an extension of the ordinary square matrix inverse which applies to any matrix (e.g., singular, rectangular). The generalized inverse has numerous important applications such as regression analysis, filtering, optimization and, more recently, linear associative memories. In this latter application known as Distributed Associative Memory, stimulus vectors are associated with response vectors and the result of many associations is spread over the entire memory matrix, which is calculated as the generalized inverse. Addition/deletion of new associations requires recalculation of the generalized inverse, which becomes computationally costly for large systems. A better solution is to calculate the generalized inverse recursively. The proposed algorithm is a modification of the well known algorithm due to Rust et al. [2], originally introduced for nonrecursive computation. We compare our algorithm with Greville's recursive algorithm and conclude that our algorithm provides better numerical stability at the expense of little extra computation time and additional storage.", acknowledgement = ack-nhfb, keywords = "algorithms; performance; theory", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Matrix inversion. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Pseudoinverses. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Keast:1991:AEM, author = "P. Keast and P. H. Muir", title = "{Algorithm 688}: {EPDCOL}: {A} More Efficient {PDECOL} Code", journal = j-TOMS, volume = "17", number = "2", pages = "153--166", month = jun, year = "1991", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 23:44:20 1994", URL = "http://doi.acm.org/10.1145/108556.108558", abstract = "The software package PDECOL [7] is a popular code among scientists wishing to solve systems of nonlinear partial differential equations. The code is based on a method-of-lines approach, with collocation in the space variable to reduce the problem to a system of ordinary differential equations. There are three principal components: the basis functions employed in the collocation; the method used to solve the system of ordinary differential equations; and the linear equation solver which handles the linear algebra. This paper will concentrate on the third component, and will report on the improvement in the performance of PDECOL resulting from replacing the current linear algebra modules of the code by modules which take full advantage of the special structure of the equations which arise. Savings of over 50 percent in total execution time can be realized.", acknowledgement = ack-nhfb, keywords = "algorithms; performance", subject = "{\bf G.1.8}: Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations. {\bf G.1.5}: Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations. {\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Blom:1991:ADC, author = "J. G. Blom and H. Brunner", title = "{Algorithm 689}: Discretized Collocation and Iterated Collocation for Nonlinear {Volterra} Integral Equations of the Second Kind", journal = j-TOMS, volume = "17", number = "2", pages = "167--177", month = jun, year = "1991", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 23:44:20 1994", URL = "http://doi.acm.org/10.1145/108556.108562", abstract = "This paper describes a FORTRAN code for calculating approximate solutions to systems of nonlinear Volterra integral equations of the second kind. The algorithm is based on polynomial spline collocation, with the possibility of combination with the corresponding iterated collocation. It exploits certain local superconvergence properties for the error estimation and the stepsize strategy.", acknowledgement = ack-nhfb, keywords = "algorithms; performance; reliability", subject = "{\bf G.1.9}: Mathematics of Computing, NUMERICAL ANALYSIS, Integral Equations, Volterra equations. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Spline and piecewise polynomial approximation. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Berzins:1991:ACP, author = "M. Berzins and P. M. Dew", title = "{Algorithm 690}: {Chebyshev} Polynomial Software for Elliptic-Parabolic Systems of {PDEs}", journal = j-TOMS, volume = "17", number = "2", pages = "178--206", month = jun, year = "1991", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 23:44:20 1994", URL = "http://doi.acm.org/10.1145/108556.108566", abstract = "PDECHEB is a FORTRAN 77 software package that semidiscretizes a wide range of time-dependent partial differential equations in one space variable. The software implements a family of spacial discretization formulas, based on piecewise Chebyshev polynomial expansions with $C^{0}$ continuity. The package has been designed to be used in conjunction with a general integrator for initial value problems to provide a powerful software tool for the solution of parabolic-elliptic PDEs with coupled differential algebraic equations. Examples are provided to illustrate the use of the package with the DASSL d.a.e integrator of Petzold [18].", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.1.8}: Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Elliptic equations. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf G.1.8}: Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Parabolic equations.", } @Article{Favati:1991:IIF, author = "Paola Favati and Grazia Lotti and Francesco Romani", title = "Interpolatory Integration Formulas for Optimal Composition", journal = j-TOMS, volume = "17", number = "2", pages = "207--217", month = jun, year = "1991", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D30", MRnumber = "92k:65035", bibdate = "Sun Sep 04 23:44:20 1994", URL = "http://doi.acm.org/10.1145/108556.108571", abstract = "A set of symmetric, closed, interpolatory integration formulas on the interval [-1, 1] with positive weights and increasing degree of precision is introduced. These formulas, called recursive monotone stable (RMS) formulas, allow applying higher order or compound rules without wasting previously computed functional values. An exhaustive search shows the existence of 27 families of RMS formulas, stemming from the simple trapezoidal rule.", acknowledgement = ack-nhfb, keywords = "algorithms; theory", subject = "{\bf G.1.4}: Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation, Adaptive quadrature. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation, Interpolation formulas.", } @Article{Favati:1991:AIQ, author = "Paola Favati and Grazia Lotti and Francesco Romani", title = "{Algorithm 691}: Improving {QUADPACK} Automatic Integration Routines", journal = j-TOMS, volume = "17", number = "2", pages = "218--232", month = jun, year = "1991", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D30 (65Y10)", MRnumber = "92k:65036", bibdate = "Sun Sep 04 23:44:20 1994", URL = "http://doi.acm.org/10.1145/108556.108580", abstract = "Two automatic adaptive integrators from QUADPACK (namely, QAG, and QAGS) are modified by substituting the Gauss-Kronrod rules used for local quadrature with recursive monotone stable (RMS) formulas. Extensive numerical tests, both for one-dimensional and two-dimensional integrals, show that the resulting programs are faster, perform less functional evaluations, and are more suitable", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.1.4}: Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation, Adaptive quadrature. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Berntsen:1991:EEA, author = "Jarle Berntsen and Terje O. Espelid", title = "Error Estimation in Automatic Quadrature Routines", journal = j-TOMS, volume = "17", number = "2", pages = "233--252", month = jun, year = "1991", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65G99 (65D20 65Y10)", MRnumber = "92m:65067", bibdate = "Sun Sep 04 23:44:20 1994", URL = "http://doi.acm.org/10.1145/108556.108575", abstract = "A new algorithm for estimating the error in quadrature approximations is presented. Based on the same integrand evaluations that we need for approximating the integral, one may, for many quadrature rules, compute a sequence of null rule approximations. These null rule approximations are then used to produce an estimate of the local error. The algorithm allows us to take advantage of the degree of precision of the basic quadrature rule. In the experiments we show that the algorithm works satisfactorily for a selection of different quadrature rules on all test families of integrals.", acknowledgement = ack-nhfb, keywords = "algorithms; experimentation", subject = "{\bf G.1.4}: Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation, Adaptive quadrature. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation.", } @Article{Dodson:1991:SEF, author = "David S. Dodson and Roger G. Grimes and John G. Lewis", title = "Sparse Extensions to the {FORTRAN Basic Linear Algebra Subroutines}", journal = j-TOMS, volume = "17", number = "2", pages = "253--263", month = jun, year = "1991", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 23:44:20 1994", URL = "http://doi.acm.org/10.1145/108556.108577", abstract = "This paper describes an extension to the set of Basic Linear Algebra Subprograms. The extension is targeted at sparse vector operations, with the goal of providing efficient, but portable, implementations of algorithms for high-performance computers.", acknowledgement = ack-nhfb, keywords = "algorithms; standardization", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse and very large systems. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Portability. {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN. {\bf D.2.2}: Software, SOFTWARE ENGINEERING, Tools and Techniques, Software libraries. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices.", } @Article{Dodson:1991:AMI, author = "David S. Dodson and Roger G. Grimes and John G. Lewis", title = "{Algorithm 692}: Model Implementation and Test Package for the Sparse {Basic Linear Algebra Subroutines}", journal = j-TOMS, volume = "17", number = "2", pages = "264--272", month = jun, year = "1991", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 23:44:20 1994", URL = "http://doi.acm.org/10.1145/108556.108582", abstract = "This paper describes a model implementation and test software for the Sparse Basic Linear Algebra Subprograms (Sparse BLAS). The Sparse BLAS perform vector operations common in sparse linear algebra, with the goal of providing efficient, but portable, implementations of algorithms for high performance computers. The model implementation provides a portable set of FORTRAN 77 Sparse BLAS for the use on machines where specially tuned implementations do not exist or are not required. The test software is designed to verify that tuned implementations meet the specifications of the Sparse BLAS and that implementations are correctly installed.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse and very large systems. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN 77.", } @Article{Smith:1991:AFP, author = "David M. Smith", title = "{Algorithm 693}: {A FORTRAN} Package for Floating-Point Multiple-Precision Arithmetic", journal = j-TOMS, volume = "17", number = "2", pages = "273--283", month = jun, year = "1991", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 23:44:20 1994", URL = "http://doi.acm.org/10.1145/108556.108585", abstract = "FM is a collection of FORTRAN-77 routines which performs floating-point multiple-precision arithmetic and elementary functions. Results are almost always correctly rounded, and due to improved algorithms used for elementary functions, reasonable efficiency is obtained.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN 77.", } @Article{Higham:1991:ACT, author = "Nicholas J. Higham", title = "{Algorithm 694}: {A} Collection of Test Matrices in {MATLAB}", journal = j-TOMS, volume = "17", number = "3", pages = "289--305", month = sep, year = "1991", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 23:52:04 1994", URL = "http://doi.acm.org/10.1145/114697.116805", acknowledgement = ack-nhfb, keywords = "algorithms; experimentation; performance; theory", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra.", } @Article{Eskow:1991:ASN, author = "Elizabeth Eskow and Robert B. Schnabel", title = "{Algorithm 695}: Software for a New Modified {Cholesky} Factorization", journal = j-TOMS, volume = "17", number = "3", pages = "306--312", month = sep, year = "1991", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 23:52:04 1994", URL = "http://doi.acm.org/10.1145/114697.116806", acknowledgement = ack-nhfb, keywords = "algorithms; theory", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra.", } @Article{Rothberg:1991:ESM, author = "Edward Rothberg and Anoop Gupta", title = "Efficient Sparse Matrix Factorization on High-Performance Workstations\emdash Exploiting the Memory Hierarchy", journal = j-TOMS, volume = "17", number = "3", pages = "313--334", month = sep, year = "1991", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 23:52:04 1994", URL = "http://doi.acm.org/10.1145/114697.116809", acknowledgement = ack-nhfb, keywords = "algorithms; design; experimentation; performance", subject = "{\bf B.3.2}: Hardware, MEMORY STRUCTURES, Design Styles, Cache memories. {\bf C.5.3}: Computer Systems Organization, COMPUTER SYSTEM IMPLEMENTATION, Microcomputers, Workstations. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse and very large systems. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Schrauf:1991:AIR, author = "G{\'e}za Schrauf", title = "{Algorithm 696}: An Inverse {Rayleigh} Iteration for Complex Band Matrices", journal = j-TOMS, volume = "17", number = "3", pages = "335--340", month = sep, year = "1991", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 23:52:04 1994", URL = "http://doi.acm.org/10.1145/114697.116807", acknowledgement = ack-nhfb, keywords = "algorithms; theory", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Eigenvalues. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices. {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN 77.", } @Article{Akima:1991:MUI, author = "Hiroshi Akima", title = "A Method for Univariate Interpolation that Has the Accuracy of a Third-Degree Polynomial", journal = j-TOMS, volume = "17", number = "3", pages = "341--366", month = sep, year = "1991", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 23:52:04 1994", URL = "http://doi.acm.org/10.1145/114697.116810", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation, Spline and piecewise polynomial interpolation.", } @Article{Akima:1991:AUI, author = "Hiroshi Akima", title = "{Algorithm 697}: Univariate Interpolation that Has the Accuracy of a Third-Degree Polynomial", journal = j-TOMS, volume = "17", number = "3", pages = "367--367", month = sep, year = "1991", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 23:52:04 1994", URL = "http://doi.acm.org/10.1145/114697.116808", acknowledgement = ack-nhfb, keywords = "algorithms; theory", subject = "{\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation, Spline and piecewise polynomial interpolation.", } @Article{Higham:1991:HCR, author = "D. J. Higham", title = "Highly Continuous {Runge-Kutta} Interpolants", journal = j-TOMS, volume = "17", number = "3", pages = "368--386", month = sep, year = "1991", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65L06", MRnumber = "92m:65092", bibdate = "Sun Sep 04 23:52:04 1994", URL = "http://doi.acm.org/10.1145/114697.103150", abstract = "To augment the discrete Runge-Kutta solution to the minimal value problem, piecewise Hermite interpolants have been used to provide a continuous approximation with a continuous first derivative. We show that it is possible to construct interpolants with arbitrarily many continuous derivatives which have the same asymptotic accuracy and basic cost as the Hermite interpolants. We also show that the usual truncation coefficient analysis can be applied to these new interpolants, allowing their accuracy to be examined in more detail. As an illustration, we present some globally $C^2$ interpolants for use with a popular 4th and 5th order Runge-Kutta pair of Dormand and Prince, and we compare them theoretically and numerically with existing interpolants.", acknowledgement = ack-nhfb, keywords = "algorithms; theory", subject = "{\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Single step methods. {\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Initial value problems. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation. {\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation.", } @Article{Sharp:1991:NCS, author = "P. W. Sharp", title = "Numerical Comparisons of Some Explicit {Runge-Kutta} Pair of Orders 3 Through 8", journal = j-TOMS, volume = "17", number = "3", pages = "387--409", month = sep, year = "1991", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 23:52:04 1994", URL = "http://doi.acm.org/10.1145/114697.116811", abstract = "We performed numerical testing of six explicit Runge-Kutta pairs ranging in order from a (3,4) pair to a (7,8) pair. All the test problems had smooth solutions and we assumed dense output was not required. The pairs were implemented in a uniform way. In particular, the stepsize selection for all pairs was based on the locally optimal formula. We tested the efficiency of the pairs, to what extent tolerance proportionality held, the accuracy of the local error estimate and stepsize prediction, and the performance on mildly stiff problems. We also showed, for these pairs, how the performance could be altered noticeably by making simple changes to the stepsize selection strategy. As part of the work, we demonstrated new ways of presenting numerical comparisons.", acknowledgement = ack-nhfb, keywords = "algorithms; performance; reliability", subject = "{\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Initial value problems. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing.", } @Article{Ziv:1991:FEE, author = "Abraham Ziv", title = "Fast Evaluation of Elementary Mathematical Functions with Correctly Rounded Last Bit", journal = j-TOMS, volume = "17", number = "3", pages = "410--423", month = sep, year = "1991", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Thu Sep 1 10:15:31 1994", bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", URL = "http://doi.acm.org/10.1145/114697.116813", acknowledgement = ack-nj, keywords = "algorithms; standardization; theory", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency.", } @Article{Higham:1991:RBF, author = "Desmond J. Higham", title = "Remark on ``{Algorithm 669}: {BRKF45}: {A FORTRAN} Subroutine for Solving First-Order Systems of Nonstiff Initial Value Problems for Ordinary Differential Equations''", journal = j-TOMS, volume = "17", number = "3", pages = "424--426", month = sep, year = "1991", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 23:52:04 1994", note = "See \cite{Cash:1989:ABF}.", URL = "http://doi.acm.org/10.1145/114697.116814", acknowledgement = ack-nhfb, keywords = "algorithms; theory", subject = "{\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation.", } @Article{Krogh:1991:AAP, author = "Fred T. Krogh", title = "{ACM} Algorithms Policy", journal = j-TOMS, volume = "17", number = "3", pages = "427--430", month = sep, year = "1991", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 23:52:04 1994", URL = "http://doi.acm.org/10.1145/114697.356357", acknowledgement = ack-nhfb, } @Article{Berntsen:1991:AAA, author = "Jarle Berntsen and Terje O. Espelid and Alan Genz", title = "An Adaptive Algorithm for the Approximate Calculation of Multiple Integrals", journal = j-TOMS, volume = "17", number = "4", pages = "437--451", month = dec, year = "1991", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65-04 (65D30)", MRnumber = "1 140 034", bibdate = "Sun Sep 04 23:59:35 1994", URL = "http://doi.acm.org/10.1145/210232.210233", acknowledgement = ack-nhfb, keywords = "algorithms; theory", subject = "{\bf G.1.4}: Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Berntsen:1991:ADA, author = "Jarle Berntsen and Terje O. Espelid and Alan Genz", title = "{Algorithm 698}: {DCUHRE}: An Adaptive Multidimensional Integration Routine for a Vector of Integrals", journal = j-TOMS, volume = "17", number = "4", pages = "452--456", month = dec, year = "1991", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65-04 (65D30)", MRnumber = "1 140 035", bibdate = "Sun Sep 04 23:59:35 1994", URL = "http://doi.acm.org/10.1145/210232.210234", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.1.4}: Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Krogh:1991:ANR, author = "Fred T. Krogh and W. Van Snyder", title = "{Algorithm 699}: {A} New Representation of {Patterson}'s Quadrature Formulae", journal = j-TOMS, volume = "17", number = "4", pages = "457--461", month = dec, year = "1991", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Sep 05 09:54:59 1994", URL = "http://doi.acm.org/10.1145/210232.210235", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.1.4}: Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Broughan:1991:SHL, author = "Kevin A. Broughan", title = "{SENAC}: {A} High-Level Interface for the {NAG} Library", journal = j-TOMS, volume = "17", number = "4", pages = "462--480", month = dec, year = "1991", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 23:59:35 1994", URL = "http://doi.acm.org/10.1145/210232.210236", acknowledgement = ack-nhfb, keywords = "design; languages; performance; theory", subject = "{\bf D.2.2}: Software, SOFTWARE ENGINEERING, Tools and Techniques. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf I.1.3}: Computing Methodologies, ALGEBRAIC MANIPULATION, Languages and Systems. {\bf I.2.2}: Computing Methodologies, ARTIFICIAL INTELLIGENCE, Automatic Programming.", } @Article{Marletta:1991:CAN, author = "Marco Marletta", title = "Certification of {Algorithm 700}: Numerical Tests of the {SLEIGN} Software for {Sturm-Liouville} Problems", journal = j-TOMS, volume = "17", number = "4", pages = "481--490", month = dec, year = "1991", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sun Sep 04 23:59:35 1994", URL = "http://doi.acm.org/10.1145/210232.210237", acknowledgement = ack-nhfb, keywords = "algorithms; performance; reliability", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf G.1}: Mathematics of Computing, NUMERICAL ANALYSIS.", } @Article{Bailey:1991:EEC, author = "Paul B. Bailey and Burton S. Garbow and Hans G. Kaper and Anton Zettl", title = "Eigenvalue and Eigenfunction Computations for {Sturm-Liouville} Problems", journal = j-TOMS, volume = "17", number = "4", pages = "491--499", month = dec, year = "1991", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65L15", MRnumber = "1 140 036", bibdate = "Sun Sep 04 23:59:35 1994", URL = "http://doi.acm.org/10.1145/210232.210238", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations.", } @Article{Bailey:1991:AFS, author = "Paul B. Bailey and Burton S. Garbow and Hans G. Kaper and Anton Zettl", title = "{Algorithm 700}: {A FORTRAN} Software Package for {Sturm-Liouville} Problems", journal = j-TOMS, volume = "17", number = "4", pages = "500--501", month = dec, year = "1991", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65L15", MRnumber = "1 140 037", bibdate = "Sun Sep 04 23:59:35 1994", URL = "http://doi.acm.org/10.1145/210232.210239", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.m}: Mathematics of Computing, MISCELLANEOUS.", } @Article{Alfeld:1991:EAS, author = "Peter Alfeld and David J. Eyre", title = "The Exact Analysis of Sparse Rectangular Linear Systems", journal = j-TOMS, volume = "17", number = "4", pages = "502--518", month = dec, year = "1991", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65-04 (65F50)", MRnumber = "1 140 038", bibdate = "Sun Sep 04 23:59:35 1994", URL = "http://doi.acm.org/10.1145/210232.210240", acknowledgement = ack-nhfb, keywords = "measurement; performance; theory", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra.", } @Article{Alfeld:1991:AGE, author = "Peter Alfeld and David J. Eyre", title = "{Algorithm 701}: {Goliath}\emdash {A} Software System for the Exact Analysis of Rank-Deficient Sparse Rational Linear Systems", journal = j-TOMS, volume = "17", number = "4", pages = "519--532", month = dec, year = "1991", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65-04 (65F50)", MRnumber = "1 140 039", bibdate = "Sun Sep 04 23:59:35 1994", URL = "http://doi.acm.org/10.1145/210232.210241", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra.", } @Article{Gustafsson:1991:CTT, author = "Kjell Gustafsson", title = "Control Theoretic Techniques for Stepsize Selection in Explicit {Runge-Kutta} Methods", journal = j-TOMS, volume = "17", number = "4", pages = "533--554", month = dec, year = "1991", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65-04 (65L06)", MRnumber = "1 140 040", bibdate = "Sun Sep 04 23:59:35 1994", URL = "http://doi.acm.org/10.1145/210232.210242", acknowledgement = ack-nhfb, keywords = "algorithms; theory", subject = "{\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Reliability and robustness.", } @Article{Boubez:1992:PED, author = "Toufic I. Boubez and Andy M. Froncioni and Richard L. Peskin", title = "A Prototyping Envelope for Differential Equations", journal = j-TOMS, volume = "18", number = "1", pages = "1--10", month = mar, year = "1992", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Sep 05 08:43:51 1994", URL = "http://doi.acm.org/10.1145/128745.128746", abstract = "A system is presented to allow end users to solve nonlinear differential equations without need to write computer programs. The system treats $n$th order space (one dimensional), first order time systems with initial and/or two point boundary value specification. Users of the system need only enter the problem in direct mathematical notation, and output is automatically presented as a solution graph. The system allows the user to alter this equations, in-situ, that is to computationally steer his model. Thus the system is suited for model prototyping. Implementation is based on an object-oriented paradigm, well established and robust numerical procedures, and distributed computing to supported needed resources for numerically intensive tasks.", acknowledgement = ack-nhfb, keywords = "design; experimentation; languages", subject = "{\bf D.2.6}: Software, SOFTWARE ENGINEERING, Programming Environments. {\bf D.2.m}: Software, SOFTWARE ENGINEERING, Miscellaneous. {\bf G.1.5}: Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations. {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, Smalltalk.", } @Article{Lucks:1992:ASM, author = "Michael Lucks and Ian Gladwell", title = "Automated Selection of Mathematical Software", journal = j-TOMS, volume = "18", number = "1", pages = "11--34", month = mar, year = "1992", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Sep 05 08:43:51 1994", URL = "http://doi.acm.org/10.1145/128745.128747", abstract = "Current approaches to recommending mathematical software are qualitative and categorical. These approaches are unsatisfactory when the problem to be solved has features that can ``trade-off'' in the recommendation process. A quantitative system is proposed that permits tradeoffs and can be built and modified incrementally. This quantitative approach extends other knowledge-engineering techniques in its knowledge representation and aggregation facilities. The system is demonstrated on the domain of ordinary differential equation initial value problems. The results are significantly superior to an existing qualitative (decision tree) system.", acknowledgement = ack-nhfb, keywords = "algorithms; performance", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Initial value problems. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf I.2.4}: Computing Methodologies, ARTIFICIAL INTELLIGENCE, Knowledge Representation Formalisms and Methods, Representation languages.", } @Article{Olszewski:1992:FTA, author = "Jan Olszewski", title = "A Flexible Thinning Algorithm Allowing Parallel, Sequential, and Distributed Application", journal = j-TOMS, volume = "18", number = "1", pages = "35--45", month = mar, year = "1992", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Sep 05 09:54:33 1994", URL = "http://doi.acm.org/10.1145/128745.128748", abstract = "A parallel thinning algorithm for digital patterns is presented. This algorithm can also be used for sequential thinning without the simulation of parallel computation. The mathematical background of the algorithm bases on the notion of the Euler characteristic. The proposed algorithm is simple and particularly faster than other parallel algorithms.", acknowledgement = ack-nhfb, keywords = "algorithms; design; theory", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Parallel algorithms. {\bf I.5.2}: Computing Methodologies, PATTERN RECOGNITION, Design Methodology. {\bf I.4.1}: Computing Methodologies, IMAGE PROCESSING, Digitization. {\bf D.1.3}: Software, PROGRAMMING TECHNIQUES, Concurrent Programming.", } @Article{Schlick:1992:TETa, author = "Tamar Schlick and Aaron Fogelson", title = "{TNPACK}\emdash {A} Truncated {Newton} Minimization Package for Large-Scale Problems: {I}. Algorithm and Usage", journal = j-TOMS, volume = "18", number = "1", pages = "46--70", month = mar, year = "1992", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Feb 10 08:50:20 1996", URL = "http://doi.acm.org/10.1145/128745.150973", abstract = "We present a FORTRAN package of subprograms for minimizing multivariate functions without constraints by a truncated Newton algorithm. The algorithm is especially suited for problems involving a large number of variables. Truncated Newton methods allow approximate, rather than exact, solutions to the Newton equations. Truncation is accomplished in the present version by using the preconditioned Conjugate Gradient algorithm (PCG) to solve approximately the Newton equations. The preconditioner $M$ is factored in PCG using a sparse modified Cholesky factorization based on the Yale Sparse Matrix Package. In this paper we briefly describe the method and provide details for program usage.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse and very large systems. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Nonlinear programming.", } @Article{Schlick:1992:TETb, author = "Tamar Schlick and Aaron Fogelson", title = "{TNPACK}\emdash {A} Truncated {Newton} Minimization Package for Large-Scale Problems: {II}. Implementation Examples", journal = j-TOMS, volume = "18", number = "1", pages = "71--111", month = mar, year = "1992", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Feb 10 08:50:15 1996", URL = "http://doi.acm.org/10.1145/128745.150975", acknowledgement = ack-nhfb, keywords = "algorithms; performance", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse and very large systems. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Nonlinear programming. {\bf I.6.3}: Computing Methodologies, SIMULATION AND MODELING, Applications. {\bf J.2}: Computer Applications, PHYSICAL SCIENCES AND ENGINEERING. {\bf J.3}: Computer Applications, LIFE AND MEDICAL SCIENCES.", } @Article{Hanson:1992:QTM, author = "R. J. Hanson and Fred T. Krogh", title = "A Quadratic-Tensor Model Algorithm for Nonlinear Least-Squares Problems with Linear Constraints", journal = j-TOMS, volume = "18", number = "2", pages = "115--133", month = jun, year = "1992", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65Y10 (49M30)", MRnumber = "1 167 883", bibdate = "Mon Sep 05 08:48:51 1994", URL = "http://doi.acm.org/10.1145/146847.146857", abstract = "A new algorithm is presented for solving nonlinear least-squares and nonlinear equation problems. The algorithm is based on approximating the nonlinear functions using the quadratic-tensor model proposed by Schnabel and Frank. The problem statement may include simple bounds or more general linear constraints on the unknowns. The algorithm uses a trust-region defined by a box containing the current values of the unknowns. The objective function (Euclidean length of the functions) is allowed to increase at intermediate steps. These increases are allowed as long as our predictor indicates that a new set of best values exists in the trust-region. There is logic provided to retreat to the current best values, should that be required. The computations for the model-problem require a constrained nonlinear least-squares solver. This is done using a simpler version of the algorithm. In its present form the algorithm is effective for problems with linear constraints and dense Jacobian matrices. Results on standard test problems are presented in the Appendix. The new algorithm appears to be efficient in terms of function and Jacobian evaluations.", acknowledgement = ack-nhfb, keywords = "algorithms; performance", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Nonlinear programming.", } @Article{Gurwitz:1992:TCE, author = "Chaya Gurwitz", title = "A Test for Cancellation Errors In Quasi-{Newton} Methods", journal = j-TOMS, volume = "18", number = "2", pages = "134--140", month = jun, year = "1992", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65K10 (90C30)", MRnumber = "1 167 884", bibdate = "Mon Sep 05 08:48:51 1994", URL = "http://doi.acm.org/10.1145/146847.146876", abstract = "It has recently been shown that cancellation errors in a quasi-Newton method can increase without bound as the method converges. A simple test is presented to determine when cancellation errors could lead to significant contamination of the approximating matrix.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Reliability and robustness.", } @Article{Schlick:1992:ATE, author = "Tamar Schlick and Aaron Fogelson", title = "{Algorithm 702}: {TNPACK}\emdash {A} Truncated {Newton} Minimization Package for Large-Scale Problems: {I}. Algorithm and Usage", journal = j-TOMS, volume = "18", number = "2", pages = "141--141", month = jun, year = "1992", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Feb 10 08:50:33 1996", note = "See remark \cite{Xie:1999:RAU}.", URL = "http://doi.acm.org/10.1145/146847.146921", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse and very large systems. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Nonlinear programming.", } @Article{Cash:1992:MCS, author = "J. R. Cash and S. Considine", title = "An {MEBDF} Code for Stiff Initial Value Problems", journal = j-TOMS, volume = "18", number = "2", pages = "142--155", month = jun, year = "1992", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D05 (65L06)", MRnumber = "1 167 885", bibdate = "Mon Sep 05 08:48:51 1994", URL = "http://doi.acm.org/10.1145/146847.146922", abstract = "In two recent papers one of the present authors has proposed a class of modified extended backward differentiation formulae for the numerical integration of stiff initial value problems. In this paper we describe a code based on this class of formulae and discuss its performance on a large set of stiff test problems.", acknowledgement = ack-nhfb, keywords = "algorithms; performance", subject = "{\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Initial value problems. {\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation. {\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Multistep methods. {\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Stiff equations. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Cash:1992:AMF, author = "J. R. Cash and S. Considine", title = "{Algorithm 703}: {MEBDF}: {A FORTRAN} Subroutine for Solving First-Order Systems of Stiff Initial Value Problems for Ordinary Differential Equations", journal = j-TOMS, volume = "18", number = "2", pages = "156--158", month = jun, year = "1992", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D05 (65L06)", MRnumber = "1 167 886", bibdate = "Mon Sep 05 08:48:51 1994", URL = "http://doi.acm.org/10.1145/146847.146923", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Initial value problems. {\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation. {\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Multistep methods. {\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Stiff equations. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Neidinger:1992:EMN, author = "Richard D. Neidinger", title = "An Efficient Method for the Numerical Evaluation of Partial Derivatives of Arbitrary Order", journal = j-TOMS, volume = "18", number = "2", pages = "159--173", month = jun, year = "1992", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D25 (65Y10)", MRnumber = "93b:65040", bibdate = "Mon Sep 05 08:48:51 1994", URL = "http://doi.acm.org/10.1145/146847.146924", abstract = "For any typical multivariable expression $f$, point $a$ in the domain of $f$, and positive integer maxorder, this method produces the numerical values of all partial derivatives at $a$ up through order maxorder. By the technique known as automatic differentiation, theoretically exact results are obtained using numerical (as opposed to symbolic) manipulation. The key ideas are a hyperpyramid data structure and a generalized Leibniz's rule. Any expression in $n$ variables corresponds to a hyperpyramid array, in $n$-dimensional space, containing the numerical values of all unique partial derivatives (not wasting space on different permutations of derivatives). The arrays for simple expressions are combined by hyperpyramid operators to form the arrays for more complicated expressions. These operators are facilitated by a generalized Leibniz's rule which, given a product of multivariable functions, produces any partial derivative by forming the minimum number of products (between two lower partials) together with a product of binomial coefficients. The algorithms are described in abstract pseudo-code. A section on implementation shows how these ideas can be converted into practical and efficient programs in a typical computing environment. For any specific problem, only the expression itself would require recoding.", acknowledgement = ack-nhfb, keywords = "algorithms; performance", subject = "{\bf G.1.4}: Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation. {\bf I.1.2}: Computing Methodologies, ALGEBRAIC MANIPULATION, Algorithms, Nonalgebraic algorithms. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency.", } @Article{Edwards:1992:EEN, author = "John A. Edwards", title = "Exact Equations of the Nonlinear Spline", journal = j-TOMS, volume = "18", number = "2", pages = "174--192", month = jun, year = "1992", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "41A15 (65D05 65D07 65K10 65Y25)", MRnumber = "93c:41018", bibdate = "Mon Sep 05 08:48:51 1994", URL = "http://doi.acm.org/10.1145/146847.146925", abstract = "We define the spline interpolating function, and obtain in directly computable form the elementary set of nonlinear equations describing nonlinear spline curves. Using Newton's and Newton-like methods, we solve typical spline configurations, and hence infer that the procedure will reliably yield precise extremum-energy solutions to nonlinear splines of arbitrary (but presumably reasonable) size and complexity.\par In order to distinguish between stable and unstable states of spline equilibria, we evaluate the energy change resulting from a perturbation, and we briefly discuss aspects of spline existence and uniqueness in relation to the solved examples. We demonstrate the abrupt transition which occurs at the threshold between spline existence and nonexistence, and conclude that proof of a spline's existence is implicit in the solution set of constants yielded by the method.\par The procedure may be regarded on the one hand as a precise and efficient research instrument for investigating the properties of true splines and elastica, and on the other as an everyday method for obtaining ``the smoothest interpolating curve of all''.\par Contact is always maintained with the physical analogue to the curve, the thin uniform elastic beam, since the four assignable parameters used in each spline interval comprise the necessary and sufficient three angles and one length dimension of the actual physical spline.\par On an historical note, the method may be seen to offer progress in the search, begun in the late 17th century, for a definitive solution to the elastica problem.", acknowledgement = ack-nhfb, keywords = "algorithms; theory", subject = "{\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation, Spline and piecewise polynomial interpolation. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Constrained optimization. {\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Boundary value problems. {\bf I.3.5}: Computing Methodologies, COMPUTER GRAPHICS, Computational Geometry and Object Modeling, Splines. {\bf J.2}: Computer Applications, PHYSICAL SCIENCES AND ENGINEERING, Engineering. {\bf J.2}: Computer Applications, PHYSICAL SCIENCES AND ENGINEERING, Physics.", } @Article{Majaess:1992:SAB, author = "Fouad Majaess and Patrick Keast and Graeme Fairweather and Karin R. Bennett", title = "The Solution of Almost Block Diagonal Linear Systems Arising in Spline Collocation at {Gaussian} Points with Monomial Basis Functions", journal = j-TOMS, volume = "18", number = "2", pages = "193--204", month = jun, year = "1992", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65-04 (65D15 65F05)", MRnumber = "93a:65002", bibdate = "Mon Sep 05 08:48:51 1994", URL = "http://doi.acm.org/10.1145/146847.146926", abstract = "Numerical techniques based on piecewise polynomial (that is, spline) collation at Gaussian points are exceedingly effective for the approximate solution of boundary value problems, both for ordinary differential equations and for time dependent partial differential equations. There are several widely available computer codes based on this approach, all of which have at their core a particular choice of basis representation for the piecewise polynomials used to approximate the solutions. Until recently, the most popular approach was to use a B-spline representation, but it has been shown that the B-spline basis is inferior, both in operation counts and conditioning, to a certain monomial basis, and the latter has come more into favor. In this paper, we describe a linear algebraic equations which arise in spline collocation at Gaussian points with such a monomial basis. It is shown that the new package, which implements an alternate column and row pivoting algorithm, is a distinct improvement over existing packages from the points of view of speed and storage requirements. In addition, we describe a second package, an important special case of the first, for solving the almost block diagonal systems which arise when condensation is applied to the systems arising in spline collocation at Gaussian points, and also in other methods for solving two-point boundary value problems, such as implicit Runge-Kutta methods and multiple shooting.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods).", } @Article{Majaess:1992:AAA, author = "Fouad Majaess and Patrick Keast and Graeme Fairweather and Karin R. Bennett", title = "{Algorithm 704}: {ABDPACK} and {ABBPACK}\emdash {FORTRAN} Programs for the Solution of Almost Block Diagonal Linear Systems Arising in Spline Collocation at {Gaussian} Points with Monomial Basis Functions", journal = j-TOMS, volume = "18", number = "2", pages = "205--210", month = jun, year = "1992", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65-04 (65F05)", MRnumber = "93a:65003", bibdate = "Mon Sep 05 08:48:51 1994", URL = "http://doi.acm.org/10.1145/146847.146927", abstract = "ABDPACK is a package of FORTRAN programs for the solution of systems of linear equations with the almost block diagonal structure arising in spline collocation at Gaussian points with monomial spline basis functions, when applied to two-point boundary value problems with separated boundary conditions. The package ABBPACK is designed to handle a subclass of such linear systems which have what may be called an almost block bidiagonal structure. Such systems result, for example, when condensation is applied to the full spline collocation linear system. This package may also be used to solve the almost block bidiagonal systems arising in multiple shooting techniques and implicit Runge-Kutta methods for solving two-point boundary value problems. The algorithms implemented in the package are based on an alternate column and row pivoting scheme which avoids most of the fill-in introduced by more commonly used techniques.", acknowledgement = ack-nhfb, keywords = "algorithms; standardization", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Spline and piecewise polynomial approximation. {\bf I.1.2}: Computing Methodologies, ALGEBRAIC MANIPULATION, Algorithms. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Tang:1992:TDI, author = "Ping Tak Peter Tang", title = "Table-Driven Implementation of the Expm1 Function in {IEEE} Floating-Point Arithmetic", journal = j-TOMS, volume = "18", number = "2", pages = "211--222", month = jun, year = "1992", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D15", MRnumber = "1 167 891", bibdate = "Mon Sep 05 08:48:51 1994", URL = "http://doi.acm.org/10.1145/146847.146928", abstract = "Algorithms and implementation details for the function $e^x - 1$ in both single and double precision of IEEE 754 arithmetic are presented here. With a table of moderate size, the implementations need only working-precision arithmetic and are provably accurate to within 0.58 ulp.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Error analysis. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Gardiner:1992:SSM, author = "Judith D. Gardiner and Alan J. Laub and James J. Amato and Cleve B. Moler", title = "Solution of the {Sylvester} Matrix Equation {$AXB^{\sc{T}}+CXD^{\sc{T}}=E$}", journal = j-TOMS, volume = "18", number = "2", pages = "223--231", month = jun, year = "1992", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65F05 (65-04 65F10 65F35)", MRnumber = "1 167 892", bibdate = "Mon Sep 05 08:48:51 1994", URL = "http://doi.acm.org/10.1145/146847.146929", abstract = "A software package has been developed to solve efficiently the Sylvester-type matrix equation $AXB^{T} + CXD^{T} = E$. A transformation method is used which employs the QZ algorithm to structure the equation in such a way that it can be solved columnwise by a back substitution technique. The algorithm is an extension of the Bartels-Stewart method and the Hessenberg-Schur method. The numerical performance of the algorithms and software is demonstrated by application to near-singular systems.", acknowledgement = ack-nhfb, keywords = "algorithms; performance", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Conditioning. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Reliability and robustness. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices.", } @Article{Gardiner:1992:AFS, author = "Judith D. Gardiner and Matthew R. Wette and Alan J. Laub and James J. Amato and Cleve B. Moler", title = "{Algorithm 705}: {A FORTRAN-77} Software Package for Solving the {Sylvester} Matrix Equation {$AXB^{\sc{T}}+CXD^{\sc{T}}=E$}", journal = j-TOMS, volume = "18", number = "2", pages = "232--238", month = jun, year = "1992", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65F05 (65-04 65F10 65F35)", MRnumber = "1 167 893", bibdate = "Tue Mar 14 17:31:30 1995", note = "See corrections \cite{Hopkins:2002:RAF}.", URL = "http://doi.acm.org/10.1145/146847.146930", abstract = "This paper documents a software package for solving the Sylvester matrix equation (1) $AXB^{T} + CXD^{T} = E$.\par All quantities are real matrices; $A$ and $C$ are $m \times n$; $B$ and $D$ are $m \times n$; and $X$ and $E$ are $m \times n$. The unknown is $X$. Two symmetric forms of Eq. (1) are treated separately for efficiency. They are the continuous-time symmetric Sylvester equation (2) $AXE^{T} + EXA^{T} + C = 0$ and the discrete time equation (3) $AXA^{T} + C = 0$, for which $A$, $E$, and $C$ is symmetric. The software also provides a means for estimating the condition number of these three equations. The algorithms employed are more fully described in an accompanying paper [3].", acknowledgement = ack-nhfb, keywords = "algorithms; performance", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Conditioning. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Reliability and robustness.", } @Article{Weerawarana:1992:PCG, author = "Sanjiva Weerawarana and Paul S. Wang", title = "A Portable Code Generator for {CRAY FORTRAN}", journal = j-TOMS, volume = "18", number = "3", pages = "241--255", month = sep, year = "1992", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Sep 05 09:15:25 1994", URL = "http://doi.acm.org/10.1145/131766.131767", abstract = "One way to combine the powers of symbolic computing with numeric computing is to automatically derive and produce numeric code. This approach has important applications in science and engineering. Once the desired formulas and procedures are derived in a symbolic manipulation system, they can be translated into a target numeric language by a {\em code generator}. GENCRAY is a code generator written in the C language for portability. GENCRAY defines a LISP-style input language that is translated into either FORTRAN 77 or CRAY FORTRAN. By defining its own input syntax, GENCRAY becomes a free-standing code translator that can be made to work with any symbolic manipulation system. GENCRAY is portable to any computer system with a standard C compiler. Input to GENCRAY can come from a file or directly from a symbolic system through a pipe. On UNIX systems with Berkeley networking, GENCRAY also runs as a network server. The input syntax is customizable to allow both Common and Franz LISP input styles. In addition to generating easily vectorizable CRAY FORTRAN code, GENCRAY also provides high-level, easy-to-use parallel programming macros to produce parallel code for the multiprocessor CRAY systems. The features, applications, usage, and implementation of GENCRAY are described. Techniques for producing parallel codes are discussed and illustrated by a substantial example contained in the Appendix.", acknowledgement = ack-nhfb, keywords = "algorithms; design; theory", subject = "{\bf D.3.4}: Software, PROGRAMMING LANGUAGES, Processors, Code generation. {\bf D.1.2}: Software, PROGRAMMING TECHNIQUES, Automatic Programming. {\bf D.1.3}: Software, PROGRAMMING TECHNIQUES, Concurrent Programming. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General. {\bf I.1.4}: Computing Methodologies, ALGEBRAIC MANIPULATION, Applications. {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN. {\bf C.1.2}: Computer Systems Organization, PROCESSOR ARCHITECTURES, Multiple Data Stream Architectures (Multiprocessors), Array and vector processors. {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, C.", } @Article{Hansen:1992:FSG, author = "Per Christian Hansen and Tony F. Chan", title = "{FORTRAN} Subroutines for General {Toeplitz} Systems", journal = j-TOMS, volume = "18", number = "3", pages = "256--273", month = sep, year = "1992", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Nov 19 13:08:40 1994", note = "See also \cite{Hansen:1994:CAF}.", URL = "http://doi.acm.org/10.1145/131766.131768", abstract = "This paper presents FORTRAN 77 implementations of the lookahead Levinson algorithm of Chan and Hansen [7, 8] for solving symmetric indefinite and general Toeplitz systems. The algorithms are numerically stable for all Toeplitz matrices that do not have many {\em consecutive} ill-conditioned leading principal submatrices, and also produce estimates of the algorithm and matrix condition numbers. In contrast, the classical Levinson algorithm is only guaranteed to be numerically stable for symmetric positive definite Toeplitz matrices, and no condition estimate is produced.", acknowledgement = ack-nhfb, keywords = "algorithms; performance", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN 77.", } @Article{Demmel:1992:SBA, author = "James W. Demmel and Nicholas J. Higham", title = "Stability of Block Algorithms with Fast Level-3 {BLAS}", journal = j-TOMS, volume = "18", number = "3", pages = "274--291", month = sep, year = "1992", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Sep 30 01:27:16 1994", note = "See \cite{Dongarra:1990:ASL,Higham:1990:EFM,Dayde:1994:PBI}.", URL = "http://doi.acm.org/10.1145/131766.131769", abstract = "Block algorithms are becoming increasingly popular in matrix computations. Since their basic unit of data is a submatrix rather than a scalar, they have a higher level of granularity than point algorithms, and this makes them well suited to high-performance computers. The numerical stability of the block algorithms in the new linear algebra program library LAPACK is investigated here. It is shown that these algorithms have backward error analyses in which the backward error bounds are commensurate with the error bounds for the underlying level-3 BLAS (BLAS3). One implication is that the block algorithms are as stable as the corresponding point algorithms when conventional BLAS3 are used. A second implication is that the use of BLAS3 based on fast matrix multiplication techniques affects the stability only insofar as it increases the constant terms in the normwise backward error bounds. For linear equation solvers employing {\em LU} factorization, it is shown that fixed precision iterative refinement helps to mitigate the effect of the larger error constants. Despite the positive results presented here, not all plausible block algorithms are stable; we illustrate this with the example of {\em LU} factorization with block triangular factors and describe how to check a block algorithm for stability without doing a full error analysis.", acknowledgement = ack-nhfb, keywords = "algorithms; performance", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices.", } @Article{Ammar:1992:IDC, author = "G. S. Ammar and L. Reichel and D. C. Sorensen", title = "An Implementation of a Divide and Conquer Algorithm for the Unitary Eigenproblem", journal = j-TOMS, volume = "18", number = "3", pages = "292--307", month = sep, year = "1992", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Nov 19 13:08:42 1994", note = "See also \cite{Ammar:1994:CAI}.", URL = "http://doi.acm.org/10.1145/131766.131770", abstract = "We present a FORTRAN implementation of a divide-and-conquer method for computing the spectral resolution of a unitary upper Hessenberg matrix H. Any such matrix $H$ of order $n$, normalized so that its subdiagonal elements are nonnegative, can be written as a product of $n-1$ Givens matrices and a diagonal matrix. This representation, which we refer to as the Schur parametric form of $H$, arises naturally in applications such as in signal processing and in the computation of Gauss-Szego quadrature rules. Our programs utilize the Schur parametrization to compute the spectral decomposition of $H$ without explicitly forming the elements of H. If only the eigenvalues and first components of the eigenvectors are desired, as in the applications mentioned above, the algorithm requires only $O(n^{2})$ arithmetic operations. Experimental results presented indicate that the algorithm is reliable and competitive with the general QR algorithm applied to this problem. Moreover, the algorithm can be easily adapted for parallel implementation.", acknowledgement = ack-nhfb, keywords = "algorithms; measurement; performance; reliability", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Eigenvalues. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices.", } @Article{Toint:1992:LFS, author = "Ph. L. Toint and D. Tuyttens", title = "{LSNNO}, {A FORTRAN} Subroutine for Solving Large-Scale Nonlinear Network Optimization Problems", journal = j-TOMS, volume = "18", number = "3", pages = "308--328", month = sep, year = "1992", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Sep 30 01:27:49 1994", URL = "http://doi.acm.org/10.1145/131766.131771", abstract = "The implementation and testing of LSNNO, a new FORTRAN subroutine for solving large-scale nonlinear network optimization problems is described. The implemented algorithm applies the concepts of partial separability and partitioned quasi-Newton updating to high-dimensional nonlinear network optimization problems. Some numerical results on both academic and practical problems are reported.", acknowledgement = ack-nhfb, keywords = "algorithms; measurement; performance", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Nonlinear programming. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Constrained optimization. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency. {\bf G.2.2}: Mathematics of Computing, DISCRETE MATHEMATICS, Graph Theory, Network problems. {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN.", } @Article{Berntsen:1992:ADA, author = "Jarle Berntsen and Terje O. Espelid", title = "{Algorithm 706}: {DCUTRI}: An Algorithm for Adaptive Cubature Over a Collection of Triangles", journal = j-TOMS, volume = "18", number = "3", pages = "329--342", month = sep, year = "1992", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Mar 09 10:18:59 1999", note = "See remark \cite{Espelid:1998:RAD}.", URL = "http://doi.acm.org/10.1145/131766.131772", abstract = "An adaptive algorithm for computing an approximation to the integral of each element in a vector function $f(x,y)$ over a two-dimensional region made up of triangles is presented. A FORTRAN implementation of the algorithm is included. The basic cubature rule used over each triangle is a 37-point symmetric rule of degree 13. Based on the same evaluation points the local error for each element in the approximation vector and for each triangle is computed using a sequence of null rule evaluations. A sophisticated error-estimation procedure tries, in a cautious manner, to decide whether we have asymptotic behavior locally for each function. Different actions are taken depending on that decision, and the procedure takes advantage of the basic rule's polynomial degree when computing the error estimate in the asymptotic case.", acknowledgement = ack-nhfb, keywords = "algorithms; reliability", subject = "{\bf G.1.4}: Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation, Adaptive quadrature. {\bf G.1.4}: Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation, Multiple quadrature. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Reliability and robustness.", } @Article{Hopkins:1992:RPG, author = "Tim Hopkins", title = "Remark on ``{Algorithm 540}: {PDECOL}, General Collocation Software for Partial Differential Equations [{D3}]''", journal = j-TOMS, volume = "18", number = "3", pages = "343--344", month = sep, year = "1992", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Sep 30 01:27:53 1994", note = "See \cite{Madsen:1979:APG}.", URL = "http://doi.acm.org/10.1145/131766.131773", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN.", } @Article{Nardin:1992:ACN, author = "Mark Nardin and W. F. Perger and Atul Bhalla", title = "{Algorithm 707}: {CONHYP}: {A} Numerical Evaluator of the Confluent Hypergeometric Function for Complex Arguments of Large Magnitudes", journal = j-TOMS, volume = "18", number = "3", pages = "345--349", month = sep, year = "1992", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Sep 30 01:28:04 1994", URL = "http://doi.acm.org/10.1145/131766.131774", abstract = "A numerical evaluator for the confluent hypergeometric function for complex arguments with large magnitudes using a direct summation of Kummer's series is presented. Extended precision subroutines using large arrays to accumulate a single numerator and denominator are ultimately used in a single division to arrive at the final result. The accuracy has been verified through a variety of tests and they show the evaluator to be consistently accurate to 13 significant figures, and on rare occasion accurate to only 9 for magnitudes of the arguments ranging into the thousands in any quadrant in the complex plane. Because the evaluator automatically determines the number of significant figures of machine precision, and because it is written in FORTRAN 77, tests on various computers have shown the evaluator to provide consistently accurate results, making the evaluator very portable. The principal drawback is that, for certain arguments, the evaluator is slow; however, the evaluator remains valuable as a benchmark even in such cases.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf J.2}: Computer Applications, PHYSICAL SCIENCES AND ENGINEERING. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN 77.", } @Article{Schweikard:1992:RZI, author = "Achim Schweikard", title = "Real Zero Isolation for Trigonometric Polynomials", journal = j-TOMS, volume = "18", number = "3", pages = "350--359", month = sep, year = "1992", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65H05 (65D15)", MRnumber = "93g:65066", bibdate = "Fri Sep 30 01:28:05 1994", URL = "http://doi.acm.org/10.1145/131766.131775", abstract = "An exact and practical method for determining the number, location, and multiplicity of all real zeros of the trigonometric polynomials is described. All computations can be performed without loss of accuracy. The method is based on zero isolation techniques for algebraic polynomials. An efficient method for the calculation of the coefficients of a corresponding algebraic polynomial is stated. The complexity of trigonometric zero isolation depending on the degree and the coefficient size of the given trigonometric polynomial is analyzed. In an experimental evaluation, the performance of the method is compared to the performance of recently developed numeric techniques for the approximate determination of all roots of trigonometric polynomials. The case of exponential or hyperbolic polynomials is treated in an appendix.", acknowledgement = ack-nhfb, keywords = "algorithms; performance", subject = "{\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on polynomials. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{DiDonato:1992:ASD, author = "Armido R. {DiDonato} and Alfred H. {Morris, Jr.}", title = "{Algorithm 708}: Significant Digit Computation of the Incomplete Beta Function Ratios", journal = j-TOMS, volume = "18", number = "3", pages = "360--373", month = sep, year = "1992", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Nov 19 13:14:47 1994", note = "See also \cite{Brown:1994:CAS}.", URL = "http://doi.acm.org/10.1145/131766.131776", abstract = "An algorithm is given for evaluating the incomplete beta function ratio $I_{x}(a,b)$ and its complement $1 - I^{x}(a,b)$. A new continued fraction and a new asymptotic series are used with classical results. A transportable Fortran subroutine based on this algorithm is currently in use. It is accurate to 14 significant digits when precision is not restricted by inherent error.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation.", } @Article{Buckley:1992:ATA, author = "A. G. Buckley", title = "{Algorithm 709}: Testing Algorithm Implementations", journal = j-TOMS, volume = "18", number = "4", pages = "375--391", month = dec, year = "1992", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Sep 30 00:52:09 1994", URL = "http://doi.acm.org/10.1145/138351.138378", acknowledgement = ack-nhfb, keywords = "algorithms; design; experimentation", subject = "{\bf D.2.5}: Software, SOFTWARE ENGINEERING, Testing and Debugging, Monitors. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Gradient methods. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Nonlinear programming. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing.", } @Article{Dongarra:1992:AFS, author = "J. J. Dongarra and G. A. Geist and C. H. Romine", title = "{Algorithm 710}: {FORTRAN} Subroutines for Computing the Eigenvalues and Eigenvectors of a General Matrix by Reduction to General Tridiagonal Form", journal = j-TOMS, volume = "18", number = "4", pages = "392--400", month = dec, year = "1992", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Sep 30 00:52:57 1994", URL = "http://doi.acm.org/10.1145/138351.138352", abstract = "This paper describes programs to reduce a nonsymmetric matrix to tridiagonal form, to compute the eigenvalues of the tridiagonal matrix, to improve the accuracy of an eigenvalue, and to compute the corresponding eigenvector. The intended purpose of the software is to find a few eigenpairs of a dense nonsymmetric matrix faster and more accurately than previous methods. The performance and accuracy of the new routines are compared to two EISPACK paths: RG and HQR-INVIT. The results show that the new routines are more accurate and also faster if less than 20 percent of the eigenpairs are needed.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Eigenvalues. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Fisher:1992:DTO, author = "M. E. Fisher and L. S. Jennings", title = "Discrete-Time Optimal Control Problems with General Constraints", journal = j-TOMS, volume = "18", number = "4", pages = "401--413", month = dec, year = "1992", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "49M05 (65K99)", MRnumber = "1 199 848", bibdate = "Fri Sep 30 00:52:58 1994", URL = "http://doi.acm.org/10.1145/138351.138356", abstract = "This paper presents a computational procedure for solving combined discrete-time optimal control and optimal parameter selection problems subject to general constraints. The approach adopted is to convert the problem into a nonlinear programming problem which can be solved using standard optimization software. The main features of the procedure are the way the controls are parametrized and the conversion of all constraints into a standard form suitable for computation. The software is available commercially as a FORTRAN program DMISER3 together with a companion program MISER3 for solving continuous-time problems.", acknowledgement = ack-nhfb, keywords = "algorithms; performance; theory", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Constrained optimization. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Nonlinear programming. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency.", } @Article{Nash:1992:ABS, author = "Stephen G. Nash and Ariela Sofer", title = "{Algorithm 711}: {BTN}: Software for Parallel Unconstrained Optimization", journal = j-TOMS, volume = "18", number = "4", pages = "414--448", month = dec, year = "1992", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Sep 30 00:53:18 1994", URL = "http://doi.acm.org/10.1145/138351.138359", abstract = "BTN is a collection of FORTRAN subroutines for solving unconstrained nonlinear optimization problems. It currently runs on both Intel hypercube computers (distributed memory) and Sequent computers (shared memory), and can take advantage of vector processors if they are available. The software can also be run on traditional computers to simulate the performance of a parallel computer. BTN is a general-purpose algorithm, capable of solving problems with a large numbers of variables and suitable for users inexperienced with parallel computing. It is designed to be as easy to use as traditional algorithms for this problem, requiring only that a (scalar) subroutine be provided to evaluate the objective function and its gradient vector of first derivatives. The algorithm is based on a block truncated-Newton method. Truncated-Newton methods obtain the search direction by approximately solving the Newton equations via some iterative method. The particular method used in BTN is a block version of the Lanczos method, which is numerically stable for nonconvex problems. In addition to the optimization software, a parallel derivative checker is also provided.", acknowledgement = ack-nhfb, keywords = "algorithms; documentation", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Parallel algorithms. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Gradient methods. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Nonlinear programming.", } @Article{Leva:1992:FNR, author = "Joseph L. Leva", title = "A Fast Normal Random Number Generator", journal = j-TOMS, volume = "18", number = "4", pages = "449--453", month = dec, year = "1992", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Sep 30 00:53:29 1994", URL = "http://doi.acm.org/10.1145/138351.138364", abstract = "A method is presented for generating pseudorandom numbers with a normal distribution. The technique uses the ratio of uniform deviates method discovered by Kinderman and Monahan with an improved set of bounding curves. An optimized quadratic fit reduces the expected number of logarithm evaluations to 0.012 per normal deviate. The method gives a theoretically correct distribution and can be implemented in 15 lines of FORTRAN. Timing and source size comparisons are made with other methods for generating normal deviates. The proposed algorithm compares favorably with some of the better algorithms.", acknowledgement = ack-nhfb, DOI = "http://doi.acm.org/10.1145/138351.138364", keywords = "algorithms; performance; theory", subject = "{\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Random number generation. {\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Statistical computing.", } @Article{Leva:1992:ANR, author = "Joseph L. Leva", title = "{Algorithm 712}: {A} Normal Random Number Generator", journal = j-TOMS, volume = "18", number = "4", pages = "454--455", month = dec, year = "1992", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Sep 30 00:53:35 1994", URL = "http://doi.acm.org/10.1145/138351.138367", acknowledgement = ack-nhfb, DOI = "http://doi.acm.org/10.1145/138351.138367", keywords = "algorithms", subject = "{\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Random number generation. {\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Statistical software.", } @Article{Boisvert:1992:PVS, author = "Ronald F. Boisvert and Bonita V. Saunders", title = "Portable Vectorized Software for {Bessel} Function Evaluation", journal = j-TOMS, volume = "18", number = "4", pages = "456--469", month = dec, year = "1992", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Sep 30 00:53:41 1994", note = "See also \cite{Boisvert:1993:CPV}.", URL = "http://doi.acm.org/10.1145/138351.138370", abstract = "A suite of computer programs for the evaluation of Bessel functions and modified Bessel functions of orders zero and one for a vector of real arguments is described. Distinguishing characteristics of these programs are that (a) they are portable across a wide range of machines, and (b) they are vectorized in the case when multiple function evaluations are to be performed. The performance of the new programs are compared with software from the FNLIB collection of Fullerton on which the new software is based.", acknowledgement = ack-nhfb, keywords = "algorithms; performance", subject = "{\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Chebyshev approximation and theory. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Parallel algorithms. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Portability.", } @Article{Drezner:1992:CMN, author = "Zvi Drezner", title = "Computation of the Multivariate Normal Integral", journal = j-TOMS, volume = "18", number = "4", pages = "470--480", month = dec, year = "1992", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Nov 19 13:08:39 1994", note = "See also \cite{Drezner:1993:CAC}.", URL = "http://doi.acm.org/10.1145/138351.138375", abstract = "This paper presents a direct computation of the multivariate normal integral by the Gauss Quadrature method. An error control method is given. Results are presented for multivariate integrals consisting of up to twelve normal distributions. A computer program in FORTRAN is given.", acknowledgement = ack-nhfb, keywords = "algorithms; performance", subject = "{\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Statistical software. {\bf G.1.4}: Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation, Multiple quadrature.", } @Article{Aberth:1992:PCU, author = "Oliver Aberth and Mark J. Schaefer", title = "Precise Computation Using Range Arithmetic, via {C++}", journal = j-TOMS, volume = "18", number = "4", pages = "481--491", month = dec, year = "1992", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Sep 30 00:53:58 1994", URL = "http://doi.acm.org/10.1145/138351.138377", abstract = "An arithmetic is described that can replace floating-point arithmetic for programming tasks requiring assured accuracy. A general explanation is given of how the arithmetic is constructed with C++, and a programming example in this language is supplied. Times for solving representative problems are presented.", acknowledgement = ack-nhfb, keywords = "algorithms; languages", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic. {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, C++.", } @Article{Cody:1993:ACP, author = "W. J. Cody", title = "{Algorithm 714}: {CELEFUNT}: {A} Portable Test Package for Complex Elementary Functions", journal = j-TOMS, volume = "19", number = "1", pages = "1--21", month = mar, year = "1993", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Sep 05 09:15:25 1994", URL = "http://doi.acm.org/10.1145/151271.151272", abstract = "This paper discusses CELEFUNT, a package of Fortran programs for testing complex elementary functions.", acknowledgement = ack-nhfb, keywords = "algorithms; measurement; performance", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms.", } @Article{Cody:1993:ASE, author = "W. J. Cody", title = "{Algorithm 715}: {SPECFUN}\emdash {A} Portable {FORTRAN} Package of Special Function Routines and Test Drivers", journal = j-TOMS, volume = "19", number = "1", pages = "22--32", month = mar, year = "1993", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Mar 09 10:23:18 1999", note = "See remark \cite{Price:1996:RA}.", URL = "http://doi.acm.org/10.1145/151271.151273", abstract = "SPECFUN is a package containing transportable FORTRAN special function programs for real arguments and accompanying test drivers. Components include Bessel functions, exponential integrals, error functions and related functions, and gamma functions and related functions.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms.", } @Article{Wu:1993:ACH, author = "Trong Wu", title = "An Accurate Computation of the Hypergeometric Distribution Function", journal = j-TOMS, volume = "19", number = "1", pages = "33--43", month = mar, year = "1993", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Sep 05 09:15:25 1994", URL = "http://doi.acm.org/10.1145/151271.151274", abstract = "The computation of the cumulative hypergeometric distribution function is of interest to many researchers who are working in the computational sciences and related areas. Presented here is a new method for computing this function that applies prime number factorization to the factorials. We also apply cancellation to the numerator and denominator to reduce the computational complexity of the initial, the tail end, or weighted probabilities to achieve maximum accuracy. The new method includes two algorithms, one using recursion and the other using iteration. These two algorithms are machine independent; precision is arbitrary, subject to storage limitation. The development of the algorithms is discussed, and some test results and the comparison of these two algorithms are given. To implement both algorithms, we use the Ada programming language that is an American National Standard Institute standardized language. The language has special features such as {\em exception handling} and {\em tasks}. {\em Exception handling} is used to make programming easier and to prevent overflow or underflow conditions during the execution of the program. {\em Tasks} are used to compute the numerator and denominator concurrently, and to maximize the possible number of integer multiplications in the numerator and denominator. All of the computations can be done on currently available machines, and the time consumed by these computations remains reasonably small.", acknowledgement = ack-nhfb, keywords = "algorithms; languages", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Statistical computing. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, Ada. {\bf D.3.3}: Software, PROGRAMMING LANGUAGES, Language Constructs and Features, Control structures.", } @Article{Kamel:1993:OES, author = "M. S. Kamel and K. S. Ma and W. H. Enright", title = "{ODEXPERT}: An Expert System to Select Numerical Solvers for Initial Value {ODE} Systems", journal = j-TOMS, volume = "19", number = "1", pages = "44--62", month = mar, year = "1993", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Sep 05 09:15:25 1994", URL = "http://doi.acm.org/10.1145/151271.151275", abstract = "ODEXPERT is a prototype knowledge-based system which selects the appropriate numerical solvers for initial value ordinary differential equations. It is capable of deriving some knowledge about the input problem by performing automated tests to detect properties and structures in the problem which guide the selection process.", acknowledgement = ack-nhfb, keywords = "algorithms; design", subject = "{\bf I.2.1}: Computing Methodologies, ARTIFICIAL INTELLIGENCE, Applications and Expert Systems. {\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Initial value problems. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Cash:1993:MAM, author = "J. R. Cash and S. Semnani", title = "A Modified {Adams} Method for {NonStiff} and Mildly Stiff Initial Value Problems", journal = j-TOMS, volume = "19", number = "1", pages = "63--80", month = mar, year = "1993", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Sep 05 09:15:25 1994", URL = "http://doi.acm.org/10.1145/151271.151276", abstract = "Adams predictor-corrector methods, and explicit Runge-Kutta formulas, have been widely used for the numerical solution of nonstiff initial value problems. Both of these classes of methods have certain drawbacks, however, and it has long been the aim of numerical analysts to derive a class of formulas that has the advantages of both Adams and Runge-Kutta methods and the disadvantages of neither! In this paper we derive a class of modified Adams formulas that attempts to achieve this aim. When used in a certain precisely defined predictor-corrector mode, these new formulas require three function evaluations per step, but have much better stability than Adams formulas. This improved stability makes the modified Adams formulas particularly effective for mildly stiff problems, and some numerical evidence of this is given. We also consider the performance of the new class of methods on the well-known DETEST test set to show their potential on general nonstiff initial value problems.", acknowledgement = ack-nhfb, keywords = "algorithms; design; performance", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing. {\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Initial value problems.", } @Article{Renka:1993:ATT, author = "R. J. Renka", title = "{Algorithm 716}: {TSPACK}: Tension Spline Curve-Fitting Package", journal = j-TOMS, volume = "19", number = "1", pages = "81--94", month = mar, year = "1993", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Thu Jul 15 18:57:35 1999", note = "See remark \cite{Testa:1999:RA}.", URL = "http://doi.acm.org/10.1145/151271.151277", abstract = "The primary purpose of TSPACK is to construct a smooth function which interpolates a discrete set of data points. The function may be required to have either one or two continuous derivatives. If the accuracy of the data does not warrant interpolation, a smoothing function (which does not pass through the data points) may be constructed instead. The fitting method is designed to avoid extraneous inflection points (associated with rapidly varying data values) and preserve local shape properties of the data (monotonicity and convexity), or to satisfy the more general constraints of bounds on function values or first derivatives. The package also provides a parametric representation for construction general planar curves and space curves.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation. {\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation.", } @Article{Snow:1993:CTP, author = "Dennis M. Snow", title = "Computing Tensor Product Decompositions", journal = j-TOMS, volume = "19", number = "1", pages = "95--108", month = mar, year = "1993", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "22-04 (17B10 22E47)", MRnumber = "94e:22001", bibdate = "Mon Sep 05 09:15:25 1994", URL = "http://doi.acm.org/10.1145/151271.151278", abstract = "An algorithm is presented for computing the decomposition of a tensor product of two irreducible representations of a semisimple complex Lie group into its irreducible components. The algorithm uses a known formula which expresses the multiplicities of the highest weight vectors in the decomposition as an alternating sum indexed by the Weyl group. This sum is accomplished with minimal memory requirements using techniques developed previously by the author for efficiently computing Weyl group orbits. Examples are given for each of the exceptional Lie groups.", acknowledgement = ack-nhfb, keywords = "algorithms; experimentation; measurement; performance; theory", reviewer = "Jeffrey Adams", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems.", } @Article{Bunch:1993:ASM, author = "David S. Bunch and David M. Gay and Roy E. Welsch", title = "{Algorithm 717}: Subroutines for Maximum Likelihood and Quasi-Likelihood Estimation of Parameters in Nonlinear Regression Models", journal = j-TOMS, volume = "19", number = "1", pages = "109--130", month = mar, year = "1993", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Sep 05 09:15:25 1994", URL = "http://doi.acm.org/10.1145/151271.151279", abstract = "We present FORTRAN 77 subroutines that solve statistical parameter estimation problems for general nonlinear models, e.g., nonlinear least-squares, maximum likelihood, maximum quasi-likelihood, generalized nonlinear least-squares, and some robust fitting problems. The accompanying test examples include members of the generalized linear model family, extensions using nonlinear predictors (``nonlinear GLIM''), and probabilistic choice models, such as linear-in-parameter multinomial probit models. The basic method, a generalization of the NL2SOL algorithm for nonlinear least-squares, employs a model/trust-region scheme for computing trial steps, exploits special structure by maintaining a secant approximation to the second-order part of the Hessian, and adaptively switches between a Gauss-Newton and an augmented Hessian approximation. Gauss-Newton steps are computed using a corrected seminormal equations approach. The subroutines include variants that handle simple bounds on the parameters, and that compute approximate regression diagnostics.", acknowledgement = ack-nhfb, subject = "{\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Statistical computing. {\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Statistical software. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Boisvert:1993:CPV, author = "Ronald F. Boisvert and Bonita V. Saunders", title = "Corrigendum: ``{Algorithm 713}: Portable Vectorized Software for {Bessel} Function Evaluation''", journal = j-TOMS, volume = "19", number = "1", pages = "131--131", month = mar, year = "1993", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Sep 05 09:33:37 1994", note = "See \cite{Boisvert:1992:PVS}.", acknowledgement = ack-nhfb, xxURL = "Missing from ACM Digital Library", } @Article{Boisvert:1993:E, author = "Ronald F. Boisvert", title = "Editorial", journal = j-TOMS, volume = "19", number = "2", pages = "135--135", month = jun, year = "1993", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Sep 05 09:34:01 1994", acknowledgement = ack-nhfb, xxURL = "Missing from ACM Digital Library", } @Article{Duff:1993:CSE, author = "I. S. Duff and J. A. Scott", title = "Computing Selected Eigenvalues of Sparse Unsymmetric Matrices Using Subspace Iteration", journal = j-TOMS, volume = "19", number = "2", pages = "137--159", month = jun, year = "1993", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65F50 (65F15)", MRnumber = "96c:65078", bibdate = "Tue Nov 14 09:56:28 1995", note = "See \cite{Duff:1995:CCS}.", URL = "http://doi.acm.org/10.1145/152613.152614", abstract = "This paper discusses the design and development of a code to calculate the eigenvalues of a large sparse real unsymmetric matrix that are the rightmost, leftmost, or are of the largest modulus. A subspace iteration algorithm is used to compute a sequence of sets of vectors that converge to an orthonormal basis for the invariant subspace corresponding to the required eigenvalues. This algorithm is combined with Chebychev acceleration if the rightmost or leftmost eigenvalues are sought, or if the eigenvalues of largest modulus are known to be the rightmost or leftmost eigenvalues. An option exists for computing the corresponding eigenvectors. The code does not need the matrix explicitly since it only requires the user to multiply sets of vectors by the matrix. Sophisticated and novel iteration controls, stopping criteria, and restart facilities are provided. The code is shown to be efficient and competitive on a range of test problems.", acknowledgement = ack-nhfb, keywords = "algorithms; design", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Eigenvalues. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Demmel:1993:GSDa, author = "James Demmel and Bo K{\aa}gstr{\"o}m", title = "The Generalized {Schur} Decomposition of an Arbitrary Pencil {$A-\lambda{B}$}: Robust Software with Error Bounds and Applications. Part {I}: {Theory} and Algorithms", journal = j-TOMS, volume = "19", number = "2", pages = "160--174", month = jun, year = "1993", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65F15 (65-04)", MRnumber = "96d:65060a", bibdate = "Fri Aug 26 23:38:18 1994", URL = "http://doi.acm.org/10.1145/152613.152615", abstract = "Robust software with error bounds for computing the generalized Schur decomposition of an arbitrary matrix pencil $A - \lambda B$ (regular or singular) is presented. The decomposition is a generalization of the Schur canonical form of $A - \lambda I$ to matrix pencils and reveals the Kronecker structure of a singular pencil. Since computing the Kronecker structure of a singular pencil is a potentially ill-posed problem, it is important to be able to compute rigorous and reliable error bounds for the computed features. The error bounds rely on perturbation theory for reducing subspaces and generalized eigenvalues of singular matrix pencils. The first part of this two-part paper presents the theory and algorithms for the decomposition and its error bounds, while the second part describes the computed generalized Schur decomposition and the software, and presents applications and an example of its use.", acknowledgement = ack-nhfb, keywords = "algorithms; geig; generalized Schur decomposition; matrix pencil; nla; reliability; theory", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Eigenvalues. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Conditioning. {\bf F.4.1}: Theory of Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical Logic. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Demmel:1993:GSDb, author = "James Demmel and Bo K{\aa}gstr{\"o}m", title = "The Generalized {Schur} Decomposition of an Arbitrary Pencil {$A-\lambda B$}: {Robust} Software with Error Bounds and Applications. Part {II}: {Software} and Applications", journal = j-TOMS, volume = "19", number = "2", pages = "175--201", month = jun, year = "1993", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65F15 (65-04)", MRnumber = "96d:65060b", bibdate = "Mon Sep 05 09:34:01 1994", URL = "http://doi.acm.org/10.1145/152613.152616", abstract = "Robust software with error bounds for computing the generalized Schur decomposition of an arbitrary matrix pencil $A - \lambda B$ (regular or singular) is presented. The decomposition is a generalization of the Schur canonical form of $A - \lambda I$ to matrix pencils and reveals the Kronecker structure of a singular pencil. The second part of this two-part paper describes the computed generalized Schur decomposition in more detail and the software, and presents applications and an example of its use. Background theory and algorithms for the decomposition and its error bounds are presented in Part I of this paper.", acknowledgement = ack-nhfb, keywords = "algorithms; geig; generalized Schur decomposition; matrix pencil; nla; reliability; theory", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Eigenvalues. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Conditioning. {\bf F.4.1}: Theory of Computation, MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Mathematical Logic. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Bai:1993:CCN, author = "Z. Bai and J. Demmel and A. McKenney", title = "On Computing Condition Numbers for the Nonsymmetric Eigenproblem", journal = j-TOMS, volume = "19", number = "2", pages = "202--223", month = jun, year = "1993", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65F35 (65-04 65F15)", MRnumber = "96c:65074", bibdate = "Mon Sep 05 09:34:01 1994", URL = "http://doi.acm.org/10.1145/152613.152617", abstract = "We review the theory of condition numbers for the nonsymmetric eigenproblem and give a tabular summary of bounds for eigenvalues, means of clusters of eigenvalues, eigenvectors, invariant subspaces, and related quantities. We describe the design of new algorithms for estimating these condition numbers. Fortran subroutines implementing these algorithms are in the LAPACK library [1].", acknowledgement = ack-nhfb, keywords = "algorithms; measurement; reliability", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Eigenvalues. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Reliability and robustness.", } @Article{Miminis:1993:AFS, author = "George Miminis and Michael Reid", title = "{Algorithm 718}: {A FORTRAN} Subroutine to Solve the Eigenvalues Allocation Problem for Single-Input Systems", journal = j-TOMS, volume = "19", number = "2", pages = "224--232", month = jun, year = "1993", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Sep 05 09:34:01 1994", URL = "http://doi.acm.org/10.1145/152613.152618", abstract = "An efficient implementation of an algorithm for the eigenvalue allocation (pole placement) problem of single-input linear systems using state feedback is given in this paper. The implementation uses the BLAS level-1 [2] subroutines when possible for better performance. A brief description of the algorithm along with some computational details is also given.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Eigenvalues. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms.", } @Article{Greenberg:1993:EAC, author = "Harvey J. Greenberg", title = "Enhancements of {ANALYZE}: {A} Computer-Assisted Analysis System for Linear Programming", journal = j-TOMS, volume = "19", number = "2", pages = "233--256", month = jun, year = "1993", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Sep 05 09:34:01 1994", URL = "http://doi.acm.org/10.1145/152613.152619", abstract = "This describes enhancements to provide more advanced computer-assisted analysis of instances of linear programming models. Three categories of enhancements are described: views, engines for obtaining information, and rule-based advising. Examples of their uses include redundancy and infeasibility diagnoses.", acknowledgement = ack-nhfb, keywords = "design; experimentation; languages; performance", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, ANALYZE. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Linear programming. {\bf I.6.2}: Computing Methodologies, SIMULATION AND MODELING, Simulation Languages. {\bf I.6.4}: Computing Methodologies, SIMULATION AND MODELING, Model Validation and Analysis.", } @Article{Fishman:1993:GSC, author = "George S. Fishman and L. Stephen Yarberry", title = "Generating a Sample from a $k$-Cell Table with Changing Probabilities in {$O(\log_2k)$} Time", journal = j-TOMS, volume = "19", number = "2", pages = "257--261", month = jun, year = "1993", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Sep 30 00:48:36 1994", URL = "http://doi.acm.org/10.1145/152613.152621", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS.", } @Article{Bentley:1993:TDI, author = "Jon L. Bentley and Mary F. Fernandez and Brian W. Kernighan and Norman L. Schryer", title = "Template-Driven Interfaces for Numerical Subroutines", journal = j-TOMS, volume = "19", number = "3", pages = "265--287", month = sep, year = "1993", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Sep 16 19:17:34 1994", URL = "http://doi.acm.org/10.1145/155743.155757", abstract = "This paper describes a set of interfaces for numerical subroutines. Typing a short (often one-line) description allows one to solve problems in application domains including least-squares data fitting, differential equations, minimization, root finding, and integration. Our approach of ``template-driven programming'' makes it easy to build such an interface: a simple one takes a few hours to construct, while a few days suffice to build the most complex program we describe.", acknowledgement = ack-nhfb, keywords = "awk; design; experimentation; Fortran; languages; Maple; UNIX shell", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf D.2.2}: Software, SOFTWARE ENGINEERING, Tools and Techniques, User interfaces. {\bf D.2.2}: Software, SOFTWARE ENGINEERING, Tools and Techniques, Software libraries. {\bf D.3.4}: Software, PROGRAMMING LANGUAGES, Processors, Preprocessors. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf D.2.m}: Software, SOFTWARE ENGINEERING, Miscellaneous, Reusable software.", } @Article{Bailey:1993:AMT, author = "David H. Bailey", title = "{Algorithm 719}: Multiprecision Translation and Execution of {FORTRAN} Programs", journal = j-TOMS, volume = "19", number = "3", pages = "288--319", month = sep, year = "1993", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Sep 16 19:17:34 1994", URL = "http://doi.acm.org/10.1145/155743.155767", abstract = "This paper describes two Fortran utilities for multiprecision computation. The first is a package of Fortran subroutines that perform a variety of arithmetic operations and transcendental functions on floating point numbers of arbitrarily high precision. This package is in some cases over 200 times faster than that of certain other packages that have been developed for this purpose.\par The second utility is a translator program, which facilitates the conversion of ordinary Fortran programs to use this package. By means of source directives (special comments) in the original Fortran program, the user declares the precision level and specifies which variables in each subprogram are to be treated as multiprecision. The translator program reads this source program and outputs a program with the appropriate multiprecision subroutine calls.\par This translator supports multiprecision integer, real, and complex datatypes. The required array space for multiprecision data types is automatically allocated. In the evaluation of computational expressions, all of the usual conventions for operator precedence and mixed mode operations are upheld. Furthermore, most of the Fortran-77 intrinsics, such as ABS, MOD, NINT, COS, EXP are supported and produce true multiprecision values.", acknowledgement = ack-nhfb, keywords = "algorithms; multiple-precision computation; multiprecision arithmetic; performance", subject = "F.2.1 [Analysis of Algorithms and Problem Complexity]: Numerical Algorithms and Problems; G.1.0 [Numerical Analysis]: General; G.1.2 [Numerical Analysis]; Approximation", } @Article{Berntsen:1993:AAA, author = "Jarle Berntsen and Ronald Cools and Terje O. Espelid", title = "{Algorithm 720}: An Algorithm for Adaptive Cubature Over a Collection of $3$-Dimensional Simplices", journal = j-TOMS, volume = "19", number = "3", pages = "320--332", month = sep, year = "1993", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Sep 16 19:17:34 1994", URL = "http://doi.acm.org/10.1145/155743.155785", abstract = "An adaptive algorithm for computing an approximation to the integral of each element in a vector of functions over a 3-dimensional region covered by simplices is presented. The algorithm is encoded in FORTRAN 77.\par Locally, a cubature formula of degree 8 with 43 points is used to approximate an integral. The local error estimate is based on the same evaluation points. The error estimation procedure tries to decide whether the approximation for each function has asymptotic behavior, and different actions are taken depending on that decision.\par The simplex with the largest error is subdivided into 8 simplices. The local procedure is then applied to each new region. This procedure is repeated until convergence.", acknowledgement = ack-nhfb, keywords = "algorithms; automatic integration; cubature; cubature rules; error estimation; null rules; reliability; symmetry; tetrahedrons", subject = "G.1.4 [Numerical Analysis]: Quadrature and Numerical Differentiation -- adaptive quadrature; multiple quadrature; G.4 [Mathematics of Computing]: Mathematical Software -- efficiency; reliability and robustness", } @Article{Duffy:1993:NIL, author = "Dean G. Duffy", title = "On the Numerical Inversion of {Laplace} Transforms: Comparison of Three New Methods on Characteristic Problems from Applications", journal = j-TOMS, volume = "19", number = "3", pages = "333--359", month = sep, year = "1993", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Sep 16 19:17:34 1994", URL = "http://doi.acm.org/10.1145/155743.155788", abstract = "Three frequently used methods for numerically inverting Laplace transforms are tested on complicated transforms taken from the literature. The first method is a straightforward application of the trapezoidal rule to Bromwich's integral. The second method, developed by Weeks [22], integrates Bromwich's integral by using Laguerre polynomials. The third method, devised by Talbot [18], deforms Bromwich's contour so that the integrand of Bromwich's integral is small at the beginning and end of the contour. These methods are also applied to joint Laplace-Fourier transform problems. All three methods give satisfactory results; Talbot's, however, has an accurate method for choosing required parameters.", acknowledgement = ack-nhfb, keywords = "algorithms; measurement; theory", subject = "F.2.1 [Analysis of Algorithms and Problem Complexity]: Numerical Algorithms and Problems", } @Article{Pruess:1993:MSS, author = "Steven Pruess and Charles T. Fulton", title = "Mathematical Software for {Sturm-Liouville} Problems", journal = j-TOMS, volume = "19", number = "3", pages = "360--376", month = sep, year = "1993", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Sep 16 19:17:34 1994", URL = "http://doi.acm.org/10.1145/155743.155791", abstract = "Software is described for the Sturm-Liouville eigenproblem. Eigenvalues, eigenfunctions, and spectral density functions can be estimated with global error control. The method of approximating the coefficients forms the mathematical basis. The underlying algorithms are briefly described, and several examples are presented.", acknowledgement = ack-nhfb, keywords = "algorithms; approximating the coefficients; eigenfunctions; performance; shooting methods; spectral classification; spectral density functions; Sturm-Liouville eigenvalues", subject = "G.1.7 [Numerical Analysis]: Ordinary Differential Equations -- boundary value problems; G.4 [Mathematics of Computing]: Mathematical Software -- algorithm analysis", } @Article{Shirts:1993:CES, author = "Randall B. Shirts", title = "The Computation of Eigenvalues and Solutions of {Mathieu}'s Differential Equation for Noninteger Order", journal = j-TOMS, volume = "19", number = "3", pages = "377--390", month = sep, year = "1993", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Sep 16 19:17:34 1994", URL = "http://doi.acm.org/10.1145/155743.155796", abstract = "Two algorithms for calculating the eigenvalues and solutions of Mathieu's differential equation for noninteger order are described. In the first algorithm, Leeb's method is generalized, expanding the Mathieu equation in Fourier series and diagonalizing the symmetric tridiagonal matrix that results. Numerical testing was used to parameterize the minimum matrix dimension that must be used to achieve accuracy in the eigenvalue of one part in $10^{12}$. This method returns a set of eigenvalues below a given order and their associated solutions simultaneously. A second algorithm is presented which uses approximations to the eigenvalues (Taylor series and asymptotic expansions) and then iteratively corrects the approximations using Newton's method until the corrections are less than a given tolerance. A backward recursion of the continued fraction expansion is used. The second algorithm is faster and is optimized to obtain accuracy of one part in $10^{14}$, but has only been implemented for orders less than 10.5.", acknowledgement = ack-nhfb, keywords = "algorithms; eigenvalues; Floquet solutions; Mathieu equation; noninteger order; numerical software; ordinary differential equations; performance", subject = "G.1.0 [Numerical Analysis]: General -- numerical algorithms", } @Article{Shirts:1993:AMM, author = "Randall B. Shirts", title = "{Algorithm 721}: {MTIEU1} and {MTIEU2}: Two Subroutines to Compute Eigenvalues and Solutions to {Mathieu}'s Differential Equation for Noninteger and Integer Order", journal = j-TOMS, volume = "19", number = "3", pages = "391--406", month = sep, year = "1993", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Sep 16 19:17:34 1994", URL = "http://doi.acm.org/10.1145/155743.155847", abstract = "Two FORTRAN routines are described which calculate eigenvalues and eigenfunctions of Mathieu's differential equation for noninteger as well as integer order, MTIEU1 uses standard matrix techniques with dimension parameterized to give accuracy in the eigenvalue of one part in $10^{12}$. MTIEU2 used continued fraction techniques and is optimized to give accuracy in the eigenvalue of one part in $10^{14}$. The limitations of the algorithms are also discussed and illustrated.", acknowledgement = ack-nhfb, keywords = "algorithms; eigenvalues; Floquet solutions; FORTRAN; Mathieu equation; noninteger order; numerical software; ordinary differential equations; performance", subject = "G.1.0 [General Numerical Analysis]", } @Article{Haag:1993:QLA, author = "J. B. Haag and D. S. Watkins", title = "{QR}-Like Algorithms for the Nonsymmetric Eigenvalue Problem", journal = j-TOMS, volume = "19", number = "3", pages = "407--418", month = sep, year = "1993", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Sep 16 19:17:34 1994", URL = "http://doi.acm.org/10.1145/155743.155849", abstract = "Hybrid codes that combine elements of the QR and LR algorithms are described. The codes can calculate the eigenvalues and, optionally, eigenvectors of real, nonsymmetric matrices. Extensive tests are presented as evidence that, for certain choices of parameters, the hybrid codes possess the same high reliability as the QR algorithm and are significantly faster. The greatest success has been achieved with the codes that calculate eigenvalues only. These can do the task in 15\% to 50\% less time than the QR algorithm.", acknowledgement = ack-nhfb, keywords = "algorithms; chasing the bulge; eigenvalue; eigenvector; experimentation; GR algorithm; LR algorithm; measurement; performance; QR algorithm; verification", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Eigenvalues. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems.", } @Article{Chang:1993:ICR, author = "S. Frank Chang and S. Thomas McCormick", title = "Implementation and Computational Results for the Hierarchical Algorithm for Making Sparse Matrices Sparser", journal = j-TOMS, volume = "19", number = "3", pages = "419--441", month = sep, year = "1993", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Sep 16 19:17:34 1994", URL = "http://doi.acm.org/10.1145/155743.152620", abstract = "If A is the (sparse) coefficient matrix of linear-equality constraints, for what nonsingular $T$ is A = TA as sparse as possible, and how can it be efficiently computed? An efficient algorithm for this {\em Sparsity Problem} (SP) would be a valuable preprocessor for linearly constrained optimization problems. In a companion paper we developed a two-pass approach to solve SP called the {\em Hierarchical Algorithm}. In this paper we report on how we implemented the Hierarchical Algorithm into a code called HASP, and our computational experience in testing HASP on the NETLIB linear-programming problems. We found that HASP substantially outperformed a previous code for SP and that it produced a net savings in optimization time on the NETLIB problems. The results allow us to give guidelines for its use in practice.", acknowledgement = ack-nhfb, keywords = "algorithms; measurement; performance; verification", subject = "F.2.1 [Analysis of Algorithms and Problem Complexity]: Numerical Algorithms and Problems -- computations on matrices; G.1.6 [Numerical Analysis]: Optimization -- linear programming; G.4 [Mathematics of Computing]: Mathematical Software -- algorithms analysis; efficiency", } @Article{Cody:1993:AFS, author = "W. J. Cody and J. T. Coonen", title = "{Algorithm 722}: Functions to Support the {IEEE} Standard for Binary Floating-Point Arithmetic", journal = j-TOMS, volume = "19", number = "4", pages = "443--451", month = dec, year = "1993", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Sep 16 20:08:53 1994", bibsource = "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt", URL = "http://doi.acm.org/10.1145/168173.168185", abstract = "This paper describes C programs for the support functions {\em copysign(x,y), logb(x), scalb(x,n), nextafter(x,y), finite(x),} and {\em isnan(x)} recommended in the Appendix to the {\em IEEE Standard for Binary Floating-Point Arithmetic.} In the case of {\em logb}, the modified definition given in the later {\em IEEE Standard for Radix-Independent Floating-Point Arithmetic} is followed. These programs should run without modification on most systems conforming to the binary standard.", acknowledgement = ack-nj, keywords = "algorithms; copysign; finite; isnan; logb; manipulative functions; nextafter; scalb", subject = "G.1.0 [Numerical Analysis]: General -- numerical algorithms; G.4 [Numerical Analysis]: Mathematical Software -- certification and testing", } @Article{Snyder:1993:AFI, author = "W. Van Snyder", title = "{Algorithm 723}: {Fresnel} Integrals", journal = j-TOMS, volume = "19", number = "4", pages = "452--456", month = dec, year = "1993", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Thu Apr 29 15:24:56 1999", note = "See remark \cite{Snyder:1996:RAF}.", URL = "http://doi.acm.org/10.1145/168173.168193", abstract = "An implementation of approximations for Fresnel integrals and associated functions is described. The approximations were originally developed by W. J. Cody, but a Fortran implementation using them has not previously been published.", acknowledgement = ack-nhfb, keywords = "algorithms; special functions", subject = "{\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Rational approximation. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing.", } @Article{Ribbens:1993:TPM, author = "Calvin J. Ribbens and Layne T. Watson and Colin Desa", title = "Toward Parallel Mathematical Software for Elliptic Partial Differential Equations", journal = j-TOMS, volume = "19", number = "4", pages = "457--473", month = dec, year = "1993", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Sep 16 19:47:29 1994", URL = "http://doi.acm.org/10.1145/168173.168383", abstract = "Three approaches to parallelizing important components of the mathematical software package ELLPACK are considered: an explicit approach using compiler directives available only on the target machine, an automatic approach using an optimizing and parallelizing precompiler, and a two-level approach based on extensive use of a set of low level computational kernels. The focus is on shared memory architectures. Each approach to parallelization is described in detail, along with a discussion of the effort involved. Performance on a test problem, using up to sixteen processors of a Sequent Symmetry S81, is reported and discussed. Implications for the parallelization of a broad class of mathematical software are drawn.", acknowledgement = ack-nhfb, keywords = "algorithms; performance", subject = "G.1.0 [Numerical Analysis]: General -- parallel algorithms; G.1.8 [Numerical Analysis]: Partial Differential Equations -- elliptic equations; G.4 [Mathematics of Computing]: Mathematical Software -- efficiency; portability", } @Article{Abernathy:1993:ASE, author = "Roger W. Abernathy and Robert P. Smith", title = "Applying Series Expansion to the Inverse Beta Distribution to Find Percentiles of the ${F}$-Distribution", journal = j-TOMS, volume = "19", number = "4", pages = "474--480", month = dec, year = "1993", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Sep 16 19:47:29 1994", URL = "http://doi.acm.org/10.1145/168173.168387", abstract = "Let $0 <= 1$ and $F$ be the cumulative distribution function (cdf) of the $F$-Distribution. We wish to find $x_{p}$ such that $F(x_{p}|n_{1}, n_{2}) = p$, where $n_{1}$ and $n_{2}$ are the degrees of freedom. Traditionally, $x_{p}$ is found using a numerical root-finding method, such as Newton's method. In this paper, a procedure based on a series expansion for finding $x_{p}$is given. The series expansion method has been applied to the normal, chi-square, and $t$ distributions, but because of computational difficulties, it has not been applied to the $F$-Distribution. These problems have been overcome by making the standard transformation to the beta distribution.\par The procedure is explained in Sections 3 and 4. Empirical results of a comparison of CPU times are given in Section 5. The series expansion is compared to some of the standard root-finding methods. A table is given for $p = 0.90$.", acknowledgement = ack-nhfb, keywords = "algorithms; cumulative distribution function; cumulative distribution function (cdf); distribution function; F-distribution; Newton's method; performance; root-finding methods; Taylor series", subject = "G.1.5 [Numerical Analysis]: Roots of Nonlinear Equations; G.3 [Probability and Statistics]", } @Article{Abernathy:1993:APC, author = "Roger W. Abernathy and Robert P. Smith", title = "{Algorithm 724}: Program to Calculate ${F}$-Percentiles", journal = j-TOMS, volume = "19", number = "4", pages = "481--483", month = dec, year = "1993", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Sep 16 19:47:29 1994", URL = "http://doi.acm.org/10.1145/168173.168405", abstract = "Let $0 < p < 1$ be given and let $F$ be the cumulative distribution function of the $F$-Distribution with $(M, N)$, degrees of freedom. This FORTRAN 77 routine is a complement to [1] where a method was presented to find the inverse of the $F$-Distribution function, FINV($M, N, P$), using a series expansion technique to find the inverse for the Beta Distribution function.", acknowledgement = ack-nhfb, keywords = "algorithms; cumulative distribution function (cdf); distribution function; experimentation; F-distribution; Newton's method; root-finding methods; Taylor series; theory", subject = "G.1.5 [Numerical Analysis]: Roots of Nonlinear Equations", } @Article{Clarkson:1993:RAF, author = "Douglas B. Clarkson and Yuan-an Fan and Harry Joe", title = "A Remark on {Algorithm 643}: {FEXACT}: An Algorithm for Performing {Fisher}'s Exact Test in $r\times{c}$ Contingency Tables", journal = j-TOMS, volume = "19", number = "4", pages = "484--488", month = dec, year = "1993", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Sep 16 19:47:29 1994", note = "See \cite{Mehta:1986:AFF}.", URL = "http://doi.acm.org/10.1145/168173.168412", acknowledgement = ack-nhfb, keywords = "algorithms; experimentation; measurement; performance; theory", subject = "{\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation.", } @Article{Hormann:1993:PRN, author = "W. H{\"o}rmann and G. Deflinger", title = "A Portable Random Number Generator Well Suited for the Rejection Method", journal = j-TOMS, volume = "19", number = "4", pages = "489--495", month = dec, year = "1993", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Sep 16 19:47:29 1994", URL = "http://doi.acm.org/10.1145/168173.168414", abstract = "Up to now, all known efficient portable implementations of linear congruential random number generators with modulus $2^{31} - 1$ have worked only with multipliers that are small compared with the modulus. We show that for nonuniform distributions, the rejection method may generate random numbers of bad qualify if combined with a linear congruential generator with small multiplier. A method is described that works for any multiplier smaller than $2^{30}$. It uses the decomposition of multiplier and seed in high-order and low-order bits to compute the upper and lower half of the product. The sum of the two halves gives the product of multiplier and seed modulo $2^{21} - 1$. Coded in ANSI-C and FORTRAN77 the method results in a portable implementation of the linear congruential generator that is as fast or faster than other portable methods.", acknowledgement = ack-nhfb, keywords = "algorithms; linear congruential generator; portability; quality of nonuniform random numbers; rejection method; uniform random number generator", subject = "G.3 [Mathematics of Computation]: Probability and Statistics -- random number generation", } @Article{Grassmann:1993:REC, author = "Winifred K. Grassmann", title = "Rounding Errors in Certain Algorithms Involving {Markov} Chains", journal = j-TOMS, volume = "19", number = "4", pages = "496--508", month = dec, year = "1993", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Feb 07 16:38:26 1997", URL = "http://doi.acm.org/10.1145/168173.168416", abstract = "A number of algorithms involving Markov chains contain no subtractions. This property makes the analysis of rounding errors particularly simple. To show this, some principles for analyzing the propagation and generation of rounding errors in algorithms containing no subtraction are discussed first. These principles are then applied in the context of a simple recursive algorithm involving the transient solution of discrete-time Markov chains, Jensen's algorithm, and state reduction. Jensen's algorithm, also known as randomization or uniformization, is an algorithm for finding transient solutions of continuous-time Markov chains. State reduction is a method for finding equilibrium probabilities for discrete-time or continuous-time Markov chains.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS. {\bf F.2.2}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems.", } @Article{Khoury:1993:TPG, author = "B. N. Khoury and P. M. Pardalos and D.-Z. Du", title = "A Test Problem Generator for the {Steiner} Problem in Graphs", journal = j-TOMS, volume = "19", number = "4", pages = "509--522", month = dec, year = "1993", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Nov 06 07:19:45 1995", URL = "http://doi.acm.org/10.1145/168173.168420", abstract = "In this paper we present a new binary-programming formulation for the Steiner problem in graphs (SPG), which is well known to be NP-hard. We use this formulation to generate test problems with known optimal solutions. The technique uses the KKT optimality conditions on the corresponding quadratically constrained optimization problem.", acknowledgement = ack-nhfb, keywords = "algorithms; experimentation; integer programming; performance; Steiner problem in graphs; test problems", subject = "G.1.6 [Numerical Analysis]: Optimization -- integer programming; G.4 [Mathematics of Computing]: Mathematical Software -- certification and testing; efficiency", } @Article{Joe:1993:ILM, author = "Stephen Joe and Ian H. Sloan", title = "Implementation of a Lattice Method for Numerical Multiple Integration", journal = j-TOMS, volume = "19", number = "4", pages = "523--545", month = dec, year = "1993", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Nov 19 13:08:44 1994", note = "See also \cite{Joe:1994:CIL}.", URL = "http://doi.acm.org/10.1145/168173.168425", abstract = "An implementation of a method for numerical multiple integration based on a sequence of imbedded lattice rules is given. Besides yielding an approximation to the integral, this implementation also provides an error estimate which does not require much extra computation. The results of some numerical experiments conclude the paper.", acknowledgement = ack-nhfb, keywords = "algorithms; lattice rules; performance", subject = "G.1.4 [Numerical Analysis]: Quadrature and Numerical Differentiation -- multiple quadrature", } @Article{Drezner:1993:CAC, author = "Zvi Drezner", title = "Corrigendum: ``{Algorithm 725}. Computation of the Multivariate Normal Integral''", journal = j-TOMS, volume = "19", number = "4", pages = "546--546", month = dec, year = "1993", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Nov 19 13:05:07 1994", note = "See \cite{Drezner:1992:CMN}.", URL = "http://doi.acm.org/10.1145/168173.168428", acknowledgement = ack-nhfb, keywords = "algorithms; multivariate normal probability", subject = "{\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Statistical software. {\bf G.1.4}: Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation, Multiple quadrature.", } @Article{Boisvert:1994:CST, author = "Ronald F. Boisvert", title = "Charter and Scope: Transactions on Mathematical Software ({TOMS})", journal = j-TOMS, volume = "20", number = "1", pages = "1--2", month = mar, year = "1994", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Sep 06 19:02:59 1994", acknowledgement = ack-nhfb, xxURL = "Missing from ACM Digital Library", } @Article{Renka:1994:CSC, author = "Robert J. Renka", title = "Charter and Scope: Collected Algorithms ({CALGO})", journal = j-TOMS, volume = "20", number = "1", pages = "3--3", month = mar, year = "1994", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Sep 06 19:02:59 1994", acknowledgement = ack-nhfb, xxURL = "Missing from ACM Digital Library", } @Article{Neusius:1994:NTA, author = "Christian Neusius and Jan Olszewski", title = "A Noniterative Thinning Algorithm", journal = j-TOMS, volume = "20", number = "1", pages = "5--20", month = mar, year = "1994", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "68U10", MRnumber = "96h:68221", bibdate = "Tue Sep 06 19:02:59 1994", URL = "http://doi.acm.org/10.1145/174603.174604", acknowledgement = ack-nhfb, } @Article{Gautschi:1994:ACP, author = "Walter Gautschi", title = "{Algorithm 726}: {ORTHPOL}\emdash {A} Package of Routines for Generating Orthogonal Polynomials and {Gauss}-Type Quadrature Rules", journal = j-TOMS, volume = "20", number = "1", pages = "21--62", month = mar, year = "1994", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Mar 09 10:16:24 1999", note = "See remark \cite{Gautschi:1998:RAO}.", URL = "http://doi.acm.org/10.1145/174603.174605", acknowledgement = ack-nhfb, } @Article{Pennington:1994:NNL, author = "S. V. Pennington and M. Berzins", title = "New {NAG} Library Software for First-Order Partial Differential Equations", journal = j-TOMS, volume = "20", number = "1", pages = "63--99", month = mar, year = "1994", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Sep 06 19:02:59 1994", URL = "http://doi.acm.org/10.1145/174603.155272", acknowledgement = ack-nhfb, } @Article{Hashem:1994:AQE, author = "Sherif Hashem and Bruce Schmeiser", title = "{Algorithm 727}: Quantile Estimation Using Overlapping Batch Statistics", journal = j-TOMS, volume = "20", number = "1", pages = "100--102", month = mar, year = "1994", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Sep 06 19:02:59 1994", URL = "http://doi.acm.org/10.1145/174603.174412", acknowledgement = ack-nhfb, } @Article{Calamai:1994:GQB, author = "Paul H. Calamai and Luis N. Vicente", title = "Generating Quadratic Bilevel Programming Test Problems", journal = j-TOMS, volume = "20", number = "1", pages = "103--119", month = mar, year = "1994", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65-04 (65K05)", MRnumber = "1 368 021", bibdate = "Tue Sep 06 19:02:59 1994", URL = "http://doi.acm.org/10.1145/174603.174411", acknowledgement = ack-nhfb, } @Article{Calamai:1994:AFS, author = "Paul H. Calamai and Luis N. Vicente", title = "{Algorithm 728}: {FORTRAN} Subroutines for Generating Quadratic Bilevel Programming Test Problems", journal = j-TOMS, volume = "20", number = "1", pages = "120--123", month = mar, year = "1994", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65-04 (65K05)", MRnumber = "1 368 022", bibdate = "Tue Sep 06 19:02:59 1994", URL = "http://doi.acm.org/10.1145/174603.174410", acknowledgement = ack-nhfb, } @Article{Jeffrey:1994:ETI, author = "D. J. Jeffrey and A. D. Rich", title = "The Evaluation of Trigonometric Integrals Avoiding Spurious Discontinuities", journal = j-TOMS, volume = "20", number = "1", pages = "124--135", month = mar, year = "1994", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D30 (65-04)", MRnumber = "96h:65034", bibdate = "Tue Sep 06 19:02:59 1994", URL = "http://doi.acm.org/10.1145/174603.174409", acknowledgement = ack-nhfb, } @Article{Matstoms:1994:SQF, author = "Pontus Matstoms", title = "Sparse {QR} Factorization in {MATLAB}", journal = j-TOMS, volume = "20", number = "1", pages = "136--159", month = mar, year = "1994", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Aug 26 23:38:18 1994", URL = "http://doi.acm.org/10.1145/174603.174408", acknowledgement = ack-nhfb, keywords = "multfr; qrd; sparse", } @Article{Hansen:1994:CAF, author = "Per Christian Hansen and Tony F. Chan", title = "Corrigendum: ``{Algorithm 729}: {FORTRAN} Subroutines for General {Toeplitz} Systems''", journal = j-TOMS, volume = "20", number = "1", pages = "160--160", month = mar, year = "1994", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Nov 19 13:10:19 1994", note = "See \cite{Hansen:1992:FSG}.", URL = "http://doi.acm.org/10.1145/174603.174407", acknowledgement = ack-nhfb, } @Article{Ammar:1994:CAI, author = "G. S. Ammar and L. Reichel and D. C. Sorensen", title = "Corrigendum: ``{Algorithm 730}: An Implementation of a Divide and Conquer Algorithm for the Unitary Eigenproblem''", journal = j-TOMS, volume = "20", number = "1", pages = "161--161", month = mar, year = "1994", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Nov 19 13:05:32 1994", note = "See \cite{Ammar:1992:IDC}.", URL = "http://doi.acm.org/10.1145/174603.174406", acknowledgement = ack-nhfb, } @Article{Salvy:1994:GMP, author = "Bruno Salvy and Paul Zimmerman", title = "{GFUN}: {A} {Maple} Package for the Manipulation of Generating and Holonomic Functions in One Variable", journal = j-TOMS, volume = "20", number = "2", pages = "163--177", month = jun, year = "1994", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Nov 19 13:27:17 1994", URL = "http://doi.acm.org/10.1145/178365.178368", acknowledgement = ack-nhfb, keywords = "algorithms; computer algebra; generating functions; linear differential equations; linear recurrences", subject = "G.2.1 [Discrete Mathematics]: Combinatorics--generating functions; recurrences and difference equations; I.1.2 [Algebraic Manipulation]: Algorithms", } @Article{Dayde:1994:PBI, author = "Michael J. Dayd{\'e} and Iain S. Duff and Antoine Petitet", title = "A Parallel Block Implementation of Level-3 {BLAS} for {MIMD} Vector Processors", journal = j-TOMS, volume = "20", number = "2", pages = "178--193", month = jun, year = "1994", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Sep 09 13:52:29 1994", note = "See \cite{Dongarra:1990:ASL,Higham:1990:EFM,Demmel:1992:SBA}.", URL = "http://doi.acm.org/10.1145/178365.174413", acknowledgement = ack-nhfb, keywords = "algorithms; Level-3 BLAS; matrix-matrix kernels; measurement; parallelization; performance; vectorization", subject = "F.2.1 [Analysis of Algorithms and Problem Complexity]: Numerical Algorithms and Problems--computations on matrices; G.1.0 [Numerical Analysis]: General--numerical algorithms; G.1.3 [Numerical Analysis]: Numerical Linear Algebra--linear systems (direct and iterative methods); G.4 [Mathematics of Computing]: Mathematical Software--certification and testing; efficiency; portability; reliability and robustness; verification", } @Article{Blom:1994:AMG, author = "J. G. Blom and P. A. Zegeling", title = "{Algorithm 731}: {A} Moving-Grid Interface for Systems of One-Dimensional Time-Dependent Partial Differential Equations", journal = j-TOMS, volume = "20", number = "2", pages = "194--214", month = jun, year = "1994", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Nov 19 13:27:31 1994", URL = "http://doi.acm.org/10.1145/178365.178391", acknowledgement = ack-nhfb, keywords = "algorithms; Lagrangian methods; mathematical software; method of lines; moving grids; partial differential equations; performance; reliability; time-dependent problems", subject = "G.1.0 [Numerical Analysis]: General; G.1.8 [Numerical Analysis]: Partial Differential Equations; G.4 [Mathematics of Computing]: Mathematical Software", } @Article{Hull:1994:ICE, author = "T. E. Hull and Thomas F. Fairgrieve and Ping Tak Peter Tang", title = "Implementing Complex Elementary Functions Using Exception Handling", journal = j-TOMS, volume = "20", number = "2", pages = "215--244", month = jun, year = "1994", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Mar 21 15:10:29 1995", note = "See \cite{Anonymous:1994:C}.", URL = "http://doi.acm.org/10.1145/178365.178404", abstract = "Algorithms are developed for reliable and accurate evaluations of the complex elementary functions required in Fortran 77 and Fortran 90, namely cabs, csqrt, cexp, clog, csin, and ccos. The algorithms are presented in a pseudocode that has a convenient exception-handling facility. A tight error bound is derived for each algorithm. Corresponding Fortran programs for an IEEE environment have also been developed to illustrate the practicality of the algorithms, and these programs have been tested very carefully to help confirm the correctness of the algorithms and their error bounds. The results are of these tests are included in the paper, but the Fortran programs are not; the programs are available from Fairgrieve, (tff@cs.toronto.edu).", acknowledgement = ack-nhfb, keywords = "algorithms; complex elementary functions; design; implementation", subject = "G.1.0 [Numerical Analysis]: General--error analysis; numerical algorithms; G.1.2 [Numerical Analysis]: Approximation--elementary function approximation; G.4 [Mathematics of Computing]: Mathematical Software--algorithm analysis; reliability and robustness; verification", } @Article{Joe:1994:CIL, author = "Stephen Joe and Ian H. Sloan", title = "Corrigendum: ``{Implementation} of a Lattice Method for Numerical Multiple Integration''", journal = j-TOMS, volume = "20", number = "2", pages = "245--245", month = jun, year = "1994", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Nov 19 13:05:52 1994", note = "See \cite{Joe:1993:ILM}.", acknowledgement = ack-nhfb, xxURL = "Missing from ACM Digital Library", } @Article{Cummins:1994:ASS, author = "Patrick F. Cummins and Geoffrey K. Vallis", title = "{Algorithm 732}: Solvers for Self-Adjoint Elliptic Problems in Irregular Two-Dimensional Domains", journal = j-TOMS, volume = "20", number = "3", pages = "247--261", month = sep, year = "1994", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Nov 19 12:53:13 1994", URL = "http://doi.acm.org/10.1145/192115.192118", acknowledgement = ack-rfb, keywords = "algorithms; capacitance iteration; capacitance matrix; elliptic equations; fast Poisson solvers; Green's function", subject = "G.1.0 [Numerical Analysis]: General -- numerical algorithms; G.1.8 [Numerical Analysis]: Partial Differential Equations -- elliptic equations", } @Article{Kraft:1994:ATF, author = "Dieter Kraft", title = "{Algorithm 733}: {TOMP}---{Fortran} Modules for Optimal Control Calculations", journal = j-TOMS, volume = "20", number = "3", pages = "262--281", month = sep, year = "1994", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Nov 22 09:25:54 1994", URL = "http://doi.acm.org/10.1145/192115.192124", acknowledgement = ack-rfb, keywords = "algorithms; boundary value problems; manipulators; optimal control; robotics; shooting method", subject = "G.1.6 [Numerical Analysis]: Optimization; G.1.7 [Numerical Analysis]: Ordinary Differential Equations; G.4 [Mathematics of Computing]: Mathematical Software; I.2.9 [Artificial Intelligence]: Robotics", } @Article{Averbukh:1994:RA, author = "Victoria Z. Averbukh and Samuel Figueroa and Tamar Schlick", title = "Remark on {Algorithm 566}", journal = j-TOMS, volume = "20", number = "3", pages = "282--285", month = sep, year = "1994", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Nov 19 12:53:17 1994", note = "See \cite{More:1981:AFS}.", URL = "http://doi.acm.org/10.1145/192115.192128", acknowledgement = ack-rfb, keywords = "Hessian subroutines; performance", subject = "D.2.7 [Software Engineering]: Distribution and Maintenance -- documentation; enhancement; G.1.6 [Numerical Analysis]: Optimization -- nonlinear programming", } @Article{More:1994:LSA, author = "Jorge J. Mor{\'e} and David J. Thuente", title = "Line Search Algorithms With Guaranteed Sufficient Decrease", journal = j-TOMS, volume = "20", number = "3", pages = "286--307", month = sep, year = "1994", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "90C30 (65K05)", MRnumber = "96k:90074", bibdate = "Sat Nov 19 12:53:17 1994", URL = "http://doi.acm.org/10.1145/192115.192132", acknowledgement = ack-nhfb, keywords = "algorithms; conjugate gradient algorithms; line search algorithms; nonlinear optimization; truncated Newton algorithms; variable metric algorithms", reviewer = "K. Schittkowski", subject = "G.1.6 [Numerical Analysis]: Optimization -- constrained optimization; gradient methods; nonlinear programming; G.4 [Mathematics of Computing]: Mathematical Software -- algorithm analysis; efficiency; reliability and robustness;", } @Article{Buckley:1994:CFC, author = "A. G. Buckley", title = "Conversion to {Fortran} 90: {A} Case Study", journal = j-TOMS, volume = "20", number = "3", pages = "308--353", month = sep, year = "1994", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Nov 19 12:53:17 1994", URL = "http://doi.acm.org/10.1145/192115.192139", acknowledgement = ack-rfb, keywords = "conversion; Fortran 90; new features; overview", } @Article{Buckley:1994:AFC, author = "A. G. Buckley", title = "{Algorithm 734}: {A} {Fortran} 90 Code for Unconstrained Nonlinear Minimization", journal = j-TOMS, volume = "20", number = "3", pages = "354--372", month = sep, year = "1994", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Nov 19 12:53:17 1994", URL = "http://doi.acm.org/10.1145/192115.192146", acknowledgement = ack-rfb, keywords = "algorithms; conversion; Fortran 90; limited memory; new features; nonlinear optimization; quasi-Newton", subject = "G.1.6 [Numerical Analysis]: Optimization -- gradient methods;", } @Article{Kim:1994:PNA, author = "K. Kim and J. L. Nazareth", title = "A Primal Null-Space Affine-Scaling Method", journal = j-TOMS, volume = "20", number = "3", pages = "373--392", month = sep, year = "1994", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "90C05 (65-04 65K05)", MRnumber = "1 367 801", bibdate = "Sat Nov 19 12:53:17 1994", URL = "http://doi.acm.org/10.1145/192115.192153", acknowledgement = ack-nhfb, keywords = "algorithms; conjugate gradients; diagonal preconditioning; interior-point algorithm; null-space affine scaling; primal method", subject = "G.1.6 [Numerical Analysis]: Optimization -- linear programming;", } @Article{Brown:1994:CAS, author = "Barry W. Brown and Lawrence Levy", title = "Certification of {Algorithm 708}: Significant Digit Computation of the Incomplete Beta", journal = j-TOMS, volume = "20", number = "3", pages = "393--397", month = sep, year = "1994", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Nov 19 12:53:17 1994", note = "See \cite{DiDonato:1992:ASD}.", URL = "http://doi.acm.org/10.1145/192115.192155", acknowledgement = ack-rfb, keywords = "algorithms; continued fractions; F-distribution", subject = "G.1.2 [Numerical Analysis]: Approximation;", } @Article{Taswell:1994:AWT, author = "Carl Taswell and Kevin C. McGill", title = "{Algorithm 735}: Wavelet Transform Algorithms for Finite-Duration Discrete-Time Signals", journal = j-TOMS, volume = "20", number = "3", pages = "398--412", month = sep, year = "1994", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Nov 22 09:25:55 1994", URL = "http://doi.acm.org/10.1145/192115.192156", acknowledgement = ack-rfb, keywords = "algorithms; multiresolution analysis; signal processing; waveform analysis; wavelet transform; wavelets", subject = "G.1.2 [Numerical Analysis]: Approximations; G.4 [Mathematics of Computing]: Mathematical Software; I.4.5 [Image Processing]: Reconstruction;", } @Article{Dunkl:1994:CHI, author = "Charles F. Dunkl and Donald E. Ramirez", title = "Computing Hyperelliptic Integrals for Surface Measure of Ellipsoids", journal = j-TOMS, volume = "20", number = "4", pages = "413--426", month = dec, year = "1994", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D30", MRnumber = "1 368 024", bibdate = "Tue Mar 14 16:16:49 1995", URL = "http://doi.acm.org/10.1145/198429.198430", acknowledgement = ack-rfb, keywords = "elliptic integral; expected radius; Lauricella's hypergeometric function; optimal designs; surface measure", subject = "G.1.4 [Numerical Analysis]: Quadrature and Numerical Differentiation -- multiple quadrature; G.3 [Mathematics of Computing]: Probability and Statistics", } @Article{Dunkl:1994:AHI, author = "Charles F. Dunkl and Donald E. Ramirez", title = "{Algorithm 736}: Hyperelliptic Integrals and the Surface Measure of Ellipsoids", journal = j-TOMS, volume = "20", number = "4", pages = "427--435", month = dec, year = "1994", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D30", MRnumber = "1 368 025", bibdate = "Tue Mar 14 16:16:51 1995", URL = "http://doi.acm.org/10.1145/198429.198431", acknowledgement = ack-rfb, keywords = "elliptic integral; expected radius; Lauricella's hypergeometric function; optimal designs; surface measure", subject = "G.1.4 [Numerical Analysis]: Quadrature and Numerical Differentiation -- multiple quadrature; G.3 [Mathematics of Computing]: Probability and Statistics", } @Article{Fruchtl:1994:NAE, author = "H. Fr{\"u}chtl and P. Otto", title = "A New Algorithm for the Evaluation of the Incomplete Gamma Function on Vector Computers", journal = j-TOMS, volume = "20", number = "4", pages = "436--446", month = dec, year = "1994", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Mar 14 16:16:52 1995", URL = "http://doi.acm.org/10.1145/198429.198432", acknowledgement = ack-rfb, keywords = "Incomplete Gamma Function; quantum chemistry; two-electron integrals", subject = "C.1.2 [Processor Architectures]: Multiple Data Stream Architectures -- array and vector processors; G.1.2 [Numerical Analysis]: Approximation -- rational approximation; G.4 [Mathematics of Computing]: Mathematical Software -- efficiency; J.2 [Computer Applications]: Physical Sciences and Engineering -- chemistry", } @Article{Kearfott:1994:AIP, author = "R. B. Kearfott and M. Dawande and K. Du and C. Hu", title = "{Algorithm 737}: {INTLIB}: {A} Portable {Fortran-77} Elementary Function Library", journal = j-TOMS, volume = "20", number = "4", pages = "447--459", month = dec, year = "1994", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Thu Apr 29 15:22:20 1999", note = "See companion interval arithmetic package \cite{Kearfott:1996:IFM}.", URL = "http://doi.acm.org/10.1145/198429.198433", acknowledgement = ack-rfb, keywords = "BLAS; Fortran 77; Fortran 90; interval arithmetic; operator overloading; standard functions", subject = "D.2.2 [Software Engineering]: Tools and Techniques -- software libraries; D.2.7 [Software Engineering]: Distribution and Maintenance -- documentation; portability; G.1.0 [Numerical Analysis]: General -- computer arithmetic; G.1.2 [Numerical Analysis]: Approximation -- elementary function approximation", } @Article{Peters:1994:EAE, author = "J{\"o}rg Peters", title = "Evaluation and Approximate Evaluation of the Multivariate {Bernstein-B{\'e}zier} Form on a Regularly Partitioned Simplex", journal = j-TOMS, volume = "20", number = "4", pages = "460--480", month = dec, year = "1994", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D17 (65-04)", MRnumber = "1 368 026", bibdate = "Tue Mar 14 16:28:34 1995", URL = "http://doi.acm.org/10.1145/198429.198434", acknowledgement = ack-rfb, keywords = "Bernstein-B{\'e}zier form; evaluation; multivariate; power form; subdivision", subject = "G.1.2 [Numerical Analysis]: Approximation; I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling", } @Article{Li:1994:RSA, author = "Kim-Hung Li", title = "Reservoir Sampling Algorithms of Time Complexity {$O(n(1+\log(N/n)))$}", journal = j-TOMS, volume = "20", number = "4", pages = "481--493", month = dec, year = "1994", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Mar 14 16:16:57 1995", URL = "http://doi.acm.org/10.1145/198429.198435", acknowledgement = ack-rfb, keywords = "analysis of algorithms; random sampling; reservoir", subject = "G.3 [Mathematics of Computing]: Probability and Statistics -- probabilistic algorithms; random number generation; statistical software; G.4 [Mathematics of Computing]: Mathematical Software -- algorithm analysis", } @Article{Bratley:1994:APG, author = "Paul Bratley and Bennett L. Fox and Harald Niederreiter", title = "{Algorithm 738}: {Programs} to Generate {Niederreiter}'s Low-discrepancy Sequences", journal = j-TOMS, volume = "20", number = "4", pages = "494--495", month = dec, year = "1994", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Apr 10 15:51:40 1995", URL = "http://doi.acm.org/10.1145/198429.198436", acknowledgement = ack-rfb, keywords = "low-discrepancy sequences; quasi-Monte Carlo; quasirandom sequences", subject = "G.1.4 [Numerical Analysis]: Quadrature and Numerical Differentiation; I.6 [Computing Methodologies]: Simulation and Modeling", } @Article{Gustafsson:1994:CTT, author = "Kjell Gustafsson", title = "Control Theoretic Techniques for Stepsize Selection in Implicit {Runge-Kutta} Methods", journal = j-TOMS, volume = "20", number = "4", pages = "496--517", month = dec, year = "1994", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65L06", MRnumber = "1 368 027", bibdate = "Tue Mar 14 16:17:00 1995", URL = "http://doi.acm.org/10.1145/198429.198437", acknowledgement = ack-rfb, keywords = "control theory; numerical integration; Runge-Kutta methods; stability; stepsize selection", subject = "G.1.7 [Numerical Analysis]: Ordinary Differential Equations -- initial value problems; single step methods; G.4 [Mathematics of Computing]: Mathematical Software -- algorithm analysis; efficiency; reliability and robustness", } @Article{Chow:1994:ASP, author = "Ta-Tung Chow and Elizabeth Eskow and Robert B. Schnabel", title = "{Algorithm 739}: {A} Software Package for Unconstrained Optimization using Tensor Methods", journal = j-TOMS, volume = "20", number = "4", pages = "518--530", month = dec, year = "1994", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Apr 10 15:51:48 1995", URL = "http://doi.acm.org/10.1145/198429.198438", acknowledgement = ack-rfb, keywords = "higher-order model; tensor method; unconstrained optimization", subject = "G.1.6 [Numerical Analysis]: Optimization -- Gradient methods; G.4 [Mathematics of Computing]: Mathematical Software -- efficiency; reliability and robustness", } @Article{Pinar:1994:DPL, author = "Mustafa Pinar and Stavros A. Zenios", title = "Data-level Parallel Linear-quadratic Penalty Algorithm for Multicommodity Network Flows", journal = j-TOMS, volume = "20", number = "4", pages = "531--552", month = dec, year = "1994", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Mar 14 16:27:42 1995", URL = "http://doi.acm.org/10.1145/198429.198439", acknowledgement = ack-rfb, keywords = "massively parallel algorithms; multicommodity network problems; parallel optimization", subject = "D.1.3 [Programming Techniques]: Concurrent Programming -- parallel programming; E.1 [Data]: Data Structures; G.1.6 [Numerical Analysis]: Optimization -- constrained optimization; nonlinear programming; G.2.2 [Discrete Mathematics]: Graph Theory -- network problems", } @Article{Anonymous:1994:C, author = "Anonymous", title = "Corrigenda", journal = j-TOMS, volume = "20", number = "4", pages = "553--553", month = dec, year = "1994", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Mar 14 16:17:03 1995", note = "See \cite{Hull:1994:ICE}", acknowledgement = ack-rfb, xxURL = "Missing from ACM Digital Library", } @Article{Boisvert:1995:PST, author = "Ronald F. Boisvert", title = "Purpose and Scope: {TOMS}", journal = j-TOMS, volume = "21", number = "1", pages = "1--2", month = mar, year = "1995", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Mar 14 16:17:05 1995", acknowledgement = ack-rfb, xxURL = "Missing from ACM Digital Library", } @Article{Hopkins:1995:PSC, author = "Tim R. Hopkins", title = "Purpose and Scope: {CALGO}", journal = j-TOMS, volume = "21", number = "1", pages = "3--3", month = mar, year = "1995", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Mar 14 16:17:06 1995", acknowledgement = ack-rfb, xxURL = "Missing from ACM Digital Library", } @Article{Jones:1995:IIC, author = "Mark T. Jones and Paul E. Plassmann", title = "An Improved Incomplete {Cholesky} Factorization", journal = j-TOMS, volume = "21", number = "1", pages = "5--17", month = mar, year = "1995", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65F10 (65F50)", MRnumber = "1 365 810", bibdate = "Tue Mar 14 16:17:12 1995", URL = "http://doi.acm.org/10.1145/200979.200981", acknowledgement = ack-rfb, keywords = "incomplete Cholesky; incomplete factorization; preconditioners; sparse matrices", subject = "G.1.3 [Numerical Analysis]: Numerical Linear Algebra -- linear systems; sparse and very large systems", } @Article{Jones:1995:AFS, author = "Mark T. Jones and Paul E. Plassmann", title = "{Algorithm 740}: {Fortran} Subroutines to Compute Improved Incomplete {Cholesky} Factorizations", journal = j-TOMS, volume = "21", number = "1", pages = "18--19", month = mar, year = "1995", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Mar 14 16:17:13 1995", URL = "http://doi.acm.org/10.1145/200979.200986", acknowledgement = ack-rfb, keywords = "incomplete Cholesky; incomplete factorization; preconditioners; sparse matrices", subject = "G.1.3 [Numerical Analysis]: Numerical Linear Algebra -- linear systems; sparse and very large systems", } @Article{Ray:1995:ALS, author = "Richard D. Ray", title = "{Algorithm 741}: Least Squares Solution of a Linear Bordered, Block-diagonal System of Equations", journal = j-TOMS, volume = "21", number = "1", pages = "20--25", month = mar, year = "1995", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Mar 14 16:17:14 1995", URL = "http://doi.acm.org/10.1145/200979.200987", acknowledgement = ack-rfb, keywords = "bordered block-diagonal equations; least-squares solutions; sparse systems", subject = "G.1.3 [Numerical Analysis]: Numerical Linear Algebra -- linear systems (direct and iterative methods); G.1.6 [Numerical Analysis]: Optimization -- least squares methods; G.4 [Mathematics of Computing]: Mathematical Software", } @Article{Fateman:1995:FFP, author = "Richard J. Fateman and Kevin A. Broughan and Diane K. Willcock and Duane Rettig", title = "Fast Floating Point Processing in {Common Lisp}", journal = j-TOMS, volume = "21", number = "1", pages = "26--62", month = mar, year = "1995", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Mar 09 10:20:50 1999", note = "See remark \cite{Reid:1996:RFF}.", URL = "http://doi.acm.org/10.1145/200979.200989", acknowledgement = ack-rfb, keywords = "C programming language; Common Lisp; compiler optimization; floating-point arithmetic; Fortran; Lisp; numerical algorithms; symbolic computation", subject = "D.3.4 [Programming Languages]: Processors -- compilers; interpreters; optimization; G.4 [Mathematics of Computing]: Mathematical Software -- efficiency; portability", } @Article{Kearfott:1995:FER, author = "R. Baker Kearfott", title = "A {Fortran} 90 Environment for Research and Prototyping of Enclosure Algorithms for Nonlinear Equations and Global Optimization", journal = j-TOMS, volume = "21", number = "1", pages = "63--78", month = mar, year = "1995", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat May 20 15:54:41 1995", URL = "http://doi.acm.org/10.1145/200979.200991", acknowledgement = ack-rfb, keywords = "automatic differentiation; Fortran 90; global optimization; nonlinear algebraic systems; symbolic computation", subject = "D.3.3 [Programming Languages]: Language Constructs; G.1.5 [Numerical Analysis]: Roots of Nonlinear Equations; G.1.6 [Numerical Analysis]: Optimization; G.4 [Mathematics of Computing]: Mathematical Software", } @Article{Dongarra:1995:SDX, author = "Jack Dongarra and Tom Rowan and Reed Wade", title = "Software Distribution using {XNETLIB}", journal = j-TOMS, volume = "21", number = "1", pages = "79--88", month = mar, year = "1995", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Mar 14 16:17:18 1995", URL = "http://doi.acm.org/10.1145/200979.200995", acknowledgement = ack-rfb, keywords = "Netlib; software repositories", subject = "C.2.3 [Computer-Communication Networks]: Network Operations -- public networks; D.2.2 [Software Engineering]: Tools and Techniques -- software libraries; user interfaces; D.2.7 [Software Engineering]: Distribution and Maintenance -- documentation; portability; G.1.0 [Numerical Analysis]: General -- numerical algorithms; G.4 [Mathematics of Computing]: Mathematical Software -- portability; H.3.0 [Information Systems Applications]: Communications Applications; H.3.3 [Information Storage and Retrieval]: Information Search and Retrieval -- search process; selection process; H.3.5 [Information Storage and Retrieval]: Online Information Services -- databank sharing; H.5.2 [Information Interfaces and Presentation]: User Interfaces -- windowing systems; K.6.3 [Management of Computing and Information Systems]: Software Management -- software development; software maintenance; software selection", } @Article{Grosse:1995:RM, author = "Eric Grosse", title = "Repository Mirroring", journal = j-TOMS, volume = "21", number = "1", pages = "89--97", month = mar, year = "1995", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Mar 14 16:17:20 1995", URL = "http://doi.acm.org/10.1145/200979.201000", acknowledgement = ack-rfb, keywords = "C.2.4 [Computer-Communication Networks]: Distributed Systems -- distributed databases", subject = "archives; checksum; distributed administration; electronic distribution; ftp", } @Article{Demetriou:1995:ALF, author = "I. C. Demetriou", title = "{Algorithm 742}: {L2CXFT}: {A Fortran} Subroutine for Least Squares Data Fitting with Nonnegative Second Divided Differences", journal = j-TOMS, volume = "21", number = "1", pages = "98--110", month = mar, year = "1995", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Mar 14 16:17:22 1995", URL = "http://doi.acm.org/10.1145/200979.201039", acknowledgement = ack-rfb, keywords = "B-splines; convex approximation; data fitting; divided difference", subject = "G.1.2 [Numerical Analysis]: Approximation -- least squares approximation; G.1.6 [Numerical Analysis]: Optimization -- quadratic programming", } @Article{Weber:1995:AIG, author = "Kenneth Weber", title = "The Accelerated Integer {GCD} Algorithm", journal = j-TOMS, volume = "21", number = "1", pages = "111--122", month = mar, year = "1995", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "68Q20 (68M07)", MRnumber = "96h:68084", bibdate = "Tue Mar 14 16:17:23 1995", URL = "http://doi.acm.org/10.1145/200979.201042", acknowledgement = ack-rfb, keywords = "GCD; integer greatest common divisor; number-theoretic computations", subject = "F.2.1 [Analysis of Algorithms and Problem Complexity]: Numerical Algorithms and Problems", } @Article{Bongartz:1995:CCU, author = "I. Bongartz and A. R. Conn and Nick Gould and Ph.L. Toint", title = "{CUTE}: Constrained and Unconstrained Testing Environment", journal = j-TOMS, volume = "21", number = "1", pages = "123--160", month = mar, year = "1995", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Mar 14 16:17:24 1995", URL = "http://doi.acm.org/10.1145/200979.201043", acknowledgement = ack-rfb, subject = "D.2.2 [Software Engineering]: Tools and Techniques -- modules and interfaces; G.1.6 [ Numerical Analysis]: Optimization -- constrained", } @Article{Barry:1995:RVW, author = "D. A. Barry and P. J. Culligan-Hensley and S. J. Barry", title = "Real Values of the {W}-Function", journal = j-TOMS, volume = "21", number = "2", pages = "161--171", month = jun, year = "1995", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D20", MRnumber = "1 342 353", bibdate = "Tue Oct 10 15:50:28 1995", URL = "http://doi.acm.org/10.1145/203082.203084", acknowledgement = ack-rfb, keywords = "W-function", subject = "G.1.2 [Numerical Analysis]: Approximation -- nonlinear approximation; G.1.5 [Numerical Analysis]: Roots of Nonlinear Equations-iterative methods", } @Article{Barry:1995:AWF, author = "D. A. Barry and S. J. Barry and P. J. Culligan-Hensley", title = "{Algorithm 743}: {WAPR}: {A Fortran} Routine for Calculating Real Values of the {W}-Function", journal = j-TOMS, volume = "21", number = "2", pages = "172--181", month = jun, year = "1995", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D20", MRnumber = "1 342 354", bibdate = "Tue Oct 10 15:50:30 1995", URL = "http://doi.acm.org/10.1145/203082.203088", acknowledgement = ack-rfb, keywords = "W-function", subject = "G.1.2 [Numerical Analysis]: Approximation -- nonlinear approximation; G.1.5 [Numerical Analysis]: Roots of Nonlinear Equations -- iterative methods", } @Article{Hormann:1995:RTS, author = "Wolfgang H{\"o}rmann", title = "A Rejection Technique for Sampling from {T}-Concave Distributions", journal = j-TOMS, volume = "21", number = "2", pages = "182--193", month = jun, year = "1995", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65D20", MRnumber = "96b:65018", bibdate = "Tue Oct 10 15:50:31 1995", URL = "http://doi.acm.org/10.1145/203082.203089", acknowledgement = ack-rfb, keywords = "Log-concave distributions; rejection method; universal method", subject = "G.3 [Probability and Statistics]: Random Number Generation", } @Article{Rabinowitz:1995:ASA, author = "F. Michael Rabinowitz", title = "{Algorithm 744}: {A} Stochastic Algorithm for Global Optimization with Constraints", journal = j-TOMS, volume = "21", number = "2", pages = "194--213", month = jun, year = "1995", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Oct 10 15:50:33 1995", URL = "http://doi.acm.org/10.1145/203082.203090", acknowledgement = ack-rfb, keywords = "Constrained optimization; global optimization; stochastic optimization; test functions", subject = "G.1.6 [Numerical Analysis]: Optimization -- nonlinear programming; G.3 [Mathematics of Computing]: Probability and Statistics -- probabilistic algorithms (including Monte Carlo); G.4 [Mathematics of Computing]: Mathematical Software -- certification and testing", } @Article{Goano:1995:ACC, author = "Michele Goano", title = "{Algorithm 745}: Computation of the Complete and Incomplete {Fermi-Dirac} Integral", journal = j-TOMS, volume = "21", number = "3", pages = "221--232", month = sep, year = "1995", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Mar 09 10:19:43 1999", note = "See remark \cite{Goano:1997:RA7}", URL = "http://doi.acm.org/10.1145/210089.210090", acknowledgement = ack-rfb, keywords = "asymptotic expansions; confluent hypergeometric functions; convergence acceleration; e[k] transforms; epsilon algorithm; Euler transformation; Fermi-Dirac integral; incomplete Fermi-Dirac integral; incomplete gamma function; Levin's u transform; Riemann's zeta function", subject = "G.1.2 [Mathematics of Computing]: Approximation; G.4 [Mathematics of Computing]: Mathematical Software; J.2 [Computer Applications]: Physical Sciences and Engineering", } @Article{Dobmann:1995:APF, author = "M. Dobmann and M. Liepelt and K. Schittkowski", title = "{Algorithm 746}: {PCOMP}: {A Fortran} Code for Automatic Differentiation", journal = j-TOMS, volume = "21", number = "3", pages = "233--266", month = sep, year = "1995", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/210089.210091", acknowledgement = ack-rfb, keywords = "automatic differentiation; forward accumulation; reverse accumulation", subject = "D.1.2 [Programming Techniques]: Automatic Programming; D.3.4 [Programming Languages]: Processors - code generation; G.1.4 [Numerical Analysis]: Quadrature and Numerical Differentiation; G.4 [Mathematics of Computing]: Mathematical Software", } @Article{Sullivan:1995:NAU, author = "Stephen J. Sullivan and Benjamin G. Zorn", title = "Numerical Analysis Using Nonprocedural Paradigms", journal = j-TOMS, volume = "21", number = "3", pages = "267--298", month = sep, year = "1995", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/210089.210093", acknowledgement = ack-rfb, keywords = "benchmarks; experimental languages; Gaussian elimination; linear algebra; programming languages; sparse matrices", subject = "G.1 [Mathematics of Computing]: Numerical Analysis", } @Article{Miminis:1995:AFS, author = "George Miminis and Helmut Roth", title = "{Algorithm 747}: {A Fortran} Subroutine to Solve the Eigenvalue Assignment Problem for Multiinput Systems Using State Feedback", journal = j-TOMS, volume = "21", number = "3", pages = "299--326", month = sep, year = "1995", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/210089.210094", acknowledgement = ack-rfb, keywords = "deflation; double steps; eigenvalue assignment; numerical efficiency; pole assignment", subject = "F.2.1 [Analysis of Algorithms and Problem Complexity]: Numerical Algorithms and Problems - computations on matrices; G.1.0 [Numerical Analysis]: General - numerical algorithms; G.1.3 [Numerical Analysis]: Numerical Linear Algebra - eigenvalues; J.2 [Computer Applications]: Physical Sciences and Engineering - aerospace; engineering; J.4 [Computer Applications]: Social and Behavioral Sciences - economics", } @Article{Alefeld:1995:AEZ, author = "G. E. Alefeld and F. A. Potra and Yixun Shi", title = "{Algorithm 748}: Enclosing Zeros of Continuous Functions", journal = j-TOMS, volume = "21", number = "3", pages = "327--344", month = sep, year = "1995", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Thu Sep 28 16:39:05 1995", URL = "http://doi.acm.org/10.1145/210089.210111", keywords = "algorithms; asymptotic efficiency index; enclosing method; inverse cubic interpolation; quadratic interpolation; simple root; theory", subject = "G.1.0 [Numerical Analysis]: General -- numerical algorithms; G.1.5 [Numerical Analysis]: Roots of Nonlinear Equations -- convergence; iterative methods", } @Article{Rizzardi:1995:MTM, author = "Mariarosaria Rizzardi", title = "A Modification of {Talbot}'s Method for the Simultaneous Approximation of Several Values of the Inverse {Laplace} Transform", journal = j-TOMS, volume = "21", number = "4", pages = "347--371", month = dec, year = "1995", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65R10", MRnumber = "96k:65084", bibdate = "Sat Feb 10 08:48:51 1996", URL = "http://doi.acm.org/10.1145/212066.212068", acknowledgement = ack-rfb, keywords = "complex inversion formula; inverse Laplace transform; numerical method; Talbot; trapezoidal rule", reviewer = "A. J. Rodrigues", subject = "G.1.0 [Numerical Analysis]: General -- error analysis; numerical algorithms; G.1.2 [Numerical Analysis]: Approximation -- nonlinear approximation; G.1.4 [Numerical Analysis]: Quadrature and Numerical Differentiation -- equal interval integration; error analysis; G.1.9 [Numerical Analysis]: Integral Equations -- Fredholm equations", } @Article{Sherlock:1995:AFD, author = "Barry G. Sherlock and Donald M. Monro", title = "{Algorithm 749}: Fast Discrete Cosine Transform", journal = j-TOMS, volume = "21", number = "4", pages = "372--378", month = dec, year = "1995", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Nov 14 09:58:14 1995", URL = "http://doi.acm.org/10.1145/212066.212071", acknowledgement = ack-rfb, keywords = "data compression; discrete cosine transform; fast transform", subject = "D.3.2 [Programming Languages]: Language Classifications -- Fortran; E.4 [Data]: Coding and Information Theory -- data compaction and compression; F.2.1 [Analysis of Algorithms and Problem Complexity]: Numerical Algorithms and Problems; G.4 [Mathematics of Computing]: Mathematical Software; I.4.2 [Image Processing]: Compression", } @Article{Bailey:1995:FBM, author = "David H. Bailey", title = "A {Fortran-90} Based Multiprecision System", journal = j-TOMS, volume = "21", number = "4", pages = "379--387", month = dec, year = "1995", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Thu Apr 29 15:15:44 1999", note = "See also extension to complex arithmetic \cite{Smith:1998:AMP}.", URL = "http://doi.acm.org/10.1145/212066.212075", acknowledgement = ack-rfb, keywords = "arithmetic; Fortran 90; multiprecision", subject = "D.3.2 [Programming Languages]: Language Classifications -- Fortran 90; D.3.4 [Programming Languages]: Processors; G.1.0 [Numerical Analysis]: General; G.1.2 [Numerical Analysis]: Approximation", } @Article{Amos:1995:RAP, author = "D. E. Amos", title = "A Remark on {Algorithm 644}: {A} Portable Package for {Bessel} Functions of a Complex Argument and Nonnegative Order", journal = j-TOMS, volume = "21", number = "4", pages = "388--393", month = dec, year = "1995", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Mar 09 10:24:54 1999", note = "See \cite{Amos:1986:APP,Amos:1990:RPP}.", URL = "http://doi.acm.org/10.1145/212066.212078", acknowledgement = ack-rfb, keywords = "complex Airy Functions; complex Bessel functions; derivatives of Airy functions; H, I, J, K, and Y Bessel functions; log gamma function", subject = "G.1.0 [Numerical Analysis]: General -- numerical algorithms; G.1.m [Numerical Analysis]: Miscellaneous; G.m [Mathematics of Computing]: Miscellaneous", } @Article{Carpaneto:1995:ESL, author = "G. Carpaneto and M. Dell'Amico and P. Toth", title = "Exact Solution of Large Scale Asymmetric Travelling Salesman Problems", journal = j-TOMS, volume = "21", number = "4", pages = "394--409", month = dec, year = "1995", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "90C27 (90C35)", MRnumber = "96m:90062a", bibdate = "Tue Nov 14 09:58:01 1995", URL = "http://doi.acm.org/10.1145/212066.212081", acknowledgement = ack-rfb, keywords = "assignment problem; asymmetric traveling salesman problem; branch and bound; reduction procedure; subtour elimination", reviewer = "N. I. Yanev", subject = "G.2.1 [Discrete Mathematics]: Combinatorics -- combinatorial algorithms; G.2.2 [Discrete Mathematics]: Graph Theory -- graph algorithms; path and circuit problems", } @Article{Carpaneto:1995:ACS, author = "G. Carpaneto and M. Dell'Amico and P. Toth", title = "{Algorithm 750}: {CDT}: {A} Subroutine for the Exact Solution of Large-Scale Asymmetric Travelling Salesman Problems", journal = j-TOMS, volume = "21", number = "4", pages = "410--415", month = dec, year = "1995", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "90C27 (90C35)", MRnumber = "96m:90062b", bibdate = "Tue Nov 14 09:57:58 1995", URL = "http://doi.acm.org/10.1145/212066.212084", acknowledgement = ack-rfb, keywords = "assignment problem; asymmetric traveling salesman problem; branch and bound; reduction procedure; subtour elimination", reviewer = "N. I. Yanev", subject = "D.3.2 [Programming Languages]: Language classifications -- Fortran; G.2.1 [Discrete Mathematics]: Combinatorics -- combinatorial algorithms; G.2.2 [Discrete Mathematics]: Graph Theory -- graph algorithms; path and circuit problems", } @Article{Doman:1995:SAP, author = "B. G. S. Doman and C. J. Pursglove and W. M. Coen", title = "A Set of {Ada} Packages for High Precision Calculations", journal = j-TOMS, volume = "21", number = "4", pages = "416--431", month = dec, year = "1995", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Nov 14 09:57:55 1995", URL = "http://doi.acm.org/10.1145/212066.212087", acknowledgement = ack-rfb, keywords = "accuracy; Ada; arithmetic elementary-function evaluation; floating-point; multiple-precision portable software", subject = "G.1.0 [Numerical Analysis]: General -- computer arithmetic; G.1.2 [Numerical Analysis]: Approximation -- elementary function approximation; G.4 [Mathematics of Computing]: Mathematical Software -- algorithm analysis; efficiency; portability", } @Article{Scott:1995:ACC, author = "Jennifer A. Scott", title = "An {Arnoldi} Code for Computing Selected Eigenvalues of Sparse, Real, Unsymmetric Matrices", journal = j-TOMS, volume = "21", number = "4", pages = "432--475", month = dec, year = "1995", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65-04 (65F15 65F50)", MRnumber = "1 364 698", bibdate = "Tue Nov 14 09:57:52 1995", URL = "http://doi.acm.org/10.1145/212066.212091", acknowledgement = ack-rfb, keyword = "Arnoldi's method; Chebychev acceleration; large sparse matrices; real unsymmetric matrices", subject = "G.1.0 [Numerical Analysis]: General -- numerical algorithms; G.1.3 [Numerical Analysis]: Numerical Linear Algebra -- eigenvalues", } @Article{Kaufman:1995:CMD, author = "Linda Kaufman", title = "Computing the ${MDM}^{T}$ decomposition", journal = j-TOMS, volume = "21", number = "4", pages = "476--489", month = dec, year = "1995", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Nov 14 09:57:49 1995", URL = "http://doi.acm.org/10.1145/212066.212092", acknowledgement = ack-rfb, keywords = "block factorizations; LAPACK; linear systems (direct methods); symmetric indefinite", subject = "G.1.3 [Numerical Analysis]: Numerical Linear Algebra -- linear systems (direct and iterative methods); G.4 [Mathematics of Computing]: Mathematical Software -- efficiency", } @Article{Duff:1995:CCS, author = "Iain S. Duff and Jennifer A. Scott", title = "Corrigendum: Computing Selected Eigenvalues of Sparse Unsymmetric Matrices Using Subspace Iteration", journal = j-TOMS, volume = "21", number = "4", pages = "490--490", month = dec, year = "1995", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Nov 14 09:57:46 1995", note = "See \cite{Duff:1993:CSE}.", URL = "http://doi.acm.org/10.1145/212066.215254", acknowledgement = ack-rfb, } @Article{Renka:1996:ATC, author = "R. J. Renka", title = "{Algorithm 751}: {TRIPACK}: a constrained two-dimensional {Delaunay} triangulation package", journal = j-TOMS, volume = "22", number = "1", pages = "1--8", month = mar, year = "1996", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Thu Jul 15 18:58:33 1999", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", note = "See remark \cite{Renka:1999:RAa}.", URL = "http://doi.acm.org/10.1145/225545.225546", abstract = "TRIPACK is a Fortran 77 software package that employs an incremental algorithm to construct a constrained Delaunay triangulation of a set of points in the plane (nodes). The triangulation covers the convex hull of the nodes but may include polygonal constraint regions whose triangles are distinguishable from those in the remainder of the triangulation. This effectively allows for a nonconvex or multiply connected triangulation (the complement of the union of constraint regions) while retaining the efficiency of searching and updating a convex triangulation. The package provides a wide range of capabilities including an efficient means of updating the triangulation with nodal additions or deletions. For $N$ nodes, the storage requirement is $13N$ integer storage locations in addition to the $2N$ nodal coordinates.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation.", } @Article{Renka:1996:ASS, author = "R. J. Renka", title = "{Algorithm 752}: {SRFPACK}: software for scattered data fitting with a constrained surface under tension", journal = j-TOMS, volume = "22", number = "1", pages = "9--17", month = mar, year = "1996", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 31 16:07:02 MDT 1996", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", note = "See remark \cite{Renka:1999:RAb}.", URL = "http://doi.acm.org/10.1145/225545.225547", abstract = "SRFPACK is a Fortran 77 software package that constructs a smooth interpolatory or approximating surface to data values associated with arbitrarily distributed points in the plane. It employs automatically selected tension factors to preserve shape properties of the data and to avoid overshoot and undershoot associated with steep gradients. The domain of the fitting function may be nonconvex or multiply connected, and the surface may be constrained to have discontinuous value or derivative across a user-specified curve representing, for example, a geological fault line. Although triangle based, the method provides a means of avoiding the inaccuracy associated with long thin triangles on the boundary of the convex hull of the data abscissae.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation.", } @Article{Buis:1996:EVP, author = "Paul E. Buis and Wayne R. Dyksen", title = "Efficient vector and parallel manipulation of tensor products", journal = j-TOMS, volume = "22", number = "1", pages = "18--23", month = mar, year = "1996", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "68Q40", MRnumber = "1 383 183", bibdate = "Sat Aug 31 16:07:02 MDT 1996", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/225545.225548", abstract = "We present efficient vector and parallel methods for manipulating tensor products of matrices. We consider both computing the matrix-vector product $(A_{1} \otimes \cdots \otimes A_{K})x$ and solving the system of linear equations $(A_{1} \otimes \cdots \otimes A_{K})x=b$. The methods described are independent of $K$. We accompany this article with a companion algorithm which describes an implementation of a complete set of tensor product routines based on LAPACK and the Level 2 and 3 Basic Linear Algebra Subprograms (BLAS) which provide vectorization and parallelization.", acknowledgement = ack-nhfb, keywords = "algorithms; performance", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra. {\bf D.1.3}: Software, PROGRAMMING TECHNIQUES, Concurrent Programming. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Buis:1996:ATL, author = "Paul E. Buis and Wayne R. Dyksen", title = "{Algorithm 753}: {TENPACK}: {A} {LAPACK-based} library for the computer manipulation of tensor products", journal = j-TOMS, volume = "22", number = "1", pages = "24--29", month = mar, year = "1996", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 31 16:07:02 MDT 1996", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/225545.225549", abstract = "This article presents the interface of an implementation of methods to manipulate equations of this form $A_{1} \otimes \cdots \otimes A_{m}$ where the $A_{i}$ are matrices. The methods described are independent of m. The code is based on LAPACK and the BLAS and supports virtually all of the matrix formats supported by those packages. Timings of the implementation on several machines are also given.", acknowledgement = ack-nhfb, keywords = "algorithms; performance", subject = "{\bf D.1.3}: Software, PROGRAMMING TECHNIQUES, Concurrent Programming. {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Duff:1996:DNF, author = "I. S. Duff and J. A. Scott", title = "The design of a new frontal code for solving sparse, unsymmetric systems", journal = j-TOMS, volume = "22", number = "1", pages = "30--45", month = mar, year = "1996", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65-04 (65F50)", MRnumber = "1 383 184", bibdate = "Sat Aug 31 16:07:02 MDT 1996", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/225545.225550", abstract = "We describe the design, implementation, and performance of a frontal code for the solution of large, sparse, unsymmetric systems of linear equations. The resulting software package, MA42, is included in Release 11 of the Harwell Subroutine Library and is intended to supersede the earlier MA32 package. We discuss in detail the extensive use of higher-level BLAS kernels within MA42 and illustrate the performance on a range of practical problems on a CRAY Y-MP, an IBM 3090, and an IBM RISC System/6000. We examine extending the frontal solution scheme to use multiple fronts to allow MA42 to be run in parallel. We indicate some directions for future development.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Freund:1996:QPQ, author = "Roland W. Freund and No{\"e}l M. Nachtigal", title = "{QMRPACK}: a package of {QMR} algorithms", journal = j-TOMS, volume = "22", number = "1", pages = "46--77", month = mar, year = "1996", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65-04 (65F10)", MRnumber = "1 383 185", bibdate = "Sat Aug 31 16:07:02 MDT 1996", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/225545.225551", abstract = "The quasi-minimal residual (QMR) algorithm is a Krylov-subspace method for the iterative solution of large non-Hermitian linear systems. QMR is based on the look-ahead Lanczos algorithm that, by itself, can also be used to obtain approximate eigenvalues of large non-Hermitian matrices. QMRPACK is a software package with Fortran 77 implementations of the QMR algorithm and variants thereof, and of the three-term and coupled two-term look-ahead Lanczos algorithms. In this article, we discuss some of the features of the algorithms in the package, with emphasis on the issues related to using the codes. We describe in some detail two routines from the package, one for the solution of linear systems and the other for the computation of eigenvalue approximations. We present some numerical examples from applications where QMRPACK was used.", acknowledgement = ack-nhfb, keywords = "algorithms; reliability; theory", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Reliability and robustness. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Eigenvalues. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency.", } @Article{Kaagstrom:1996:LAS, author = "Bo K{\aa}gstr{\"o}m and Peter Poromaa", title = "{LAPACK-style} algorithms and software for solving the generalized {Sylvester} equation and estimating the separation between regular matrix pairs", journal = j-TOMS, volume = "22", number = "1", pages = "78--103", month = mar, year = "1996", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65-04 (65F30)", MRnumber = "1 383 186", bibdate = "Sat Aug 31 16:07:02 MDT 1996", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/225545.225552", abstract = "Robust and fast software to solve the generalized Sylvester equation ($AR - LB = C, DR - LE = F$) for unknowns $R$ and $L$ is presented. This special linear system of equations, and its transpose, arises in computing error bounds for computed eigenvalues and eigenspaces of the generalized eigenvalue problem $S-\lambda T$, in computing deflating subspaces of the same problem, and in computing certain decompositions of transfer matrices arising in control theory. Our contributions are twofold. First, we reorganize the standard algorithm for this problem to use Level 3 BLAS operations, like matrix multiplication, in its inner loop. This speeds up the algorithm by a factor of 9 on an IBM RS6000. Second, we develop and compare several condition estimation algorithms, which inexpensively but accurately estimate the sensitivity of the solution of this linear system.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Reliability and robustness. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Conditioning. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Eigenvalues. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Matrix inversion.", } @Article{Resende:1996:AFS, author = "Mauricio G. C. Resende and Panos M. Pardalos and Yong Li", title = "{Algorithm 754}: {Fortran} subroutines for approximate solution of dense quadratic assignment problems using {GRASP}", journal = j-TOMS, volume = "22", number = "1", pages = "104--118", month = mar, year = "1996", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 31 16:07:02 MDT 1996", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/225545.225553", abstract = "In the NP-complete quadratic assignment problem (QAP), $n$ facilities are to be assigned to $n$ sites at minimum cost. The contribution of assigning facility $i$ to site $k$ and facility $j$ to site $l$ to the total cost is $f_{ij} - d_{kl}$, where $f_{ij}$ is the flow between facilities $i$ and $j$, and $d_{kl}$ is the distance between sites $k$ and $l$. Only very small ($n\le20$) instances of the QAP have been solved exactly, and heuristics are therefore used to produce approximate solutions. This article describes a set of Fortran subroutines to find approximate solutions to dense quadratic assignment problems, having at least one symmetric flow or distance matrix. A greedy, randomized, adaptive search procedure (GRASP) is used to produce the solutions. The design and implementation of the code are described in detail, and extensive computational experiments are reported, illustrating solution quality as a function of running time.", acknowledgement = ack-nhfb, keywords = "algorithms; performance", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Integer programming. {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN. {\bf G.2.1}: Mathematics of Computing, DISCRETE MATHEMATICS, Combinatorics, Combinatorial algorithms.", } @Article{Wallace:1996:FPG, author = "C. S. Wallace", title = "Fast pseudorandom generators for normal and exponential variates", journal = j-TOMS, volume = "22", number = "1", pages = "119--127", month = mar, year = "1996", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 31 16:07:02 MDT 1996", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/225545.225554", abstract = "Fast algorithms for generating pseudorandom numbers from the unit-normal and unit-exponential distributions are described. The methods are unusual in that they do not rely on a source of uniform random numbers, but generate the target distributions directly by using their maximal-entropy properties. The algorithms are fast. The normal generator is faster than the commonly used Unix library uniform generator ``random'' when the latter is used to yield real values. Their statistical properties seem satisfactory, but only a limited suite of tests has been conducted. They are written in C and as written assume 32-bit integer arithmetic. The code is publicly available as C source and can easily be adopted for longer word lengths and/or vector processing.", acknowledgement = ack-nhfb, keywords = "algorithms; design; performance", subject = "{\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Random number generation. {\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Statistical computing.", } @Article{Griewank:1996:AAP, author = "Andreas Griewank and David Juedes and Jean Utke", title = "{Algorithm 755}: {ADOL-C}: a package for the automatic differentiation of algorithms written in {C\slash C++}", journal = j-TOMS, volume = "22", number = "2", pages = "131--167", month = jun, year = "1996", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 31 16:07:02 MDT 1996", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/229473.229474", abstract = "The C++ package ADOL-C described here facilitates the evaluation of first and higher derivatives of vector functions that are defined by computer programs written in C or C++. The resulting derivative evaluation routines may be called from C/C++, Fortran, or any other language that can be linked with C. The numerical values of derivative vectors are obtained free of truncation errors at a small multiple of the run-time and randomly accessed memory of the given function evaluation program. Derivative matrices are obtained by columns or rows. For solution curves defined by ordinary differential equations, special routines are provided that evaluate the Taylor coefficient vectors and their Jacobians with respect to the current state vector. The derivative calculations involve a possibly substantial (but always predictable) amount of data that are accessed strictly sequentially and are therefore automatically paged out to external files.", acknowledgement = ack-nhfb, keywords = "algorithms; performance", subject = "{\bf G.1.4}: Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation. {\bf I.1.2}: Computing Methodologies, ALGEBRAIC MANIPULATION, Algorithms, Analysis of algorithms. {\bf I.1.2}: Computing Methodologies, ALGEBRAIC MANIPULATION, Algorithms.", } @Article{Driscoll:1996:AMT, author = "Tobin A. Driscoll", title = "{Algorithm 756}: a {MATLAB} Toolbox for {Schwarz-Christoffel} mapping", journal = j-TOMS, volume = "22", number = "2", pages = "168--186", month = jun, year = "1996", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 31 16:07:02 MDT 1996", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/229473.229475", abstract = "The Schwarz-Christoffel transformation and its variations yield formulas for conformal maps from standard regions to the interiors or exteriors of possibly unbounded polygons. Computations involving these maps generally require a computer, and although the numerical aspects of these transformations have been studied, there are few software implementations that are widely available and suited for general use. The Schwarz-Christoffel Toolbox for MATLAB is a new implementation of Schwarz-Christoffel formulas for maps from the disk, half-plane, strip, and rectangle domains to polygon interiors, and from the disk to polygon exteriors. The toolbox, written entirely in the MATLAB script language, exploits the high-level functions, interactive environment, visualization tools, and graphical user interface elements supplied by current versions of MATLAB, and is suitable for use both as a standalone tool and as a library for applications written in MATLAB, Fortran, or C. Several examples and simple applications are presented to demonstrate the toolbox's capabilities.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.1.m}: Mathematics of Computing, NUMERICAL ANALYSIS, Miscellaneous. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, MATLAB. {\bf J.2}: Computer Applications, PHYSICAL SCIENCES AND ENGINEERING.", } @Article{Duff:1996:DMC, author = "I. S. Duff and J. K. Reid", title = "The design of {MA48}: a code for the direct solution of sparse unsymmetric linear systems of equations", journal = j-TOMS, volume = "22", number = "2", pages = "187--226", month = jun, year = "1996", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 31 16:07:02 MDT 1996", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/229473.229476", abstract = "We describe the design of a new code for the direct solution of sparse unsymmetric linear systems of equations. The new code utilizes a novel restructuring of the symbolic and numerical phases, which increases speed and saves storage without sacrifice of numerical stability. Other features include switching to full-matrix processing in all phases of the computation enabling the use of all three levels of BLAS, treatment of rectangular or rank-deficient matrices, partial factorization, and integrated facilities for iterative refinement and error estimation.", acknowledgement = ack-nhfb, keywords = "algorithms; performance", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse and very large systems.", } @Article{Duff:1996:EZD, author = "I. S. Duff and J. K. Reid", title = "Exploiting zeros on the diagonal in the direct solution of indefinite sparse symmetric linear systems", journal = j-TOMS, volume = "22", number = "2", pages = "227--257", month = jun, year = "1996", CODEN = "ACMSCU", ISSN = "0098-3500", MRclass = "65F50", MRnumber = "1 408 491", bibdate = "Sat Aug 31 16:07:02 MDT 1996", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/229473.229480", abstract = "We describe the design of a new code for the solution of sparse indefinite symmetric linear systems of equations. The principal difference between this new code and earlier work lies in the exploitation of the additional sparsity available when the matrix has a significant number of zero diagonal entries. Other new features have been included to enhance the execution speed, particularly on vector and parallel machines.", acknowledgement = ack-nhfb, keywords = "algorithms; performance", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse and very large systems.", } @Article{Price:1996:RA, author = "David T. Price", title = "Remark on {Algorithm 715}", journal = j-TOMS, volume = "22", number = "2", pages = "258--258", month = jun, year = "1996", CODEN = "ACMSCU", ISSN = "0098-3500", note = "See \cite{Cody:1993:ASE}", URL = "http://doi.acm.org/10.1145/229473.236186", } @Article{Hull:1996:MBP, author = "T. E. Hull and R. Mathon", title = "The mathematical basis and a prototype implementation of a new polynomial rootfinder with quadratic convergence", journal = j-TOMS, volume = "22", number = "3", pages = "261--280", month = sep, year = "1996", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 31 16:07:02 MDT 1996", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/232826.232830", abstract = "Formulas developed originally by Weierstrass have been used since the 1960s by many others for the simultaneous determination of all the roots of a polynomial. Convergence to simple roots is quadratic, but individual approximations to a multiple root converge only linearly. However, it is shown here that the mean of such individual approximations converges quadratically to that root. This result, along with some detail about the behavior of such approximations in the neighborhood of the multiple root, suggests a new approach to the design of polynomial rootfinders. It should also be noted that the technique is well suited to take advantage of a parallel environment. This article first provides the relevant mathematical results: a short derivation of the formulas, convergence proofs, an indication of the behavior near a multiple root, and some error bounds. It then provides the outline of an algorithm based on these results, along with some graphical and numerical results to illustrate the major theoretical points. Finally, a new program based on this algorithm, but with a more efficient way of choosing starting values, is described and then compared with corresponding programs from IMSL and NAG with good results. This program is available from Mathon (\path=combin@cs.utoronto.ca=).", acknowledgement = ack-nhfb, keywords = "algorithms; design", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Error analysis. {\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf G.1.5}: Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Convergence. {\bf G.1.5}: Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Error analysis. {\bf G.1.5}: Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Iterative methods. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Sosonkina:1996:NEG, author = "Maria Sosonkina and Layne T. Watson and David E. Stewart", title = "Note on the end game in homotopy zero curve tracking", journal = j-TOMS, volume = "22", number = "3", pages = "281--287", month = sep, year = "1996", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 31 16:07:02 MDT 1996", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/232826.232843", abstract = "Homotopy algorithms to solve a nonlinear system of equations $f(x) = 0$ involve tracking the zero curve of a homotopy map $p(a, \lambda, x)$ from $\lambda = 0$ until $\lambda = 1$. When the algorithm nears or crosses the hyperplane $\lambda = 1$, an ``end game'' phase is begun to compute the solution *** satisfying $p(a, \lambda, ***) = f(**) = 0$. This note compares several end game strategies, including the one implemented in the normal flow code FIXPNF in the homotopy software package HOMPACK.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.1.5}: Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Systems of equations. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Macleod:1996:AMS, author = "Allan J. Macleod", title = "{Algorithm 757}: {MISCFUN}, a software package to compute uncommon special functions", journal = j-TOMS, volume = "22", number = "3", pages = "288--301", month = sep, year = "1996", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 31 16:07:02 MDT 1996", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/232826.232846", abstract = "MISCFUN (MISCellaneous FUNctions) is a Fortran package for the evaluation of several special functions, which are not used often enough to have been included in the standard libraries or packages. The package uses Chebyshev expansions as the underlying method of approximation, with the Chebyshev coefficients given to 20D. A wide variety of functions are included, and the package is designed so that other functions can be added in a standard manner.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Chebyshev approximation and theory. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing.", } @Article{Blom:1996:AVVa, author = "J. G. Blom and R. A. Trompert and J. G. Verwer", title = "{Algorithm 758}: {VLUGR2}: a vectorizable adaptive-grid solver for {PDEs} in {2D}", journal = j-TOMS, volume = "22", number = "3", pages = "302--328", month = sep, year = "1996", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 31 16:07:02 MDT 1996", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/232826.232850", abstract = "This article deals with an adaptive-grid finite-difference solver for time-dependent two-dimensional systems of partial differential equations. It describes the ANSI Fortran 77 code, VLUGR2, autovectorizable on the Cray Y-MP, that is based on this method. The robustness and the efficiency of the solver, both for vector and scalar processors, are illustrated by the application of the code to two example problems arising from a groundwater-flow model.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN. {\bf G.1.8}: Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Blom:1996:AVVb, author = "J. G. Blom and J. G. Verwer", title = "{Algorithm 759}: {VLUGR3}: a vectorizable adaptive-grid solver for {PDEs} in {3D} --- Part {II}. code description", journal = j-TOMS, volume = "22", number = "3", pages = "329--347", month = sep, year = "1996", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 31 16:07:02 MDT 1996", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/232826.232853", abstract = "This article describes an ANSI Fortran 77 code, VLUGR3, autovectorizable on the Cray Y-MP, that is based on an adaptive-grid finite-difference method to solve time-dependent three-dimensional systems of partial differential equations.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN. {\bf G.1.8}: Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Andersen:1996:MSM, author = "Knud D. Andersen", title = "A modified {Schur-complement} method for handling dense columns in interior-point methods for linear programming", journal = j-TOMS, volume = "22", number = "3", pages = "348--356", month = sep, year = "1996", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 31 16:07:02 MDT 1996", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/232826.232937", abstract = "The main computational work in interior-point methods for linear programming (LP) is to solve a least-squares problem. The normal equations are often used, but if the LP constraint matrix contains a nearly dense column the normal-equations matrix will be nearly dense. Assuming that the nondense part of the constraint matrix is of full rank, the Schur complement can be used to handle dense columns. In this article we propose a modified Schur-complement method that relaxes this assumption. Encouraging numerical results are presented.", acknowledgement = ack-nhfb, subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Linear programming.", } @Article{Akima:1996:ARS, author = "Hiroshi Akima", title = "{Algorithm 760}: rectangular-grid-data surface fitting that has the accuracy of a bicubic polynomial", journal = j-TOMS, volume = "22", number = "3", pages = "357--361", month = sep, year = "1996", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Aug 31 16:07:02 MDT 1996", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/232826.232854", abstract = "A local algorithm for smooth surface fitting for rectangular-grid data has been presented. It has the accuracy of a bicubic polynomial.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN. {\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Akima:1996:ASS, author = "Hiroshi Akima", title = "{Algorithm 761}: scattered-data surface fitting that has the accuracy of a cubic polynomial", journal = j-TOMS, volume = "22", number = "3", pages = "362--371", month = sep, year = "1996", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Mar 09 10:11:35 1999", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", note = "See remarks \cite{Renka:1998:RA,deTisi:2000:RAS}.", URL = "http://doi.acm.org/10.1145/232826.232856", abstract = "An algorithm for smooth surface fitting for scattered data has been presented. It has the accuracy of a cubic polynomial in most cases and is a local, triangle-based algorithm.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN. {\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Brown:1996:ALL, author = "Barry W. Brown and Lawrence B. Levy and James Lovato and Kathy Russell and Floyd M. Spears", title = "{Algorithm 762}: {LLDRLF}, log-likelihood and some derivatives for {log-F} models", journal = j-TOMS, volume = "22", number = "3", pages = "372--382", month = sep, year = "1996", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Mar 28 11:11:08 2003", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/232826.232858", abstract = "The flexible statistical models incorporating the log-F distribution are little used because of numeric difficulties. We describe a method for calculating the log-likelihood and two derivatives with respect to the data argument. Fortran subroutines incorporating these calculations are provided.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation.", } @Article{Kearfott:1996:IFM, author = "R. Baker Kearfott", title = "{Algorithm 763}: {INTERVAL\_ARITHMETIC}: {A Fortran 90} Module for an Interval Data Type", journal = j-TOMS, volume = "22", number = "4", pages = "385--392", month = dec, year = "1996", CODEN = "ACMSCU", ISSN = "0098-3500", note = "See \cite{Kearfott:1994:AIP}.", URL = "http://doi.acm.org/10.1145/235815.235816", abstract = "Interval arithmetic is useful in {\it automatically verified computation}, that is, in computations in which the algorithm itself rigorously proves that the answer must lie within certain bounds. In addition to rigor, interval arithmetic also provides a simple and somewhat sharp method of bounding ranges of functions for global optimization and other tasks. Convenient use of interval arithmetic requires an interval data type in the programming language. Although various packages supply such a data type, previous ones are machine specific, obsolete, and unsupported, for languages other than Fortran, or commercial. The Fortran 90 module {INTERVAL\_ARITHMETIC} provides a portable interval data type in Fortran 90. This data type is based on two double-precision real Fortran storage unit. Module {INTERVAL\_ARITHMETIC} uses the Fortran 77 library {INTLIB} (ACM TOMS {Algorithm 737}) as a supporting library. The module has been employed extensively in the author's own research.", acknowledgement = ack-rfb, keywords = "algorithms, languages", subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN 90. {\bf G.1.0}: Mathematics of Computation, NUMERICAL ANALYSIS, General, Computer arithmetic, Error analysis, Numerical algorithms.", } @Article{Lehoucq:1996:CEU, author = "R. B. Lehoucq", title = "The Computation of Elementary Unitary Matrices", journal = j-TOMS, volume = "22", number = "4", pages = "393--400", month = dec, year = "1996", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/235815.235817", abstract = "The construction of elementary unitary matrices that transform a complex vector to a multiple of $e_1$, the first column of the identity matrix, is studied. We present four variants and their software implementation, including a discussion on the {LAPACK} subroutine {CLARFG}. Comparisons are also given.", acknowledgement = ack-rfb, keywords = "algorithms", subject = "{\bf F.2}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Butcher:1996:DMS, author = "J. C. Butcher and J. R. Cash and M. T. Diamantakis", title = "{DESI} Methods for Stiff Initial Value Problems", journal = j-TOMS, volume = "22", number = "4", pages = "401--422", month = dec, year = "1996", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/235815.235818", abstract = "Recently, the so-called DESI (diagonally extended singly implicit) {Runge}-{Kutta} methods were introduced to overcome some of the limitations of singly implicit methods. Preliminary experiments have shown that these methods are usually more efficient than the standard singly implicit {Runge}-{Kutta} (SIRK) methods and, in many cases, are competitive with backward differentiation formulae (BDF). This article presents an algorithm for determining the full coefficient matrix from the stability function, which is already chosen to make the method {A}-stable. Because of their unconventional nature, DESI methods have to be implemented in a special way. In particular, the effectiveness of these methods depends heavily on how the starting values are chosen for the stage iterations. These and other implementation questions are discussed in detail, and the design choices we have made form the basis of an experimental code for the solution of stiff problems by DESI methods. We present here a small subset of the numerical results obtained with our code. Many of these results are quite satisfactory and suggest that DESI methods have a useful role in the solution of this type of problem.", acknowledgement = ack-rfb, subject = "{\bf G.1}: Mathematics of Computing, NUMERICAL ANALYSIS. {\bf G.1.7}: Mathematics of Computing, ORDINARY DIFFERENTIAL EQUATIONS, Initial value problems, Stiff equations.", } @Article{Eastham:1996:USP, author = "Michael S. P. Eastham and Charles T. Fulton and Steven Pruess", title = "Using the {SLEDGE} Package on {Sturm-Liouville} Problems Having Nonempty Essential Spectrum", journal = j-TOMS, volume = "22", number = "4", pages = "423--446", month = dec, year = "1996", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Oct 24 15:44:41 1998", URL = "http://doi.acm.org/10.1145/235815.235819", abstract = "We describe the performance of the Sturn-Liouville software package SLEDGE on a variety of problems having continuous spectra. The code's output is shown to be in good accord with a wide range of known theoretical results.", acknowledgement = ack-rfb, keywords = "algorithms, performance", subject = "{\bf G.1.7}: Mathematics of Computing, ORDINARY DIFFERENTIAL EQUATIONS, Boundary value problems. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.", } @Article{Weerawarana:1996:PKB, author = "Sanjiva Weerawarana and Elias N. Houstis and John R. Rice and Anupam Joshi and Catherine E. Houstis", title = "{PYTHIA}: {A} Knowledge Based System for Intelligent Scientific Computing", journal = j-TOMS, volume = "22", number = "4", pages = "447--468", month = dec, year = "1996", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/235815.235820", abstract = "Problem-solving Environments (PSEs) interact with the user in a language ``natural'' to the associated discipline, and they provide a high-level abstraction of the underlying, computationally complex model. The knowledge-based system PYTHIA addresses the problem of {\tt (parameter, algorithm)} pair selection within a scientific computing domain assuming some minimum user-specified computational objectives and some characteristics of the given problem. PYTHIA's framework and methodology are general and applicable to any class of scientific problems and solvers. PYTHIA is applied in the context of Parallel ELLPACK where there are many alternatives for the numerical solution of elliptic partial differential equations (PDEs). PYTHIA matches the characteristics of the given problem with those of PDEs in an existing problem population and then uses performance profiles of the various solvers to select the appropriate method given user-specified error and solution time bounds. The profiles are automatically generated for each solver of the Parallel ELLPACK library.", acknowledgement = ack-rfb, keywords = "algorithms, performance", subject = "{\bf G.1.8}: Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations. {\bf I.2.1}: Computing Methodologies, ARTIFICIAL INTELLIGIENCE, Applications and expert systems.", } @Article{Barber:1996:QAC, author = "C. Bradford Barber and David P. Dobkin and Hannu Huhdanpaa", title = "The Quickhull Algorithm for Convex Hulls", journal = j-TOMS, volume = "22", number = "4", pages = "469--483", month = dec, year = "1996", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/235815.235821", abstract = "The convex hull of a set of points is the smallest convex set that contains the points. This article presents a practical convex hull algorithm that combines the two-dimensional Quickhull Algorithm with the general-dimensional Beneath-Beyond Algorithm. It is similar to the randomized, incremental algorithms for convex hull and Delaunay triangulation. We provide empirical evidence that the algorithm runs faster when the input contains nonextreme points and that it uses less memory. Computational geometry algorithms have traditionally assumed that input sets are well behaved. When an algorithm is implemented with floating-point arithmetic, this assumption can lead to serious errors. We briefly describe a solution to this problem when computing the convex hull in two, three, or four dimensions. The output is a set of ``thick'' facets that contain all possible exact convex hulls of the input. A variation is effective in five or more dimensions.", acknowledgement = ack-rfb, keywords = "algorithms, reliability", subject = "{\bf I.3.5}: Computing Methodologies, COMPUTER GRAPHICS, Computational Geometry and Object Modeling, Geometric algorithms, languages and systems.", } @Article{Sarkar:1996:CAM, author = "T. K. Sarkar", title = "A Composition-Alias Method for Generating Gamma Variates with Shape Parameter Greater than 1", journal = j-TOMS, volume = "22", number = "4", pages = "484--492", month = dec, year = "1996", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/235815.235822", abstract = "In this article the author describes a procedure for generating gamma variates with shape parameter $> 1$. Given a supply of ``good'' uniform $(0,1)$ variates, the procedure makes use of composition method, squeeze method, and aliasing to generate gamma variates. Comparison with existing methods shows that the author's method is faster in terms of computer time and uses a smaller number of uniform $(0,1)$ variates. The method is also statistically exact.", acknowledgement = ack-rfb, keywords = "algorithms, theory", subject = "{\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS. {\bf I.6.1}: Computing Methodologies, SIMULATION AND MODELING, Simulation Theory.", } @Article{Koenker:1996:RBC, author = "Roger W. Koenker and Pin T. Ng", title = "A Remark on {Bartels} and {Conn}'s Linearly Constrained, Discrete $l_1$ Problems", journal = j-TOMS, volume = "22", number = "4", pages = "493--495", month = dec, year = "1996", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Mar 9 10:22:02 1999", note = "See \cite{Bartels:1980:APL}.", URL = "http://doi.acm.org/10.1145/235815.235823", abstract = "Two modifications of Bartels and Conn's algorithm for solving linearly constrained discrete $l_1$ problems are described. The modifications are designed to improve performance of the algorithm under conditions of degeneracy.", acknowledgement = ack-rfb, keywords = "algorithms, performance, reliability, theory", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Constrained optimization, Gradient methods, Linear programming. {\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Statistical computing.", } @Article{Reid:1996:RFF, author = "J. K. Reid", title = "Remark on ``{Fast} Floating-Point Processing in {Common Lisp}''", journal = j-TOMS, volume = "22", number = "4", pages = "496--497", month = dec, year = "1996", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Mar 9 10:21:08 1999", note = "See \cite{Fateman:1995:FFP}.", URL = "http://doi.acm.org/10.1145/235815.235824", abstract = "We explain why we feel that the comparison between Common Lisp and Fortran in a recent article by Fateman et al. in this journal is not entirely fair.", acknowledgement = ack-rfb, keywords = "languages, standardization", subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, General, Standards. {\bf D.3.3}: Software, PROGRAMMING LANGUAGES, Language Constructs and Features, Modules, packages.", } @Article{Snyder:1996:RAF, author = "W. Van Snyder", title = "Remark on {Algorithm 723}: {Fresnel} Integrals", journal = j-TOMS, volume = "22", number = "4", pages = "498--500", month = dec, year = "1996", CODEN = "ACMSCU", ISSN = "0098-3500", note = "See \cite{Snyder:1993:AFI}.", URL = "http://doi.acm.org/10.1145/235815.235825", abstract = "{/it {Algorithm 723}: Fresnal Integrals} has been improved to provide more precise results for $x \gg 0$.", acknowledgement = ack-rfb, keywords = "algorithms, performance", subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Rational approximation. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing.", } @Article{Cools:1997:ACC, author = "Ronald Cools and Dirk Laurie and Luc Pluym", title = "{Algorithm 764}: {Cubpack++} --- {A C++} Package for Automatic Two-Dimensional Cubature", journal = j-TOMS, volume = "23", number = "1", pages = "1--15", month = mar, year = "1997", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/244768.244770", abstract = "In this article, software for the numerical approximation of double integrals over a variety of regions is described. The software was written in C++. Classes for a large number of shapes are provided. A global adaptive integration algorithm is used based on transformations and subdivisions of regions.", acknowledgement = ack-rfb # " and " # ack-kr, keywords = "algorithms", subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, C++. {\bf G.1.4}: Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation, adaptive quadrature, multiple quadrature. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, efficiency, reliability and robustness.", } @Article{Favati:1997:LEE, author = "Paola Favati and Guiseppe Fiorentino and Grazia Lotti and Francesco Romani", title = "Local Error Estimates and Regularity Tests for the Implementation of Double Adaptive Quadrature", journal = j-TOMS, volume = "23", number = "1", pages = "16--31", month = mar, year = "1997", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/244768.244772", abstract = "This article presents a device which is suitable for a practical and efficient implementation of Double Adaptive Quadrature. The device includes local error estimates and attempts to detect the presence of numerical difficulties in the integrand function. If a family of rules with suitable properties is chosen, then this can be achieved without affecting the overall computational cost. Extensive numerical testing has been performed on a comprehensive set of functions showing the effectiveness of the device and its efficiency.", acknowledgement = ack-rfb # " and " # ack-kr, keywords = "algorithms", subject = "{\bf G.1.4}: Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation, adaptive quadrature. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, efficiency, reliability and robustness.", } @Article{Machiels:1997:FEO, author = "L. Machiels and M. O. Deville", title = "{Fortran 90}: An Entry to Object-Oriented Programming for Solution of Partial Differential Equations", journal = j-TOMS, volume = "23", number = "1", pages = "32--49", month = mar, year = "1997", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/244768.244774", abstract = "The aim of this work is to set up a programming model suitable for numerical computing while taking benefit of Fortran 90's features. The use of concepts from object-oriented programming avoids the weaknesses of the traditional global data programming model of Fortran 77. This work supports the view that object-oriented concepts are not in contradiction with good Fortran 77 programming practices but complement them. These concepts can be embodied in a module-based programming style and result in an efficient and easy-to-maintain code (maintainability means code clarity, scope for further enhancements and ease of debugging). After introducing the terminology associated with object-oriented programming, it is shown how these concepts are implemented in the framework of Fortran 90. Then, we present an object-oriented implementation of a spectral element solver for a Poisson equation.", acknowledgement = ack-rfb # " and " # ack-kr, keywords = "design", subject = "{\bf D.1.5}: Software, PROGRAMMING TECHNIQUES, Object-Oriented Programming. {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN 90. {\bf G.1.8}: Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations.", } @Article{Bruaset:1997:OOD, author = "Are Magnus Bruaset and Hans Petter Langtangen", title = "Object-Oriented Design of Preconditioned Iterative Methods in {Diffpack}", journal = j-TOMS, volume = "23", number = "1", pages = "50--80", month = mar, year = "1997", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/244768.244776", abstract = "As modern programming methodologies migrate from computer science to scientific computing, developers of numerical software are faced with new possibilities and challenges. Based on experiences from an ongoing project that develops C++ software for the solution of partial differential equations, this article has its focus on object-oriented design of iterative solvers for linear systems of equations. Special attention is paid to possible conflicts that have to be resolved in order to achieve a flexible, yet efficient, code.", acknowledgement = ack-rfb # " and " # ack-kr, keywords = "design, performance", subject = "{\bf D.2.8}: Software, SOFTWARE ENGINEERING, Tools and Techniques, software libraries. {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, C++. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, linear systems, sparse and very large systems.", } @Article{Bouaricha:1997:ASS, author = "Ali Bouaricha", title = "{Algorithm 765}: {STENMIN} --- {A} Software Package for Large, Sparse Unconstrained Optimization Using Tensor Methods", journal = j-TOMS, volume = "23", number = "1", pages = "81--90", month = mar, year = "1997", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/244768.244788", abstract = "We describe a new package for minimizing an unconstrained nonlinear function where the Hessian is large and sparse. The software allows the user to select between a tensor method and a standard method based upon a quadratic model. The tensor method models the objective function by a fourth-order model, where the third- and fourth-order terms are chosen such that the extra cost of forming and solving the model is small. The new contribution of this package consists of the incorporation of an entirely new way of minimizing the tensor model that makes it suitable for solving large, sparse optimization problems efficiently. The test results indicate that, in general, the tensor method is often more efficient and more reliable than the standard Newton method for solving large, sparse unconstrained optimization problems.", acknowledgement = ack-rfb # " and " # ack-kr, keywords = "algorithms", subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, Fortran. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, sparse and very large systems. {\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, unconstrained optimization. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Cabay:1997:AEW, author = "S. Cabay and A. R. Jones and G. Labahn", title = "{Algorithm 766}: Experiments with a Weakly Stable Algorithm for Computing {Pad{\'e}} and Simultaneous {Pad{\'e}} Approximants", journal = j-TOMS, volume = "23", number = "1", pages = "91--110", month = mar, year = "1997", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/244768.244790", abstract = "In a recent paper, Cabay, Jones and Labahn develop a fast, iterative, lookahead algorithm for numerically computing Pad{\'e}-Hermite systems and simultaneous Pad{\'e} systems along a diagonal of the associated Pad{\'e} tables. Included in their work is a detailed error analysis showing that the algorithm is weakly stable. In this article, we describe a Fortran implementation, VECTOR\_PADE, of this algorithm together with a number of numerical experiments. These experiments show that the theoretical error bounds obtained by Cabay, Jones, and Labahn reflect the general behavior of the actual error, but that in practice these bounds are large overestimates.", acknowledgement = ack-rfb # " and " # ack-kr, keywords = "algorithms, experimentation", subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, Fortran. {\bf G.1}: Mathematics of Computing, NUMERICAL ANALYSIS. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, rational approximation. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, error analysis, linear systems, matrix inversion.", } @Article{Geurts:1997:AFP, author = "A. J. Geurts and C. Praagman", title = "{Algorithm 767}: {A} {Fortran 77} Package for Column Reduction of Polynomial Matrices", journal = j-TOMS, volume = "23", number = "1", pages = "111--129", month = mar, year = "1997", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/244768.244791", abstract = "A polynomial matrix is called column reduced if its column degrees are as low as possible in some sense. Two polynomial matrices $P$ and $R$ are called unimodularly equivalent if there exists a unimodular polynomial matrix $U$ such that $PU = R$. Every polynomial matrix is unimodularly equivalent to a column-reduced polynomial matrix. In this article a subroutine is described that takes a polynomial matrix $P$ as input and yields on output a unimodular matrix $U$ and a column-reduced matrix $R$ such that $PU = R$; actually, $PU - R$ is near zero. The subroutine is based on an algorithm, described in a paper by Neven and Praagman. The subroutine has been tested with a number of examples on different computers, with comparable results. The performance of the subroutine on every example tried is satisfactory in the sense that the magnitude of the elements of the residual matrix $PU-R$ is about $\parallel P \parallel \parallel U \parallel EPS$, where $EPS$ is the machine precision. To obtain these results a tolerance, used to determine the rank of some (sub)matrices, has to be set properly. The influence of this tolerance on the performance of the algorithm is discussed, from which a guideline for the usage of the subroutine is derived.", acknowledgement = ack-rfb # " and " # ack-kr, keywords = "algorithms, reliability", subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, Fortran. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, linear systems. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, algorithm analysis.", } @Article{Blackford:1997:PEN, author = "L. S. Blackford and A. Cleary and A. Petitet and R. C. Whaley and J. Demmel and I. Dhillon and H. Ren and K. Stanley and J. Dongarra and S. Hammarling", title = "Practical Experience in the Numerical Dangers of Heterogeneous Computing", journal = j-TOMS, volume = "23", number = "2", pages = "133--147", month = jun, year = "1997", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/264029.264030", abstract = "Special challenges exist in writing reliable numerical library software for heterogeneous computing environments. Although a lot of software for distributed-memory parallel computers has been written, porting this software to a network of workstations requires careful consideration. The symptoms of heterogeneous computing failures can range from erroneous results without warning to deadlock. Some of the problems are straightforward to solve, but for others the solutions are not so obvious, or incur an unacceptable overhead. Making software robust on heterogeneous systems often requires additional communication. We describe and illustrate the problems encountered during the development of ScaLAPACK and the NAG Numerical PVM Library. Where possible, we suggest ways to avoid potential pitfalls, or if that is not possible, we recommend that the software not be used on heterogeneous networks.", acknowledgement = ack-rfb # " and " # ack-kr, keywords = "distributed-memory systems, floating-point arithmetic, heterogeneous processor networks, message passing, numerical software, reliability", subject = "{\bf D.1.3} Software, PROGRAMMING TECHNIQUES, Concurrent Programming, Distributed programming. {\bf G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic. {\bf G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS, General, Parallel algorithms.", } @Article{Ho:1997:DND, author = "James K. Ho and R. P. Sundarraj", title = "Distributed Nested Decomposition of Staircase Linear Programs", journal = j-TOMS, volume = "23", number = "2", pages = "148--173", month = jun, year = "1997", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/264029.264031", abstract = "This article considers the application of a primal nested-decomposition method to solve staircase linear programs (SLPs) on distributed-memory, multiple-instruction-multiple-data computers. Due to the coupling that exist among the stages of an SLP, a standard parallel-decomposition algorithm for these problems would allow only a subset of the subproblem processes to overlap with one another at any give time. We propose algorithms that seek to increase the amount of overlap among the processes as well as utilize idle time beneficially. Computational results testing the effectiveness of our algorithms are reported, using a standard set of test problems.", acknowledgement = ack-rfb # " and " # ack-kr, keywords = "computational linear programming, distributed computation", subject = "{\bf C.1.2} Computer Systems Organization, PROCESSOR ARCHITECTURES, Multiple Data Stream Architectures (Multiprocessors), Multiple-instruction-stream, multiple-data-stream processors (MIMD). {\bf G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS, General, Parallel algorithms. {\bf G.1.6} Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Linear programming.", } @Article{Bouaricha:1997:TSP, author = "Ali Bouaricha and Robert B. Schnabel", title = "{Algorithm 768}: {TENSOLVE}: {A} Software Package for Solving Systems of Nonlinear Equations and Nonlinear Least-squares Problems Using Tensor Methods", journal = j-TOMS, volume = "23", number = "2", pages = "174--195", month = jun, year = "1997", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/264029.264032", abstract = "This article describes a modular software package for solving systems of nonlinear equations and nonlinear problems, using a new class of methods called tensor methods. It is intended for small- to medium-sized problems, say with up to 100 equations and unknowns, in cases where it is reasonable to calculate the Jacobian matrix or to approximate it by finite differences at each iteration. The software allows the user to choose between a tensor method and a standard method based on a linear model. The tensor method approximates F(x) by a quadratic model, where the second-order term is chosen so that the model is hardly more expensive to form, store, or solve than the standard linear model. Moreover, the software provides two different global strategies: a line search approach and a two-dimensional trust region approach. Test results indicate that, in general, tensor methods are significantly more efficient and robust than standard methods on small- and medium-sized problems in iterations and function evaluations.", acknowledgement = ack-rfb # " and " # ack-kr, keywords = "nonlinear equations, nonlinear least squares, rank-deficient matrices, tensor methods", subject = "{\bf G.1.5} Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Systems of equations. {\bf G.1.6} Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Least squares methods. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Pardalos:1997:AFS, author = "Panos M. Pardalos and Leonidas S. Pitsolulis and Mauricio G. C. Resende", title = "{Algorithm 769}: {Fortran} Subroutines for Approximate Solution of Sparse Quadratic Assignment Problems Using {GRASP}", journal = j-TOMS, volume = "23", number = "2", pages = "196--208", month = jun, year = "1997", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/264029.264038", abstract = "We describe Fortran subroutines for finding approximate solutions of sparse instances of the Quadratic Assignment Problem (QAP) using a Greedy Randomized Adaptive Search Procedure (GRASP). The design and implementation of the code are described in detail. Computational results comparing the new subroutines with a dense version of the code (Algorithm 754, ACM TOMS) show that the speedup increases with the sparsity of the data.", acknowledgement = ack-rfb # " and " # ack-kr, keywords = "combinatorial optimization, Fortran subroutines, GRASP, local search, quadratic assignment problem", subject = "{\bf G.1.6} Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Integer programming. {\bf G.2.1} Mathematics of Computing, DISCRETE MATHEMATICS, Combinatorics, Combinatorial algorithms. {\bf G.m} Mathematics of Computing, MISCELLANEOUS.", } @Article{Siarry:1997:ESA, author = "Patrick Siarry and G{\'e}rard Berthiau and Fran\c{c}ois Durdin and Jacques Haussy", title = "Enhanced Simulated Annealing for Globally Minimizing Functions of Many-continuous Variables", journal = j-TOMS, volume = "23", number = "2", pages = "209--228", month = jun, year = "1997", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/264029.264043", abstract = "A new global optimization algorithm for functions of many continuous variables is presented, derived from the basic Simulated annealing method. Our main contribution lies in dealing with high-dimensionality minimization problems, which are often difficult to solve by all known minimization methods with or without gradient. In this article we take a special interest in the variables discretization issue. We also develop and implement several complementary stopping criteria. The original Metropolis iterative random search, which takes place in a Euclidean space Rn, is replaced by another similar exploration, performed within a succession of Euclidean spaces Rp, with p << n. This Enhanced Simulated Annealing (ESA) algorithm was validated first on classical highly multimodal functions of 2 to 100 variables. We obtained significant reductions in the number of function evaluations compared to six other global optimization algorithms, selected according to previously published computational results for the same set of test functions. In most cases, ESA was able to closely approximate known global optima. The reduced ESA computational cost helped us to refine further the obtained global results, through the use of some local search. We have used this new minimizing procedure to solve complex circuit design problems, for which the objective function evaluation can be exceedingly costly.", acknowledgement = ack-rfb # " and " # ack-kr, keywords = "global optimization, stochastic optimization, test functions", subject = "{\bf G.1.6} Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Nonlinear programming. {\bf G.3} Mathematics of Computing, PROBABILITY AND STATISTICS, Probabilistic algorithms (including Monte Carlo). {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing.", } @Article{Costantini:1997:BVS, author = "P. Costantini", title = "Boundary-Valued Shape-Preserving Interpolating Splines", journal = j-TOMS, volume = "23", number = "2", pages = "229--251", month = jun, year = "1997", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/264029.264050", abstract = "This article describes a general-purpose method for computing interpolating polynomial splines with arbitrary constraints on their shape and satisfying separable or nonseparable boundary conditions. Examples of applications of the related Fortran code are periodic shape-preserving spline interpolation and the construction of visually pleasing closed curves.", acknowledgement = ack-rfb # " and " # ack-kr, keywords = "Bernstein-B\'{e}zier polynomials, dynamic programming, spline interpolation", subject = "{\bf G.1.1} Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation.", } @Article{Costantini:1997:APC, author = "P. Costantini", title = "{Algorithm 770}: {BVSPIS}---{A} Package for Computing Boundary-Valued Shape-Preserving Interpolating Splines", journal = j-TOMS, volume = "23", number = "2", pages = "252--254", month = jun, year = "1997", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/264029.264059", abstract = "This article describes a software package for computing interpolating polynomial splines with arbitrary constraints on their shape and satisfying separable or nonseparable boundary conditions.", acknowledgement = ack-rfb # " and " # ack-kr, keywords = "Bernstein-B\'{e}zier polynomials, dynamic programming, spline interpolation", subject = "{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN. {\bf G.1.1} Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Wu:1997:MVR, author = "Pei-Chi Wu", title = "Multiplicative, congruential random-number generators with multiplier $\pm 2^{k_1} \pm 2^{k_2}$ and modulus $^2p - 1$", journal = j-TOMS, volume = "23", number = "2", pages = "255--265", month = jun, year = "1997", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/264029.264056", abstract = "The demand for random numbers in scientific applications in increasing. However, the most widely used multiplicative, congruential random-number generators with modulus $2^31 - 1$ have a cycle length of about $2.1 \times 10^9$. Moreover, developing portable and efficient generators with a larger modulus such as $2^61 - 1$ is more difficult than those with modulus $2^31 - 1$. This article presents the development of multiplicative, congruential generators with modulus $m = 2p - 1$ and four forms of multipliers: $2^{k_1} - 2^{k_2}, 2^{k_1} + 2^{k_2}, m - 2^{k_1} + 2^{k_2}$, and $m - 2^{k_1} - 2^{k_2}, {k_1} > {k_2}$. The multipliers for modulus 2^31 - 1 and 2^61 - 1 are measured by spectral tests, and the best ones are presented. The generators with these multipliers are portable and vary fast. They have also passed several empirical tests, including the frequency test, the urn test, and the maximum-of-t test.", acknowledgement = ack-rfb # " and " # ack-kr, keywords = "cycle length, efficiency, multiplicative congruential random-number generators, portability, spectral test", subject = "{\bf G.3} Mathematics of Computing, PROBABILITY AND STATISTICS, Random number generation.", } @Article{Kocis:1997:CIL, author = "Ladislav Kocis and William J. Whiten", title = "Computational Investigations of Low-discrepancy Sequences", journal = j-TOMS, volume = "23", number = "2", pages = "266--294", month = jun, year = "1997", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/264029.264064", abstract = "The Halton, Sobol, and Faure sequences and the Braaten-Weller construction of the generalized Halton sequence are studied in order to assess their applicability for the quasi Monte Carlo integration with large number of variates. A modification of the Halton sequence (the Halton sequence leaped) and a new construction of the generalized Halton sequence are suggested for unrestricted number of dimensions and are show to improve considerably on the original Halton sequence. Problems associated with estimation of the error in quasi Monte Carlo integration and with the selection of test functions are identified. Then an estimate of the maximum error of the quasi Monte Carlo integration of nine test functions is computed for up to 400 dimensions and is used to evaluate the known generators mentioned above and the two new generators. An empirical formula for the error of the quasi Monte Carlo integration is suggested.", acknowledgement = ack-rfb # " and " # ack-kr, keywords = "discrepancy, error of numerical integration, Faure sequence, generalized Halton sequence, Halton sequence, low-discrepancy sequences, Monte Carlo and quasi Monte Carlo integration, Sobol sequence", subject = "{\bf G.1.4} Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation. {\bf I.6} Computing Methodologies, SIMULATION AND MODELING.", } @Article{Goano:1997:RA7, author = "Michele Goano", title = "Remark on {Algorithm 745}", journal = j-TOMS, volume = "23", number = "2", pages = "295--295", month = jun, year = "1997", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Mar 9 10:19:38 1999", note = "See \cite{Goano:1995:ACC}.", URL = "http://doi.acm.org/10.1145/264029.643581", acknowledgement = ack-rfb # " and " # ack-kr, } @Article{Hull:1997:ICA, author = "T. E. Hull and Thomas F. Fairgrieve and Ping Tak Peter Tang", title = "Implementing the Complex Arcsine and Arccosine Functions Using Exception Handling", journal = j-TOMS, volume = "23", number = "3", pages = "299--335", month = sep, year = "1997", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Wed May 6 11:23:41 1998", URL = "http://doi.acm.org/10.1145/275323.275324", abstract = "We develop efficient algorithms for reliable and accurate evaluations of the complex arcsine and arccosine functions. A tight error bound is derived for each algorithm; the results are valid for all machine-representable points in the complex plane. The algorithms are presented in a pseudocode that has a convenient exception-handling facility. Corresponding Fortran 77 programs for an IEEE environment have also been developed to illustrate the practicality of the algorithms, and these programs have been tested very carefully to help confirm the correctness of the algorithms and their error bounds. The results of these tests are included in the article, but the Fortran 77 programs are not (these programs are available from Fairgrieve). Tests of other widely available programs fail at many points in the complex plane, and otherwise are slower and produce much less accurate results.", accepted = "February 1997", acknowledgement = ack-rfb # " and " # ack-kr, keywords = "algorithms, design, complex elementary functions, implementation", subject = "{\bf G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS, General, error analysis, Numerical algorithms. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, elementary function approximation. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, algorithm analysis, reliability and robustness, verification.", } @Article{Carr:1997:CBD, author = "Steve Carr and R. B. Lehoucq", title = "Compiler Blockability of Dense Matrix Factorizations", journal = j-TOMS, volume = "23", number = "3", pages = "336--361", month = sep, year = "1997", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Wed May 6 11:23:41 1998", URL = "http://doi.acm.org/10.1145/275323.275325", abstract = "The goal of the LAPACK project is to provide efficient and portable software for dense numerical linear algebra computations. By recasting many of the fundamental dense matrix computations in terms of calls to an efficient implementation of the BLAS (Basic Linear Algebra Subprograms), the LAPACK project has, in large part, achieved its goal. Unfortunately, the efficient implementation of the BLAS results often in machine-specific code that is not portable across multiple architectures without a significant loss in performance or significant effort to reoptimize them. This article examines whether most of the hand optimizations performed on matrix factorization codes are unnecessary because they can (and should) be performed by the compiler. We believe that it is better for the programmer to express algorithms in a machine-independent form and allow the compiler to handle the machine-dependent details. This gives the algorithms portability across architectures and removes the error-prone, expensive, and tedious process of hand optimization. Although there currently exist no production compilers that can perform all the loop transformations discussed in this article, a description of current research in compiler technology is provided that will prove beneficial to the numerical linear algebra community. We show that the Cholesky and optimized automatically by a compiler to be as efficient as the same hand-optimized version found in LAPACK. We also show that the QR factorization may be optimized by the compiler to perform comparably with the hand-optimized LAPACK version on modest matrix sizes. Our approach allows us to conclude that with the advent of the compiler optimizations discussed in this article, matrix factorizations may be efficiently implemented in a BLAS-less form.", accepted = "February 1997", acknowledgement = ack-rfb # " and " # ack-kr, keywords = "languages, performance, BLAS, cache optimization, Cholesky decomposition, LAPACK, LU decomposition, QR decomposition", subject = "{\bf D.3.4}: Software, PROGRAMMING LANGUAGES, Processors, Compilers, optimization. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, efficiency, portability.", } @Article{Carrig:1997:EHQ, author = "James J. {Carrig Jr.} and Gerald G. L. Meyer", title = "Efficient {Householder} {QR} Factorization for Superscalar Processors", journal = j-TOMS, volume = "23", number = "3", pages = "362--378", month = sep, year = "1997", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Wed May 6 11:23:41 1998", URL = "http://doi.acm.org/10.1145/275323.275326", abstract = "To extract the potential promised by superscalar processors, algorithm designers must streamline memory references and allow for efficient data reuse throughout the memory hierarchy. Two parameterized Householder QR factorization algorithms are presented that take into account the caches and registers typical of such processors. Guidelines are developed for choosing parameter values that obtain near-optimal cache and register utilization. The new algorithms are implemented and performance-tuned on an Intel Pentium Pro system, a single this POWER2 node of the IBM Scalable Parallel System 2 (SP2), and a single R8000 processor of a Silicon Graphics POWER Challenge XL.", accepted = "February 1997", acknowledgement = ack-rfb # " and " # ack-kr, keywords = "algorithms, performance, cache model, Householder QR factorization, register model", subject = "{\bf B.3.2}: Hardware, MEMORY STRUCTURES, Design Styles, Cache memories. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, linear systems (direct and iterative methods). {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, algorithm analysis, efficiency, portability.", } @Article{Duff:1997:LTB, author = "Iain Duff and Michele Marrone and Giuseppe Radicati and Carlo Vittoli", title = "Level 3 Basic Linear Algebra Subprograms for Sparse Matrices: a User Level Interface", journal = j-TOMS, volume = "23", number = "3", pages = "379--401", month = sep, year = "1997", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Wed May 6 11:23:41 1998", URL = "http://doi.acm.org/10.1145/275323.275327", abstract = "This article proposes a set of Level 3 Basic Linear Algebra Subprograms and associated kernels for sparse matrices. A major goal is to design and develop a common framework to enable efficient, and portable, implementations of iterative algorithms for sparse matrices on high-performance computers. We have designed the routines to shield the developer of mathematical software from most of the complexities of the various data structures used for sparse matrices. We have kept the interface and suite of codes as simple as possible while at the same time including sufficient functionality to cover most sparse matrix data structures. An important aspect of our framework is that it can be easily extended to incorporate new kernels if the need arises. We discuss the design, implementation, and use of subprograms for the multiplication of a full matrix by a sparse one and for the solution of sparse triangular systems with one or more (full) right-hand sides. We include a routine for checking the input data, generating a new sparse data structure from that input, and scaling a sparse matrix. The new data structure for the transformation can be specified by the user or can be chosen automatically by vendors to be efficient on their machines. We also include a routine for permuting the columns of a sparse matrix and one for permuting the rows of a full matrix.", accepted = "March 1997", acknowledgement = ack-rfb # " and " # ack-kr, keywords = "algorithms, performance, reliability, high-performance computing, iterative solution, programming standards, sparse BLAS, sparse data structures, sparse matrices", subject = "{\bf D.2.2}: Software, SOFTWARE ENGINEERING, Tools and Techniques, user interfaces. {\bf D.2.2}: Software, SOFTWARE ENGINEERING, Coding, standards. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, certification and testing, efficiency, portability, reliability and robustness, verification.", } @Article{Brankin:1997:ARF, author = "R. W. Brankin and I. Gladwell", title = "{Algorithm 771}. {\tt rksuite\_90}: {Fortran} Software for Ordinary Differential Equation Initial Value Problems", journal = j-TOMS, volume = "23", number = "3", pages = "402--415", month = sep, year = "1997", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Wed May 6 11:23:41 1998", URL = "http://doi.acm.org/10.1145/275323.275328", abstract = "We present Fortran 90 software for the initial-value problem in ordinary differential equations, including the interfaces and how Fortran 90 language features afford the opportunity to address different types and structures of variables and to provide additional functionality. A novel feature of this software is the availability of Unix scripts which enable presentation of the software for multiple problem types.", accepted = "January 1997", acknowledgement = ack-rfb # " and " # ack-kr, keywords = "algorithms, complex, recursion", subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, Fortran 90. {\bf G.1.7}: Mathematics of Computing, ORDINARY DIFFERENTIAL EQUATIONS, Initial value problems. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Renka:1997:ASD, author = "Robert J. Renka", title = "{Algorithm 772}. {STRIPACK}: {Delaunay} Triangulation and {Voronoi} Diagram on the Surface of a Sphere", journal = j-TOMS, volume = "23", number = "3", pages = "416--434", month = sep, year = "1997", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Wed May 6 11:23:41 1998", URL = "http://doi.acm.org/10.1145/275323.275329", abstract = "STRIPACK is a Fortran 77 software package that employs an incremental algorithm to construct a Delaunay triangulation and, optionally, a Voronoi diagram of a set of points (nodes) on the surface of the unit sphere. The triangulation covers the convex hull of the nodes, which need not be the entire surface, while the Voronoi diagram covers the entire surface. The package provides a wide range of capabilities including an efficient means of updating the triangulation with nodal additions or deletions. For N nodes, the storage requirement for the triangulation is 13N integer storage locations in addition to 3N nodal coordinates. Using an off-line algorithm and work space of size 3N, the triangulation can be constructed with time complexity O(NlogN).", accepted = "March 1997", acknowledgement = ack-rfb # " and " # ack-kr, keywords = "algorithms, Delaunay triangulation, Dirichlet tessellation, sphere, Thiessen regions, Voronoi diagram", subject = "{\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Renka:1997:ASI, author = "Robert J. Renka", title = "{Algorithm 773}. {SSRFPACK}: Interpolation of Scattered Data on the Surface of a Sphere with a Surface under Tension", journal = j-TOMS, volume = "23", number = "3", pages = "435--442", month = sep, year = "1997", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Wed May 6 11:23:41 1998", URL = "http://doi.acm.org/10.1145/275323.275330", abstract = "SSRFPACK is a Fortran 77 software package that constructs a smooth interpolatory or approximating surface to data values associated with arbitrarily distributed points on the surface of a sphere. It employs automatically selected tension factors to preserve shape properties of the data and avoid overshoot and undershoot associated with steep gradients.", accepted = "March 1997", acknowledgement = ack-rfb # " and " # ack-kr, keywords = "algorithms, scattered data fitting, smoothing, surface under tension, triangle-based interpolation", subject = "{\bf G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Facchinei:1997:GBC, author = "Francisco Facchinei and Joaquim J{\'u}dice and Jo{\~a}o Soares", title = "Generating Box Constrained Optimization Problems", journal = j-TOMS, volume = "23", number = "3", pages = "443--447", month = sep, year = "1997", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Wed May 6 11:23:41 1998", URL = "http://doi.acm.org/10.1145/275323.275331", abstract = "We present a method for generating box-constrained nonlinear programming test problems. The technique allows the user to control some properties of the generated test problems that are known to influence the behavior of algorithms for their solution. A corresponding set of Fortran 77 routines is described in a companion algorithm (774).", accepted = "February 1997", acknowledgement = ack-rfb # " and " # ack-kr, keywords = "algorithms, performance, verification, nonlinear programming test problems, optimization, test problems generation", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, certification and testing, verification.", } @Article{Facchinei:1997:AFS, author = "Francisco Facchinei and Joaquim J{\'u}dice and Jo{\~a}o Soares", title = "{Algorithm 774}. {FORTRAN} Subroutine for Generating Box Constrained Optimization Problems", journal = j-TOMS, volume = "23", number = "3", pages = "448--450", month = sep, year = "1997", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Wed May 6 11:23:41 1998", URL = "http://doi.acm.org/10.1145/275323.275332", abstract = "We describe a set of Fortran routines for generating box-constrained nonlinear programming test problems. The technique, as described by Facchinei et al. (this issue), allows the user to control relevant properties of the generated problems.", accepted = "February 1997", acknowledgement = ack-rfb # " and " # ack-kr, keywords = "algorithms, performance, verification, nonlinear programming test problems, optimization, test problems generation", subject = "{\bf G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS, Optimization. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, certification and testing, verification.", } @Article{Greenberg:1997:ACS, author = "Leon Greenberg and Marco Marletta", title = "{Algorithm 775}. The Code {SLEUTH} for Solving Fourth-Order {Sturm-Liouville} Problems", journal = j-TOMS, volume = "23", number = "4", pages = "453--493", month = dec, year = "1997", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Thu Sep 17 15:28:33 1998", URL = "http://doi.acm.org/10.1145/279232.279231", abstract = "We describe a new code (SLEUTH) for numerical solution of regular two-point fourth-order Sturm-Liouville eigenvalue problems. Eigenvalues are computed according to index: the user specifies an integer $k \geq 0$, and the code computes an approximation to the $k$th eigenvalue. Eigenfunctions are also available through an auxiliary routine, called after the eigenvalue has been determined. The code will be made available through netlib.", accepted = "March 1997", acknowledgement = ack-rfb # " and " # ack-kr, keywords = "algorithms, SLEUTH", subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, Fortran 77. {\bf G.1.7}: Mathematics of Computing, ORDINARY DIFFERENTIAL EQUATIONS, Boundary value problems. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Bai:1997:ASF, author = "Z. Bai and G. W. Stewart", title = "{Algorithm 776}. {SRRIT} --- {A} {FORTRAN} Subroutine to Calculate the Dominant Invariant Subspace of a Nonsymmetric Matrix", journal = j-TOMS, volume = "23", number = "4", pages = "494--513", month = dec, year = "1997", CODEN = "CACMA2", ISSN = "0001-0782", URL = "http://doi.acm.org/10.1145/279232.279234", abstract = "SRRIT is a Fortran program to calculate an approximate orthonormal basis for a dominant invariant subspace of a real matrix $A$ by the method of simultaneous iteration. Specifically, given an integer $m$, SRRIT computes a matrix $Q$ with $m$ orthonormal columns and real quasi-triangular matrix $T$ of order $m$ such that the equation $AQ = QT$ is satisfied up to a tolerance specified by the user. The eigenvalues of $T$ are approximations to the $m$ eigenvalues of largest absolute magnitude of $A$, and the columns of $Q$ span the invariant subspace corresponding to those eigenvalues. SRRIT references $A$ only through a user-provided subroutine to form the product $AQ$; hence it is suitable for large sparse problems.", accepted = "March 1997", acknowledgement = ack-rfb # " and " # ack-kr, keywords = "algorithms, invariant subspace, nonsymmetric eigenvalue problem, project method", subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, Fortran. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices. {\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, eigenvalues. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, certification and testing.", } @Article{Watson:1997:ASF, author = "Layne T. Watson and Robert C. Melville and Alexander P. Morgan and Homer F. Walker", title = "{Algorithm 777}. {HOMPACK90}: {A} Suite of {Fortran} 90 Codes for Globally Convergent Homotopy Algorithms", journal = j-TOMS, volume = "23", number = "4", pages = "514--549", month = dec, year = "1997", CODEN = "CACMA2", ISSN = "0001-0782", URL = "http://doi.acm.org/10.1145/279232.279235", abstract = "HOMPACK90 is a Fortran 90 version of the Fortran 77 package HOMPACK (Algorithm 652), a collection of codes for finding zeros of fixed points of nonlinear systems using globally convergent probability-one homotopy algorithms. Three qualitatively different algorithms --- ordinary differential equation based, normal flow, quasi-Newton augmented Jacobian matrix --- are provided for tracking homotopy zero curves, as well as separate routine for dense and sparse Jacobian matrices. A high level driver for the special case of polynomial systems is also provided. Changes to HOMPACK include numerous minor improvements, simpler and more elegant interfaces, use of modules, new end games, support for several sparse matrix data structures, and new iterative algorithms for large sparse Jacobian matrices.", accepted = "April 1997", acknowledgement = ack-rfb # " and " # ack-kr, keywords = "algorithms, Chow-Yorke algorithm, curve tracking, fixed point, globally convergent, homotopy methods, polynomial systems, probability-one, zero.", subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, Fortran. {\bf G.1.5}: Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Systems of equations. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Zhu:1997:ALF, author = "Ciyou Zhu and Richard H. Byrd and Peihuang Lu and Jorge Nocedal", title = "{Algorithm 778}. {L-BFGS-B}: {Fortran} Subroutines for {Large-Scale} Bound Constrained Optimization", journal = j-TOMS, volume = "23", number = "4", pages = "550--560", month = dec, year = "1997", CODEN = "CACMA2", ISSN = "0001-0782", URL = "http://doi.acm.org/10.1145/279232.279236", abstract = "L-BFGS-B is a limited-memory algorithm for solving large nonlinear optimization problems subject to simple bounds on the variables. It is intended for problems in which information on the Hessian matrix is difficult to obtain, or for large dense problems. L-BFGS-B can also be user for unconstrained problems and in this case performs similarly to its predecessor, algorithm L-BFGS (Harwell routine VA15). The algorithm is implemented in Fortran 77.", accepted = "April 1997", acknowledgement = ack-rfb # " and " # ack-kr, keywords = "algorithms, large-scale optimization, limited-memory method, nonlinear optimization, variable metric method.", subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, Fortran. G.1.6 [Numerical Analysis]: Optimization -- constrained optimization; gradient methods; nonlinear programming; G.4 [Mathematics of Computing]: Mathematical Software", } @Article{Karp:1997:HPD, author = "Alan H. Karp and Peter Markstein", title = "High-Precision Division and Square Root", journal = j-TOMS, volume = "23", number = "4", pages = "561--589", month = dec, year = "1997", CODEN = "CACMA2", ISSN = "0001-0782", URL = "http://doi.acm.org/10.1145/279232.279237", abstract = "We present division and square root algorithms for calculation with more bits than are handled by the floating-point hardware. These algorithms avoid the need to multiply two high-precision numbers, speeding up the last iteration by as much as a factor of 10. We also show how to produce the floating-point number closest to the exact result with relatively few additional operations.", accepted = "June 1997", acknowledgement = ack-rfb # " and " # ack-kr, keywords = "algorithms, performance, division, quad precision, square root.", subject = "G.1.0 [Numerical Analysis]: General -- computer arithmetic. G.4 [Mathematics of Computing]: Mathematical Software.", } @Article{MacLeod:1998:AFD, author = "Allan J. MacLeod", title = "{Algorithm 779}: {Fermi-Dirac} Functions of Order $-1/2, 1/2, 3/2, 5/2$", journal = j-TOMS, volume = "24", number = "1", pages = "1--12", month = mar, year = "1998", CODEN = "CACMA2", ISSN = "0001-0782", URL = "http://doi.acm.org/10.1145/285861.285862", abstract = "The computations of Fermi-Dirac ${\cal F}_k$ integrals is discussed for the values $k = -1, 1/2, 3/2, 5/2$. We derive Chebyshev polynomial expansions which allow the computation of these functions to double precision IEEE accuracy.", accepted = "May 1997", acknowledgement = ack-rfb # " and " # ack-kr, keywords = "algorithms, Chebyshev polynomials, collocation, Fermi-Dirac, floating-point arithmetic.", subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN. {\bf F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems. {\bf G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation.", } @Article{Sharp:1998:GHO, author = "P. W. Sharp and J. H. Verner", title = "Generation of High-order Interpolants for Explicit {Runge-Kutta} Pairs", journal = j-TOMS, volume = "24", number = "1", pages = "13--29", month = mar, year = "1998", CODEN = "CACMA2", ISSN = "0001-0782", URL = "http://doi.acm.org/10.1145/285861.285863", abstract = "Explicit Runge-Kutta paris can be enhanced by providing them with interpolants. Enhancements include the ability to estimate and control the defect, to produce dense output, and to calculate past values in delay differential equations. The coefficients of an interpolant are easily generated by bootstrapping on the order conditions. However, the generation of high-order interpolants requires a large number of arithmetic operations. We describe an efficient algorithm for the generation of high-order interpolants and illustrate the use of the algorithm with three applications.", accepted = "June 1997", acknowledgement = ack-rfb # " and " # ack-kr, keywords = "algorithms, explicit, generation, high order, interpolants, pairs, Runge-Kutta.", subject = "{\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations.", } @Article{Houstis:1998:PPS, author = "E. N. Houstis and J. R. Rice and S. Weerawarana and A. C. Catlin and P. Papachiou and K.-Y. Wang and M. Gaitatzes", title = "{PELLPACK}: {A} Problem Solving Environment for {PDE} Based Applications on Multicomputer Platforms", journal = j-TOMS, volume = "24", number = "1", pages = "30--73", month = mar, year = "1998", CODEN = "CACMA2", ISSN = "0001-0782", URL = "http://doi.acm.org/10.1145/285861.285864", abstract = "This article presents the software architecture and implementation of the problem-solving environment (PSE) PELLPACK for modeling physical objects described by partial differential equations (PDEs). The scope of this PDE is broad, as PELLPACK incorporates many PDE solving systems, and some of these, in turn, include several specific PDE solving methods. Its coverage for 1D, 2D, and 3D elliptic or parabolic problems is quite broad, and it handles some hyperbolic problems. Since a PSE should provide complete support for the problem-solving process, PELLPACK also contains a large amount of code to support graphical user interfaces, analytic tools, user help, domain or mesh partitioning, machine and data selection, visualization, and various other tasks. Its total size is well over 1 million lines of code. Its open-ended software architecture consists of several software layers. The top layer is an interactive graphical interface for specifying the PDE model and its solution framework. This interface saves the results of the user specification in the form of a very high level PDE language which is an alternate interface to the PELLPACK system. This language also allows a user to specify the PDE problem and its solution framework textually in a natural form. The PELLPACK language preprocessor generates a Fortran control program with the interfaces, calls to specified components and libraries of the PDE solution framework, and functions defining the PDE problem. The PELLPACK program execution is supported by a high-level tool where the virtual parallel system is defined, where the execution mode, file system, and hardware resources are selected, and where the compilation, loading, and execution are controlled. Finally, the PELLPACK PSE integrates several PDE libraries and PDE systems available in the public domain. The system employs several parallel reuse methodologies based on the decomposition of discrete geometric data to map sparse PDE computations to parallel machines. An instance of the system is available as a Web server (WebPELLPACK) for public use at http://pellpack.cs.purdue.edu.", accepted = "June 1997", acknowledgement = ack-rfb # " and " # ack-kr, keywords = "algorithms, design, languages, management, performance, execution models, knowledge bases, libraries, parallel reuse methodologies, PDE language, problem-solving environments, programming-in-the-large, software bus.", subject = "{\bf C.3}: Computer Systems Organization, SPECIAL-PURPOSE AND APPLICATION-BASED SYSTEMS. {\bf D.2.6}: Software, SOFTWARE ENGINEERING, Programming Environments, Graphical environments, interactive environments and integrated environments. {\bf D.2.11}: Software, SOFTWARE ENGINEERING, Software Architectures, Domain-specific architectures. {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, Very high-level languages. {\bf G.1.8}: Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Domain decomposition methods, elliptic equations, hyperbolic equations, iterative solution techniques, multigrid and multilevel methods, and parabolic equations. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Parallel and vector implementations. {\bf I.2.5}: Computing Methodologies, ARTIFICIAL INTELLIGENCE, Programming Languages and Software, Expert system tools and techniques. {\bf J.2}: Computer Applications, PHYSICAL SCIENCES AND ENGINEERING, Engineering, and mathematics and statistics.", } @Article{Gupta:1998:DIE, author = "Anshul Gupta and Fred G. Gustavson and Mahesh Joshi and Sivan Toledo", title = "The Design, Implementation and Evaluation of a Symmetric Banded Linear Solver for Distributed-Memory Parallel Computers", journal = j-TOMS, volume = "24", number = "1", pages = "74--101", month = mar, year = "1998", CODEN = "CACMA2", ISSN = "0001-0782", URL = "http://doi.acm.org/10.1145/285861.285865", abstract = "This article describes the design, implementation, and evaluation of a parallel algorithm for the Cholesky factorization of symmetric banded matrices. The algorithm is part of IBM's parallel engineering and scientific subroutine library version 1.2 and is compatible with ScaLAPACK's banded solver. Analysis, as well as experiments on an IBM SP2 distributed-memory parallel computer, shows that the algorithm efficiently factors banded matrices with wide bandwidth. For example, a 31-mode SP2 factors a large matrix more than 16 times faster than a single node would factor it using the best sequential algorithm, and more than 20 times faster than a single node would using LAPACK's DPBTRF. The algorithm uses novel ideas in the area of distributed dense-matrix computations that include the use of a dynamic schedule for a blocked systolic-like algorithm and the separation of the input and output layouts from the layout the algorithm uses internally. The algorithm alson uses known techniques such as blocking to improve its communication-to-computation ratio and its data-cache behavior.", accepted = "June 1997", acknowledgement = ack-rfb # " and " # ack-kr, keywords = "Algorithms, performance, banded matrices, Cholesky factorization, distributed memory, parallel algorithms.", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm design and analysis, and efficiency.", } @Article{Hamilton:1998:AEP, author = "K. G. Hamilton", title = "{Algorithm 780}: Exponential Pseudorandom Distribution", journal = j-TOMS, volume = "24", number = "1", pages = "102--106", month = mar, year = "1998", CODEN = "CACMA2", ISSN = "0001-0782", URL = "http://doi.acm.org/10.1145/285861.285866", abstract = "An algorithm is presented for the calculation of exponentially distributed random numbers. It is based on mathematics that was published by Ahrend and Dieter, but some errors have been corrected.", accepted = "June 1997", acknowledgement = ack-rfb # " and " # ack-kr, keywords = "algorithms, exponential distribution, random numbers, pseudorandom numbers.", subject = "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language Classifications, Fortran 90. {\bf G.3}: Mathematics of Computing, PROBABILITY AND STATISTICS, Random number generation. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing. {\bf I.6.0}: Computing Methodologies, SIMULATION AND MODELING, General.", } @Article{Fulton:1998:CSD, author = "Charles T. Fulton and Steven Pruess", title = "The Computation of Spectral Density Functions for Singular {Sturm-Liouville} Problems Involving Simple Continuous Spectra", journal = j-TOMS, volume = "24", number = "1", pages = "107--129", month = mar, year = "1998", CODEN = "CACMA2", ISSN = "0001-0782", URL = "http://doi.acm.org/10.1145/285861.285867", abstract = "The software package SLEDGE has as one of its options the estimation of spectral density functions $p(t)$ for a wide class of singular Sturm-Liouville problems. In this article the underlying theory and implementation issues are discussed. Several examples exhibiting quite varied asymptotic behavior in $p$ are presented.", accepted = "June 1997", acknowledgement = ack-rfb # " and " # ack-kr, keywords = "Algorithms, performance, continuous spectrum, eigenfunction norm, eigenvalue, limit circle, limit point, oscillatory, singular endpoints, spectral density functions, Sturm-Liouville problems.", subject = "{\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Boundary value problems. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm design and analysis.", } @Article{Sidje:1998:ESP, author = "Roger B. Sidje", title = "{EXPOKIT}: Software Package for Computing Matrix Exponentials", journal = j-TOMS, volume = "24", number = "1", pages = "130--156", month = mar, year = "1998", CODEN = "CACMA2", ISSN = "0001-0782", URL = "http://doi.acm.org/10.1145/285861.285868", abstract = "Expokit provides a set of routines aimed at computing matrix exponentials. More precisely, it computes either a small matrix exponential in full, the action of a large sparse matrix exponential on an operand vector, or the solution of a system of linear ODEs with constant inhomogeneity. The backbone of the sparse routines consists of matrix-free Krylov subspace projection methods (Arnoldi and Lanczos processes), and that is why the toolkit is capable of coping with sparse matrices of large dimension. The software handles real and complex matrices and provides specific routines for symmetric and Hermitian matrices. The computation of matrix exponentials is a numerical issue of critical importance in the area of Markov chains and furthermore, the computed solution is subject to probabilistic constraints. In addition to addressing general matrix exponentials, a distinct attention is assigned to the computation of transient states of Markov chains.", accepted = "June 1997", acknowledgement = ack-rfb # " and " # ack-kr, keywords = "Algorithms, Krylov methods, Markov chains, matrix exponential.", subject = "{\bf G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra. {\bf G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Initial value problems. {\bf G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Chow:1998:OFB, author = "Edmond Chow and Michael A. Heroux", title = "An object-oriented framework for block preconditioning", journal = j-TOMS, volume = "24", number = "2", pages = "159--183", month = jun, year = "1998", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Feb 8 17:51:43 MST 1999", bibsource = "http://www.acm.org/pubs/contents/journals/toms/1998-24/", URL = "http://doi.acm.org/10.1145/290200.287639", abstract = "General software for preconditioning the iterative solution of linear systems is greatly lagging behind the literature. This is partly because specific problems and specific matrix and preconditioner data structures in order to be solved efficiently, i.e., multiple implementations of a preconditioner with specialized data structures are required. This article presents a framework to support preconditioning with various, possibly user-defined, data structures for matrices that are partitioned into blocks. The main idea is to define data structures for the blocks, and an upper layer of software which uses these blocks transparently of their data structure. This transparency can be accomplished by using an object-oriented language. Thus, various preconditioners, such as block relaxations and block-incomplete factorizations, only need to be defined once and will work with any block type. In addition, it is possible to transparently interchange various approximate or exact techniques for inverting pivot blocks, or solving systems whose coefficient matrices are diagonal blocks. This leads to a rich variety of preconditioners that can be selected. Operations with the blocks are performed with optimized libraries or fundamental data types. Comparisons with an optimized Fortran 77 code on both workstations and Cray supercomputers show that this framework can approach the efficiency of Fortran 77, as long as suitable block sized and block types are chosen.", acknowledgement = ack-nhfb, keywords = "design", subject = "{\bf G.1.3} Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf G.1.3} Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse, structured, and very large systems (direct and iterative methods). {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices.", } @Article{Breinholt:1998:AGH, author = "Greg Breinholt and Christoph Schierz", title = "{Algorithm 781}: generating {Hilbert}'s space-filling curve by recursion", journal = j-TOMS, volume = "24", number = "2", pages = "184--189", month = jun, year = "1998", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Feb 8 17:51:43 MST 1999", bibsource = "http://www.acm.org/pubs/contents/journals/toms/1998-24/", URL = "http://doi.acm.org/10.1145/290200.290219", abstract = "An efficient algorithm for the generation of Hilbert's space-filling curve is given. The algorithm implements a recursive procedure that involves simple integer operations and quickly converges to the set of points that make the Hilbert curve. The algorithm is elegant, short, and considerably easier to implement than previous recursive and nonrecursive algorithms and can be efficiently implemented in all programming languages that have integer operations and allow recursion. The fundamental Hilbert shape (a line joining the four corners of a square) is represented by two variables with values of either 0 or 1. This coding technique could be successfully applied to the generation of other regular space-filling curves, such as the Peano curve.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf F.2.2} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Geometrical problems and computations. {\bf I.3.3} Computing Methodologies, COMPUTER GRAPHICS, Picture/Image Generation, Line and curve generation. {\bf I.3.5} Computing Methodologies, COMPUTER GRAPHICS, Computational Geometry and Object Modeling, Curve, surface, solid, and object representations.", } @Article{Bik:1998:AGS, author = "Aart J. C. Bik and Peter J. H. Brinkhaus and Peter M. W. Knijnenburg and Harry A. G. Wijshoff", title = "The automatic generation of sparse primitives", journal = j-TOMS, volume = "24", number = "2", pages = "190--225", month = jun, year = "1998", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Feb 8 17:51:43 MST 1999", bibsource = "http://www.acm.org/pubs/contents/journals/toms/1998-24/", URL = "http://doi.acm.org/10.1145/290200.287636", abstract = "Primitives in mathematical software are usually written and optimized by hand. With the implementation of a ``sparse compiler'' that is capable of automatically converting a dense program into sparse code, however, a completely different approach to the generation of sparse primitives can be taken. A {\em dense\/} implementation of a particular primitive is supplied to the sparse compiler, after which it can be converted into many different {\em sparse\/} versions of this primitive. Each version is specifically tailored to a class of sparse matrices having a specific nonzero structure. In this article, we discuss some of our experiences with this new approach.", acknowledgement = ack-nhfb, keywords = "algorithms; experimentation; performance", subject = "{\bf G.1.3} Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse, structured, and very large systems (direct and iterative methods). {\bf D.1.2} Software, PROGRAMMING TECHNIQUES, Automatic Programming. {\bf D.3.4} Software, PROGRAMMING LANGUAGES, Processors, Compilers. {\bf E.2} Data, DATA STORAGE REPRESENTATIONS. {\bf G.1.3} Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Matrix inversion. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices.", } @Article{Bischof:1998:CRQ, author = "Christian H. Bischof and G. Quintana--Ort{\'\i}", title = "Computing rank-revealing {$QR$} factorizations of dense matrices", journal = j-TOMS, volume = "24", number = "2", pages = "226--253", month = jun, year = "1998", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Feb 8 17:51:43 MST 1999", bibsource = "http://www.acm.org/pubs/contents/journals/toms/1998-24/", URL = "http://doi.acm.org/10.1145/290200.287637", abstract = "We develop algorithms and implementations for computing rank-revealing QR (RRQR) factorizations of dense matrices. First, we develop an efficient block algorithm for approximating an RRQR factorization, employing a windowed version of the commonly used Golub pivoting strategy, aided by incremental condition estimation. Second, we develop efficiently implementable variants of guaranteed reliable RRQR algorithms for triangular matrices originally suggested by Chandrasekaran and Ipsen and by Pan and Tang. We suggest algorithmic improvements with respect to condition estimation, termination criteria, and Givens updating. By combining the block algorithm with one of the triangular postprocessing steps, we arrive at an efficient and reliable algorithm for computing an RRQR factorization of a dense matrix. Experimental results on IBM RS/6000 SGI R8000 platforms show that this approach performs up to three times faster that the less reliable QR factorization with column pivoting as it is currently implemented in LAPACK, and comes within 15\% of the performance of the LAPACK block algorithm for computing a QR factorization without any column exchanges. Thus, we expect this routine to be useful in may circumstances where numerical rank deficiency cannot be ruled out, but currently has been ignored because of the computational cost of dealing with it.", acknowledgement = ack-nhfb, keywords = "algorithms; performance", subject = "{\bf G.1.3} Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices.", } @Article{Bischof:1998:ACR, author = "C. H. Bischof and G. Quintana-Ort{\'\i}", title = "{Algorithm 782}: {Codes} for rank-revealing {$QR$} factorizations of dense matrices", journal = j-TOMS, volume = "24", number = "2", pages = "254--257", month = jun, year = "1998", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Feb 8 17:51:43 MST 1999", bibsource = "http://www.acm.org/pubs/contents/journals/toms/1998-24/", URL = "http://doi.acm.org/10.1145/290200.287638", abstract = "This article describes a suite of codes as well as associated testing and timing drivers for computing rank-revealing QR (RRQR) factorizations of dense matrices. The main contribution is an efficient block algorithm for approximating an RRQR factorization, employing a windowed version of the commonly used Golub pivoting strategy and improved versions of the RRQR algorithms for triangular matrices originally suggested by Chandrasekaran and Ipsen and by Pan and Tang, respectively, We highlight usage and features of these codes.", acknowledgement = ack-nhfb, keywords = "algorithms; performance", subject = "{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN 77. {\bf G.1.3} Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE, Mathematica.", } @Article{Peters:1998:APF, author = "J{\"o}rg Peters", title = "{Algorithm 783}: {Pcp2Nurb} --- smooth free-form surfacing with linearly trimmed bicubic {B}-splines", journal = j-TOMS, volume = "24", number = "3", pages = "261--267", month = sep, year = "1998", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Feb 8 17:51:43 MST 1999", bibsource = "http://www.acm.org/pubs/contents/journals/toms/1998-24/", URL = "http://doi.acm.org/10.1145/292395.292399", abstract = "Unrestricted control polyhedra facilitate modeling free-form surfaces of arbitrary topology and local patch-layout by allowing {\em n\/}-sided, possibly nonplanar, facets and {\em m\/}-valent vertices. By cutting off edges and corners, the smoothing of an unrestricted control polyhedron can be reduced to the smoothing of a {\em planar-cut polyhedron\/}. A planar-cut polyhedron is a generalization of the well-known tensor-product control structure. The routine Pcp2Nurb in turn translates planar-cut polyhedra to a collection of four-sided linearly trimmed bicubic B-splines and untrimmed biquadratic B-splines. The routine can thus serve as central building block for overcoming topological constraints in the mathematical modeling of smooth surfaces that are stored, transmitted, and rendered using only the standard representation in industry. Specifically, on input of a nine-point subnet of a planar-cut polyhedron, the routine outputs a trimmed bicubic NURBS patch. If the subnet does not have geometrically redundant edges, this patch joins smoothly with patches from adjacent subnets as a four-sided piece of a regular {\em C1\/} surface. The patch integrates smoothly with untrimmed biquadratic tensor-product surfaces derived from subnets with tensor-product structure. Sharp features can be retained in this representation by using geometrically redundant edges in the planar-cut polyhedron. The resulting surface follows the outlines of the planar-cut polyhedron in the manner traditional tensor-product splines follow the outline of their rectilinear control polyhedron. In particular, it stays in the local convex hull of the planar-cut polyhedron.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf I.3.5} Computing Methodologies, COMPUTER GRAPHICS, Computational Geometry and Object Modeling, Splines. {\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, C. {\bf G.1.1} Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation, Spline and piecewise polynomial interpolation. {\bf G.1.2} Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Spline and piecewise polynomial approximation. {\bf I.3.5} Computing Methodologies, COMPUTER GRAPHICS, Computational Geometry and Object Modeling, Boundary representations.", } @Article{Kaagstrom:1998:GLB, author = "Bo K{\aa}gstr{\"o}m and Per Ling and Charles Van Loan", title = "{GEMM-based} level 3 {BLAS}: high-performance model implementations and performance evaluation benchmark", journal = j-TOMS, volume = "24", number = "3", pages = "268--302", month = sep, year = "1998", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Feb 8 17:51:43 MST 1999", bibsource = "http://www.acm.org/pubs/contents/journals/toms/1998-24/", URL = "http://doi.acm.org/10.1145/292395.292412", abstract = "The level 3 Basic Linear Algebra Subprograms (BLAS) are designed to perform various matrix multiply and triangular system solving computations. Due to the complex hardware organization of advanced computer architectures the development of optimal level 3 BLAS code is costly and time consuming. However, it is possible to develop a portable and high-performance level 3 BLAS library mainly relying on a highly optimized GEMM, the routine for the general matrix multiply and add operation. With suitable partitioning, all the other level 3 BLAS can be defined in terms of GEMM and a small amount of level 1 and level 2 computations. Our contribution is twofold. First, the model implementations in Fortran 77 of the GEMM-based level 3 BLAS are structured to reduced effectively data traffic in a memory hierarchy. Second, the GEMM-based level 3 BLAS performance evaluation benchmark is a tool for evaluating and comparing different implementations of the level 3 BLAS with the GEMM-based model implementations.", acknowledgement = ack-nhfb, keywords = "algorithms; measurement; performance", subject = "{\bf G.1.3} Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN 77. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE, Portability**. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE, Reliability and robustness. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE, Verification**.", } @Article{Kaagstrom:1998:AGL, author = "Bo K{\aa}gstr{\"o}m and Per Ling and Charles Van Loan", title = "{Algorithm 784}: {GEMM-based} level 3 {BLAS}: portability and optimization issues", journal = j-TOMS, volume = "24", number = "3", pages = "303--316", month = sep, year = "1998", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Feb 8 17:51:43 MST 1999", bibsource = "http://www.acm.org/pubs/contents/journals/toms/1998-24/", URL = "http://doi.acm.org/10.1145/292395.292426", abstract = "This companion article discusses portability and optimization issues of the GEMM-based level 3 BLAS model implementations and the performance evaluation benchmark. All software comes in all four data types (single- and double-precision, real and complex) and are designed to be easy to implement and use on different platforms. Each of the GEMM-based routines has a few machine-dependent parameters that specify internal block sizes, cache characteristics, and branch points for alternative code sections. These parameters provide means for adjustment to the characteristics of a memory hierarchy.", acknowledgement = ack-nhfb, keywords = "algorithms; measurement; performance", subject = "{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN 77. {\bf F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices. {\bf G.1.3} Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE, Portability**. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE, Reliability and robustness. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE, Verification**.", } @Article{Hu:1998:ASP, author = "Chenglie Hu", title = "{Algorithm 785}: a software package for computing {Schwarz-Christoffel} conformal transformation for doubly connected polygonal regions", journal = j-TOMS, volume = "24", number = "3", pages = "317--333", month = sep, year = "1998", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Feb 8 17:51:43 MST 1999", bibsource = "http://www.acm.org/pubs/contents/journals/toms/1998-24/", URL = "http://doi.acm.org/10.1145/292395.291204", abstract = "A software package implementing Schwarz-Christoffel Conformal transformation (or mapping) of doubly connected polygonal regions is fully described in this article from mathematical, numerical, and practical perspectives. The package solves the so-called accessory parameter problem associated with the mapping function as well as evaluates forward and inverse maps. The robustness of the package is reflected by the flexibility in choosing the accuracy of the parameters to be computed, the speed of computation, the ability of mapping ``difficult'' regions (to be specified in Section 2), and being user friendly. Several examples are presented to demonstrate the capabilities of the package.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.1.m} Mathematics of Computing, NUMERICAL ANALYSIS, Miscellaneous. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE, Reliability and robustness.", } @Article{Espelid:1998:RAD, author = "Terje O. Espelid", title = "Remark on {Algorithm 706}: {DCUTRI} --- an algorithm for adaptive cubature over a collection of triangles", journal = j-TOMS, volume = "24", number = "3", pages = "334--335", month = sep, year = "1998", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Mar 09 10:18:39 1999", bibsource = "http://www.acm.org/pubs/contents/journals/toms/1998-24/", note = "See \cite{Berntsen:1992:ADA}.", URL = "http://doi.acm.org/10.1145/292395.291205", abstract = "We present corrections to {Algorithm 706} ({\em ACM Trans. Math. Softw.\/} 18, 3, Sept. 1992, pages 329-342; CALGO supplement 123).", acknowledgement = ack-nhfb, keywords = "algorithms; reliability", subject = "{\bf G.1.4} Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation, Adaptive and iterative quadrature. {\bf G.1.4} Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation, Multidimensional (multiple) quadrature. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE, Reliability and robustness.", } @Article{Levin:1998:RAS, author = "Stewart A. Levin", title = "Remark on {Algorithm 622}: a simple macroprocessor", journal = j-TOMS, volume = "24", number = "3", pages = "336--340", month = sep, year = "1998", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Mar 09 10:17:52 1999", bibsource = "http://www.acm.org/pubs/contents/journals/toms/1998-24/", note = "See \cite{Rice:1984:ASM}.", URL = "http://doi.acm.org/10.1145/292395.292448", abstract = "A number of updates to the macroprocessor are described that bring the code into line with the Fortran 77 standard. This is followed by an outline of how the macroprocessor was used for the rapid porting of geophysical software from a 64-bit supercomputer environment to a number of different Unix workstations. Finally a number of deficiencies remaining in the macroprocessor are noted and workarounds suggested where possible.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, Macro and assembly languages. {\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN 77. {\bf D.3.4} Software, PROGRAMMING LANGUAGES, Processors, Preprocessors.", } @Article{Marsaglia:1998:MPM, author = "George Marsaglia and Wai Wan Tsang", title = "The {Monty Python} method for generating random variables", journal = j-TOMS, volume = "24", number = "3", pages = "341--350", month = sep, year = "1998", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Feb 8 17:51:43 MST 1999", bibsource = "http://www.acm.org/pubs/contents/journals/toms/1998-24/", URL = "http://doi.acm.org/10.1145/292395.292453", abstract = "We suggest an interesting and fast method for generating normal, exponential, t, von Mises, and certain other important random variables used in Monte Carlo studies. The right half of a symmetric density is cut into pieces, then, using simple area-preserving transformations, reassembled into a rectangle from which the x-coordinate---or a linear function of the x-coordinate---of a random point provides the required variate. To illustrate the speed and simplicity of the Monty Python method, we provide a small C program, self-contained, for rapid generation of normal (Gaussian) variables. It is self-contained in the sense that required uniform variates are generated in-line, as pairs of 16-bit integers by means of the remarkable new multiply-with-carry method.", acknowledgement = ack-nhfb, keywords = "algorithms; theory", subject = "{\bf G.3} Mathematics of Computing, PROBABILITY AND STATISTICS. {\bf I.6.1} Computing Methodologies, SIMULATION AND MODELING, Simulation Theory.", } @Article{Hopkins:1998:CAF, author = "Tim Hopkins", title = "Certification of {Algorithm 734}: a {Fortran 90} code for unconstrained nonlinear minimization", journal = j-TOMS, volume = "24", number = "3", pages = "351--354", month = sep, year = "1998", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Feb 8 17:51:43 MST 1999", bibsource = "http://www.acm.org/pubs/contents/journals/toms/1998-24/", URL = "http://doi.acm.org/10.1145/292395.292460", abstract = "A Fortran 90 Code for Unconstrained Nonlinear Minimization ({\em ACM Trans. Math. Softw. 20\/}, 3 (Sept. 1994), pages 354-372; CALGO Supplement 131) was ported to a number of compiler-platform combinations. The necessary changes to the code are given along with some comparative timings.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, Fortran 90. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing. {\bf G.1.6} Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Gradient methods.", } @Article{Gautschi:1998:RAO, author = "Walter Gautschi", title = "Remark on {Algorithm 726}: {ORTHPOL} --- {A} package of routines for generating orthogonal polynomials and {Gauss}-type quadrature rules", journal = j-TOMS, volume = "24", number = "3", pages = "355--355", month = sep, year = "1998", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Mar 09 10:16:21 1999", bibsource = "http://www.acm.org/pubs/contents/journals/toms/1998-24/", note = "See \cite{Gautschi:1994:ACP}.", URL = "http://doi.acm.org/10.1145/292395.292467", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.1.2} Mathematics of Computing, NUMERICAL ANALYSIS, Approximation. {\bf G.1.4} Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Smith:1998:AMP, author = "David M. Smith", title = "{Algorithm 786}: Multiple-Precision Complex Arithmetic and Functions", journal = j-TOMS, volume = "24", number = "4", pages = "359--367", month = dec, year = "1998", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Mar 09 10:09:51 1999", bibsource = "http://www.acm.org/pubs/contents/journals/toms/1998-24/", note = "See also \cite{Bailey:1995:FBM,Brent:1978:AMF,Brent:1979:RMF,Brent:1980:AIB}.", URL = "http://doi.acm.org/10.1145/293686.293687", abstract = "The article describes a collection of Fortran routines for multiple-precision complex arithmetic and elementary functions. The package provides good exception handling, flexible input and output, trace features, and results that are almost always correctly rounded. For best efficiency on different machines, the user can change the arithmetic type used to represent the multiple-precision numbers.", acknowledgement = ack-nhfb, keywords = "algorithms; performance; reliability", subject = "{\bf G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic. {\bf G.1.2} Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Elementary function approximation. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm design and analysis. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE, Efficiency. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE, Portability**.", } @Article{Ekeland:1998:SDE, author = "Kersti Ekeland and Brynjulf Owren and Eivor {\O}ines", title = "Stiffness Detection and Estimation of Dominant Spectra with Explicit {Runge-Kutta} Methods", journal = j-TOMS, volume = "24", number = "4", pages = "368--382", month = dec, year = "1998", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Feb 8 17:51:43 MST 1999", bibsource = "http://www.acm.org/pubs/contents/journals/toms/1998-24/", URL = "http://doi.acm.org/10.1145/293686.287641", abstract = "A new stiffness detection scheme based on explicit Runge-Kutta methods is proposed. It uses a Krylov subspace approximation to estimate the eigenvalues of the Jacobian of the differential system. The numerical examples indicate that this technique is a worthwhile alternative to other known stiffness detection schemes, especially when the systems are large and when it is desirable to know more about the spectrum of the Jacobian than just the spectral radius.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.1.7} Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Initial value problems. {\bf G.1.7} Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, One-step (single step) methods. {\bf G.1.7} Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Stiff equations.", } @Article{Renka:1998:RA, author = "Robert J. Renka and Ron Brown", title = "Remark on {Algorithm 761}", journal = j-TOMS, volume = "24", number = "4", pages = "383--385", month = dec, year = "1998", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Mar 09 10:12:24 1999", bibsource = "http://www.acm.org/pubs/contents/journals/toms/1998-24/", note = "See \cite{Akima:1996:ASS,deTisi:2000:RAS}.", URL = "http://doi.acm.org/10.1145/293686.293689", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN. {\bf G.1.1} Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation, Interpolation formulas. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Resende:1998:AFS, author = "Mauricio G. C. Resende and Thomas A. Feo and Stuart H. Smith", title = "{Algorithm 787}: {Fortran} Subroutines for Approximate Solution of Maximum Independent Set Problems Using {GRASP}", journal = j-TOMS, volume = "24", number = "4", pages = "386--394", month = dec, year = "1998", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Mar 09 10:13:13 1999", bibsource = "http://www.acm.org/pubs/contents/journals/toms/1998-24/", URL = "http://doi.acm.org/10.1145/293686.293690", abstract = "Let G=(V, E) be an undirected graph where V and E are the sets of ver tices and edges of G, respectively. A subset of the vertices S *** V is independent if all of its members are pairwise nonadjacent, i.e., have no edge between them. A solution to the NP-hard maximum independent set problem is an independent set of maximum cardinality. This article describes gmis, a set of Fortran subroutines to find an approximate solution of a maximum independent set problem. A greedy randomized adaptive search procedure (GRASP) is used to produce the solutions. The algorithm is described in detail. Implementation and usage of the package is outlined, and computational experiments are reported, illustrating solution quality as a function of running time.", acknowledgement = ack-nhfb, keywords = "algorithms; performance", subject = "{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN. {\bf G.1.6} Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Integer programming. {\bf G.2.1} Mathematics of Computing, DISCRETE MATHEMATICS, Combinatorics, Combinatorial algorithms. {\bf G.m} Mathematics of Computing, MISCELLANEOUS.", } @Article{Atkinson:1998:AAB, author = "Kendall Atkinson and Youngmok Jeon", title = "{Algorithm 787}: {Automatic} Boundary Integral Equation Programs for the Planar {Laplace} Equation", journal = j-TOMS, volume = "24", number = "4", pages = "395--417", month = dec, year = "1998", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Feb 8 17:51:43 MST 1999", bibsource = "http://www.acm.org/pubs/contents/journals/toms/1998-24/", URL = "http://doi.acm.org/10.1145/293686.293692", abstract = "Algorithms with automatic error control are described for the solution of Laplace's equation on both interior and exterior regions, with both Dirichlet and Neumann boundary conditions. The algorithms are based on standard reformulations of each boundary value problem as a boundary integral equation of the second kind. The Nystr{\"o}m method is used to solve the integral equations, and convergence of arbitrary high order is observed when the boundary data are analytic. The Kelvin transformation is introduced to allow a simple conversion between internal and external problems. Two Fortran program implementations, DRCHLT and NEUMAN, are defined, analyzed, and illustrated.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN. {\bf G.1.8} Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations. {\bf G.1.9} Mathematics of Computing, NUMERICAL ANALYSIS, Integral Equations.", } @Article{Govaerts:1998:IHD, author = "W. Govaerts and F. W. O. Kuznetsov and B. Sijnave", title = "Implementation of {Hopf} and Double-{Hopf} Continuation Using Bordering Methods", journal = j-TOMS, volume = "24", number = "4", pages = "418--436", month = dec, year = "1998", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Feb 8 17:51:43 MST 1999", bibsource = "http://www.acm.org/pubs/contents/journals/toms/1998-24/", URL = "http://doi.acm.org/10.1145/293686.293693", abstract = "We discuss the computational study of curves of Hopf and double-Hopf points in the software package CONTENT developed at CWI, Amsterdam. These are important points in the numerical study of dynamical systems characterized by the occurrence of one or two conjugate pairs of pure imaginary eigenvalues in the spectrum of the Jacobian matrix. The bialternate product of matrices is extensively used in three codes for the numerical continuation of curves of Hopf points and in one for the continuation of curves of double-Hopf points. In the double-Hopf and two of the single-Hopf cases this is combined with a bordered matrix method. We use this software to find special points on a Hopf curve in a model of chemical oscillations and by computing a Hopf and a double-Hopf curve in a realistic model of a neuron.", acknowledgement = ack-nhfb, keywords = "algorithms; design", subject = "{\bf D.2.6} Software, SOFTWARE ENGINEERING, Programming Environments. {\bf G.1.7} Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Giering:1998:RAC, author = "Ralf Giering and Thomas Kaminski", title = "Recipes for Adjoint Code Construction", journal = j-TOMS, volume = "24", number = "4", pages = "437--474", month = dec, year = "1998", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Feb 8 17:51:43 MST 1999", bibsource = "http://www.acm.org/pubs/contents/journals/toms/1998-24/", URL = "http://doi.acm.org/10.1145/293686.293695", abstract = "Adjoint models are increasingly being developed for use in meteorology and oceanography. Typical applications are data assimilation, model tuning, sensitivity analysis, and determination of singular vectors. The adjoint model computes the gradient of a cost function with respect to control variables. Generation of adjoint code may be seen as the special case of differentiation of algorithms in reverse mode, where the dependent function is a scalar. The described method for adjoint code generation is based on a few basic principles, which permits the establishment of simple construction rules for adjoint statements and complete adjoint subprograms. These rules are presented and illustrated with some examples. Conflicts that occur due to loops and redefinition of variables are also discussed. Direct coding of the adjoint of a more sophisticated model is extremely time consuming and subject to errors. Hence, automatic generation of adjoint code represents a distinct advantage. An implementation of the method, described in this article, is the tangent linear and adjoint model compiler (TAMC).", acknowledgement = ack-nhfb, keywords = "algorithms; theory", subject = "{\bf D.3.4} Software, PROGRAMMING LANGUAGES, Processors, Preprocessors. {\bf G.1.4} Mathematics of Computing, NUMERICAL ANALYSIS, Quadrature and Numerical Differentiation, Automatic differentiation. {\bf G.1.6} Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Gradient methods. {\bf I.2.2} Computing Methodologies, ARTIFICIAL INTELLIGENCE, Automatic Programming, Program transformation.", } @Article{Berzins:1998:SAS, author = "M. Berzins and R. Fairlie and S. V. Pennington and J. M. Ware and L. E. Scales", title = "{SPRINT2D}: adaptive software for {PDEs}", journal = j-TOMS, volume = "24", number = "4", pages = "475--499", month = dec, year = "1998", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Mon Feb 8 17:51:43 MST 1999", bibsource = "http://www.acm.org/pubs/contents/journals/toms/1998-24/", URL = "http://doi.acm.org/10.1145/293686.293696", abstract = "SPRINT2D is a set of software tools for solving both steady and unstea dy partial differential equations in two-space variables. The software consists of a set of coupled modules for mesh generation, spatial discretization, time integration, nonlinear equations, linear algebra, spatial adaptivity, and visualization. The software uses unstructured triangular meshes and adaptive local error control in both space and time. the class of problems solved includes systems of parabolic, elliptic, and hyperbolic equations; for the latter by use of Riemann-solve-based methods. This article describes the software and show how the adaptive techniques may be used to increase the reliability of the solution for a Burgers' equations problem, an electrostatics problem from elastohydrodynamic lubrication, and a challenging gas jet problem.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.1.8} Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Method of lines. {\bf G.1.8} Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Hyperbolic equations. {\bf G.1.8} Mathematics of Computing, NUMERICAL ANALYSIS, Partial Differential Equations, Elliptic equations. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Anonymous:1998:AI, author = "Anonymous", title = "1998 Author Index", journal = j-TOMS, volume = "24", number = "4", pages = "500--502", month = dec, year = "1998", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Mar 09 17:22:53 1999", acknowledgement = ack-nhfb, xxURL = "Missing from ACM Digital Library", } @Article{Davis:1999:CUM, author = "Timothy A. Davis and Iain S. Duff", title = "Combined Unifrontal\slash Multifrontal Method for Unsymmetric Sparse Matrices", journal = j-TOMS, volume = "25", number = "1", pages = "1--20", month = mar, year = "1999", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Thu Jul 15 19:01:02 1999", bibsource = "http://www.acm.org/pubs/contents/journals/toms/1999-25/", URL = "http://doi.acm.org/10.1145/305658.287640", abstract = "We discuss the organization of frontal matrices in multifrontal methods for the solution of large sparse sets of unsymmetric linear equations. In the multifrontal method, work on a frontal matrix can be suspended, the frontal matrix can be stored for later reuse, and a new frontal matrix can be generated. There are thus several frontal matrices stored during the factorization, and one or more of these are assembled (summed) when creating a new frontal matrix. Although this means that arbitrary sparsity patterns can be handled efficiently, extra work is required to sum the frontal matrices together and can be costly because indirect addressing is required. The (uni)frontal method avoids this extra work by factorizing the matrix with a single frontal matrix. Rows and columns are added to the frontal matrix, and pivot rows and columns are removed. Data movement is simpler, but higher fill-in can result if the matrix cannot be permuted into a variable-band form with small profile. We consider a combined unifrontal/multifrontal algorithm to enable general fill-in reduction orderings to be applied without the data movement of previous multifrontal approaches. We discuss this technique in the context of a code designed for the solution of sparse systems with unsymmetric pattern.", acknowledgement = ack-nhfb, keywords = "algorithms; experimentation; performance", subject = "{\bf G.1.3} Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear systems (direct and iterative methods). {\bf G.1.3} Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse, structured, and very large systems (direct and iterative methods). {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm design and analysis.", } @Article{Pryce:1999:TPS, author = "J. D. Pryce", title = "A Test Package for {Sturm-Liouville} Solvers", journal = j-TOMS, volume = "25", number = "1", pages = "21--57", month = mar, year = "1999", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Thu Jul 15 19:01:02 1999", URL = "http://doi.acm.org/10.1145/305658.287651", abstract = "The author and colleagues have produced a collection of 60 test problems which offer a realistic performance test of the currently available automatic codes for eigenvalues of the classical Sturm-Liouville problem. We describe a Fortran implementation and the considerations that went into its design. A novel feature is that (almost) all the code defining one problem is textually contiguous in the Fortran text, unlike for example the DETEST package for ODE initial-value solvers where the definition of a problem is spread over several routines. The described implementation forms the infrastructure of the SLDRVER interactive package which supports exploration of a set of Sturm-Liouville problems with the four SL-solvers SLEIGN, SLEDGE, SL02F, and SLEIGN2. A ``standard'' set of 60 problems is provided, but it is simple to replace this by another one.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf D.2.5} Software, SOFTWARE ENGINEERING, Testing and Debugging. {\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN 77. {\bf G.1.7} Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Boundary value problems. {/bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing. {/bf I.2.4} Computing Methodologies, ARTIFICIAL INTELLIGENCE, Knowledge Representation Formalisms and Methods.", } @Article{Pryce:1999:AST, author = "J. D. Pryce", title = "{Algorithm 789}: {SLTSTPAK}: {A} Test Package for {Sturm-Liouville} Solvers", journal = j-TOMS, volume = "25", number = "1", pages = "58--69", month = mar, year = "1999", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Thu Jul 15 19:01:02 1999", URL = "http://doi.acm.org/10.1145/305658.287652", abstract = "We give technical details of the Sturm-Liouville test package SLTSTPAK, complementing the companion article (this issue) on its design. SLTSTPAK comprises the following: a specification of how to write a routine TSTSET containing a set of Sturm-Liouville problems; a number of routines that act as a harness between a TSTSET, written to this specification, and a driver program. A set of 60 standard problems is provided, but it is simple to replace this by another one.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{/bf D.2.5} Software, SOFTWARE ENGINEERING, Testing and Debugging. {\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN 77. {\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, Fortran 90. {\bf G.1.7} Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary Differential Equations, Boundary value problems. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing.", } @Article{Renka:1999:ACC, author = "R. J. Renka", title = "{Algorithm 790}: {CSHEP2D}: Cubic {Shepard} Method for Bivariate Interpolation of Scattered Data", journal = j-TOMS, volume = "25", number = "1", pages = "70--73", month = mar, year = "1999", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Thu Jul 15 19:01:02 1999", URL = "http://doi.acm.org/10.1145/305658.305737", abstract = "We describe a new algorithm for scattered data interpolation. The method is similar to that of Algorithm 660 but achieves cubic precision and C2 continuity at very little additional cost. An accompanying article presents test results that show the method to be among the most accurate available.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.1.1} Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation. {\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN 77. {\bf G.1.2} Mathematics of Computing, NUMERICAL ANALYSIS, Approximation. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Renka:1999:ATC, author = "R. J. Renka and Ron Brown", title = "{Algorithm 791}: {TSHEP2D}: Cosine series {Shepard} Method for Bivariate Interpolation of Scattered Data", journal = j-TOMS, volume = "25", number = "1", pages = "74--77", month = mar, year = "1999", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Thu Jul 15 19:01:02 1999", URL = "http://doi.acm.org/10.1145/305658.305754", abstract = "We describe a new algorithm for scattered data interpolation. It is based on a modified Shepard method similar to that of Algorithm 660 but uses 10-parameter cosine series nodal functions in place of quadratic polynomials. Also, the interpolant has continuous second partial derivatives. An accompanying survey article presents test results that show the method to be more accurate that polynomial-based methods in terms of reproducing test functions with large variations and steep gradients.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.1.1} Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation. {\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN 77. {\bf G.1.2} Mathematics of Computing, NUMERICAL ANALYSIS, Approximation. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Renka:1999:AAT, author = "R. J. Renka and Ron Brown", title = "{Algorithm 792}: Accuracy Tests of {ACM} Algorithms for Interpolation of Scattered Data in the Plane", journal = j-TOMS, volume = "25", number = "1", pages = "78--94", month = mar, year = "1999", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Thu Jul 15 19:01:02 1999", URL = "http://doi.acm.org/10.1145/305658.305745", abstract = "We present results of accuracy tests on scattered-data fitting methods that have been published as ACM algorithms. The algorithms include seven triangulation-based methods and three modified Shepard methods, two of which are new algorithms. Our purpose is twofold: to guide potential users in the selection of an appropriate algorithm and to provide a test suite for assessing the accuracy of new methods (or existing methods that are not included in this survey). Our test suite consists of five sets of nodes, with nodes counts ranging from 25 to 100, and 10 test functions. These are made available in the form of three Fortran subroutines: TESTDT returns one of the node sets; TSTFN1 returns a value and, optionally, a gradient value, of one of the test function; and TSTFN2 returns a value, first partials, and second partial derivatives of one of the test functions.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.1.1} Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation. {\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN 77. {\bf G.1.2} Mathematics of Computing, NUMERICAL ANALYSIS, Approximation. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Testa:1999:RA, author = "F. J. Testa and R. J. Renka", title = "Remark on {Algorithm 716}", journal = j-TOMS, volume = "25", number = "1", pages = "95--96", month = mar, year = "1999", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Thu Jul 15 19:01:02 1999", note = "See \cite{Renka:1993:ATT}.", URL = "http://doi.acm.org/10.1145/305658.287656", abstract = "The curve-fitting package TSPACK has been converted to double precision. Also, portability has been improved by eliminating some potential errors.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.1.1} Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation. {\bf G.1.2} Mathematics of Computing, NUMERICAL ANALYSIS, Approximation. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Renka:1999:RAa, author = "R. J. Renka", title = "Remark on {Algorithm 751}", journal = j-TOMS, volume = "25", number = "1", pages = "97--98", month = mar, year = "1999", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Thu Jul 15 19:01:02 1999", note = "See \cite{Renka:1996:ATC}.", URL = "http://doi.acm.org/10.1145/305658.305726", abstract = "The triangulation package TRIPACK has been revised to run more efficiently and to eliminate some potential errors. Also, a portable triangulation plotting routine was added.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.1.1} Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation. {\bf G.1.2} Mathematics of Computing, NUMERICAL ANALYSIS, Approximation. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Renka:1999:RAb, author = "R. J. Renka", title = "Remark on {Algorithm 752}", journal = j-TOMS, volume = "25", number = "1", pages = "99--100", month = mar, year = "1999", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Thu Jul 15 19:01:02 1999", note = "See \cite{Renka:1996:ASS}.", URL = "http://doi.acm.org/10.1145/305658.305731", abstract = "The triangulation-based scattered-data fitting package SRFPACK was updated for (a) compatibility with a revised interface to the triangulation package TRIPACK, (b) the elimination of potential errors in the treatment of tension factors and in the extrapolation procedure, and (c) the addition of a more accurate local gradient-estimation procedure and a simple but portable contour-plotting capability.", acknowledgement = ack-nhfb, keywords = "algorithms", subject = "{\bf G.1.1} Mathematics of Computing, NUMERICAL ANALYSIS, Interpolation. {\bf G.1.2} Mathematics of Computing, NUMERICAL ANALYSIS, Approximation. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE.", } @Article{Gautschi:1999:NRC, author = "Walter Gautschi", title = "A Note on the Recursive Calculation of Incomplete Gamma Functions", journal = j-TOMS, volume = "25", number = "1", pages = "101--107", month = mar, year = "1999", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Thu Jul 15 19:01:02 1999", URL = "http://doi.acm.org/10.1145/305658.305717", abstract = "It is known that the recurrence relation for incomplete gamma functions $\Gamma(a + n, x), 0 \le a < 1$, $n = 0, 1, 2 \ldots$, when $x$ is positive, is unstable---more so the larger $x$. Nevertheless, the recursion can be used in the range $0 \le n \le x$ practically without error growth, and in larger ranges $0 \le n \le N$ with a loss of accuracy that can be controlled by suitably limiting $N$.", acknowledgement = ack-nhfb, keywords = "algorithms; reliability", subject = "{\bf G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS, General, Stability (and instability). {\bf G.1.2} Mathematics of Computing, NUMERICAL ANALYSIS, Approximation.", } @Article{Xie:1999:RAU, author = "Dexuan Xie and Tamar Schlick", title = "Remark on {Algorithm 702}: The Updated Truncated {Newton} Minimization Package", journal = j-TOMS, volume = "25", number = "1", pages = "108--122", month = mar, year = "1999", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Thu Jul 15 19:01:02 1999", note = "See \cite{Schlick:1992:ATE}.", URL = "http://doi.acm.org/10.1145/305658.305698", abstract = "A truncated Newton minimization package, TNPACK, was described in ACM Transactions on Mathematical Software 14, 1 (Mar. 1992), pp.46-111. Modifications to enhance performance, especially for large-scale minimization of molecular potential functions, are described here. They involve three program segments of TNPACK: negative curvature test, modified Cholesky factorization, and line-search stopping rule.", acknowledgement = ack-nhfb, keywords = "algorithms; performance", subject = "{\bf G.1.6} Mathematics of Computing, NUMERICAL ANALYSIS, Optimization, Nonlinear programming. {\bf G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf J.3} Computer Applications, LIFE AND MEDICAL SCIENCES.", } @Article{Gay:1999:SAF, author = "David M. Gay and Eric Grosse", title = "Self-adapting {Fortran 77} Machine Constants: Comment on {Algorithm 528}", journal = j-TOMS, volume = "25", number = "1", pages = "123--126", month = mar, year = "1999", CODEN = "CACMA2", ISSN = "0001-0782", bibdate = "Wed Oct 20 12:38:08 1999", note = "See \cite{Fox:1978:AFP}.", URL = "http://doi.acm.org/10.1145/305658.305711", abstract = "This note discusses user dissatisfaction with the need to uncomment data statements in Algorithm 528, comments on alternative approaches tried by the community, and proposes a solution that is both automatic and safe.", acknowledgement = ack-nhfb, keywords = "algorithms; d1mach; languages; machine environment parameters", subject = "{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN 77. {\bf G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS, General, Computer arithmetic.", } @Article{Flores:1999:CFR, author = "Juan Flores", title = "Complex Fans: {A} Representation for Vectors in Polar Form with Interval Attributes", journal = j-TOMS, volume = "25", number = "2", pages = "129--156", month = jun, year = "1999", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Wed Oct 20 18:21:35 MDT 1999", bibsource = "http://www.acm.org/pubs/toc/", URL = "http://doi.acm.org/10.1145/317275.317277", abstract = "If we allow the magnitude and angle of a complex number (expressed in polar form) to range over an interval, it describes a semicircular region, similar to a fan; these regions are what we call complex fans. Complex numbers are a special case of complex fans, where the magnitude and angle are point intervals. Operations (especially addition) with complex numbers in polar form are complicated. What most applications do is to convert them to rectangular form, perform operations, and return the result to polar form. However, if the complex number is a Complex Fan, that transformation increases ambiguity in the result. That is, the resulting Fan is not the smallest Fan that contains all possible results. The need for minimal results took us to develop algorithms to perform the basic arithmetic operations with complex fans, ensuring the result will always be the smallest possible complex fan. We have developed the arithmetic operations of addition, negation, subtraction, product, and division of complex fans. The algorithms presented in this article are written in pseudocode, and the programs in Common Lisp, making use of CLOS (Common Lisp Object System). Translation to any other high-level programming language should be straightforward.", accepted = "March 1999", acknowledgement = ack-nhfb, keywords = "abstract data type; complex fans; complex numbers; interval computation; qualitative reasoning", subject = "Mathematics of Computing - Mathematical Software ({\bf G.4}): Algorithm design and analysis; Computing Methodologies -Artificial Intelligence - Knowledge Representation Formalisms and Methods ({\bf I.2}); Computer Applications - Physical Sciences and Engineering ({\bf J.2}): Engineering", } @Article{Heinkenschloss:1999:IBO, author = "Matthias Heinkenschloss and Luis N. Vicente", title = "An Interface Between Optimization and Application for the Numerical Solution of Optimal Control Problems", journal = j-TOMS, volume = "25", number = "2", pages = "157--190", month = jun, year = "1999", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Wed Oct 20 18:21:35 MDT 1999", bibsource = "http://www.acm.org/pubs/toc/", URL = "http://doi.acm.org/10.1145/317275.317278", abstract = "An interface between the application problem and the nonlinear optimization algorithm is proposed for the numerical solution of distributed optimal control problems. By using this interface, numerical optimization algorithms can be designed to take advantage of inherent problem features like the splitting of the variables into states and controls and the scaling inherited from the functional scalar products. Further, the interface allows the optimization algorithm to make efficient use of user-provided function evaluations and derivative calculations.", accepted = "February 1999", acknowledgement = ack-nhfb, keywords = "optimal control; optimization; simulation", subject = "Mathematics of Computing --- Mathematical Software (G.4); Mathematics of Computing --- Numerical Analysis --- Optimization (G.1.6): Constrained optimization; General Terms: Algorithms, Design", } @Article{Gockenbach:1999:CCL, author = "Mark S. Gockenbach and Matthew J. Petro and William W. Symes", title = "{C++} Classes for Linking Optimization with Complex Simulations", journal = j-TOMS, volume = "25", number = "2", pages = "191--212", month = jun, year = "1999", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Wed Oct 20 18:21:35 MDT 1999", bibsource = "http://www.acm.org/pubs/toc/", URL = "http://doi.acm.org/10.1145/317275.317280", abstract = "The object-oriented programming paradigm can be used to overcome the incompatibilities between off-the-shelf optimization software and application software. The Hilbert Class Library (HCL) defines the fundamental mathematical objects arising in optimization problems, such as vectors, linear operators, and so forth, as C++ classes, making it possible to write optimization code in a natural fashion, while allowing application software such as simulators to use the most convenient data structures and programming style. In spite of the poor reputation C++ has for runtime performance, the use of mixed-language programming allows performance equal to that achieved by standard Fortran packages, as comparisons with the popular code LBFGS and ARPACK demonstrate.", accepted = "April 1999", acknowledgement = ack-nhfb, keywords = "object-oriented design; optimization; simulation", subject = "Software --- Programming Techniques --- Object-oriented Programming (D.1.5); General Terms: Algorithms, Languages, Performance", } @Article{Gautschi:1999:AGG, author = "Walter Gautschi", title = "{Algorithm 793}: {GQRAT} --- {Gauss} Quadrature for Rational Functions", journal = j-TOMS, volume = "25", number = "2", pages = "213--239", month = jun, year = "1999", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Wed Oct 20 18:21:35 MDT 1999", bibsource = "http://www.acm.org/pubs/toc/", URL = "http://doi.acm.org/10.1145/317275.317282", abstract = "The concern here is with Gauss-type quadrature rules that are exact for a mixture of polynomials and rational functions, the latter being selected so as to simulate poles that may be present in the integrand. The underlying theory is presented as well as methods for constructing such rational Gauss formulae. Relevant computer routines are provided and applied to a number examples, including Fermi-Dirac and Bose-Einstein integrals of interest in solid state physics.", acknowledgement = ack-nhfb, keywords = "Gaussian quadrature exact for rational functions; construction of quadrature rules; generalized Fermi-Dirac and Bose Einstein integrals", subject = "Software --- Programming Languages --- Language Classifications (D.3.2): FORTRAN 77; Mathematics of Computing --- Numerical Analysis --- Quadrature and Numerical Differentiation (G.1.4); General Terms: Algorithms", } @Article{Wieder:1999:ANH, author = "Thomas Wieder", title = "{Algorithm 794}: Numerical {Hankel} transform by the {Fortran} program {HANKEL}", journal = j-TOMS, volume = "25", number = "2", pages = "240--250", month = jun, year = "1999", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Wed Oct 20 18:21:35 MDT 1999", bibsource = "http://www.acm.org/pubs/toc/", URL = "http://doi.acm.org/10.1145/317275.317284", abstract = "The numerical evaluation of the Hankel transform poses the problems of both infinite integration and Bessel function calculation. Using the corresponding numerical program routines from the literature, a Fortran program has been written to perform the Hankel transform for real functions, given either in analytical form as subroutines or in discrete form as tabulated data.", accepted = "February 1999", acknowledgement = ack-nhfb, keywords = "Hankel transform; numerical analysis", subject = "Software --- Programming Languages --- Language Classifications (D.3.2): FORTRAN 77; Theory of Computation --- Analysis of Algorithms and Problem Complexity --- Numerical Algorithms and Problems (F.2.1): Computation of transforms;", } @Article{Verschelde:1999:APG, author = "Jan Verschelde", title = "{Algorithm 795}: {PHCPACK}: {A} general-purpose solver for polynomial systems by homotopy continuation", journal = j-TOMS, volume = "25", number = "2", pages = "251--276", month = jun, year = "1999", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Wed Oct 20 18:21:35 MDT 1999", bibsource = "http://www.acm.org/pubs/toc/", URL = "http://doi.acm.org/10.1145/317275.317286", abstract = "Polynomial systems occur in a wide variety of application domains. Homotopy continuation methods are reliable and powerful methods to compute numerically approximations to all isolated complex solutions. During the last decade considerable progress has been accomplished on exploiting structure in a polynomial system, in particular its sparsity. In this article the structure and design of the software package PHC is described. The main program operates in several modes, is menu driven, and is file oriented. This package features great variety of root-counting methods among its tools. The outline of one black-box solver is sketched, and a report is given on its performance on a large database of test problems. The software has been developed on four different machine architectures. Its portability is ensured by the gnu-ada compiler.", accepted = "15 feb 1999", acknowledgement = ack-nhfb, keywords = "B\'ezout's theorem; Bernshtein's theorem; B{\'e}zout number; enumerative geometry; homotopy continuation; mixed volume; polyhedral homotopy; polynomial systems; root count; Schubert calculus; start system", subject = "Software --- Programming Languages --- Language Classifications (D.3.2): Ada; Mathematics of Computing --- Numerical Analysis --- Roots of Nonlinear Equations (G.1.5): Systems of equations; Mathematics of Computing --- Numerical Analysis --- Roots of Nonlinear Equations (G.1.5): Polynomials, methods for; Mathematics of Computing --- Discrete Mathematics --- Combinatorics (G.2.1): Counting problems; Mathematics of Computing --- Mathematical Software (G)", } @Article{DAmore:1999:IFS, author = "Luisa D'Amore and Giuliano Laccetti and Almerico Murli", title = "An Implementation of a {Fourier} Series Method for the Numerical Inversion of the {Laplace} Transform", journal = j-TOMS, volume = "25", number = "3", pages = "279--305", month = sep, year = "1999", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Apr 4 16:36:33 MDT 2000", URL = "http://doi.acm.org/10.1145/326147.326148", abstract = "Our method is based on the numerical evaluation of the integral which occurs in the Riemann Inversion formula. The trapezoidal rule approximation to this integral reduces to a Fourier series. We analyze the corresponding discretization error and demonstrate how this expression can be used in the development of an {\em automatic routine}, one in which the user needs to specify only the required accuracy", accepted = "10 feb 1999", acknowledgement = ack-nhfb, keywords = "automatic stopping criterion; Fourier series methods; Laplace transform inversion", subject = "Software --- Programming Languages --- Language Classifications (D.3.2): FORTRAN 77; Mathematics of Computing --- Numerical Analysis --- General (G.1.0): Numerical algorithms; Mathematics of Computing --- Numerical Analysis --- Integral Equations (G.1.9); Mathematics of Computing --- Numerical Analysis --- Approximation (G.1.2): Nonlinear approximation; General Terms: Algorithms", } @Article{DAmore:1999:AFS, author = "Luisa D'Amore and Guiliano Laccetti and Almerico Murli", title = "{Algorithm 796}: {A} {Fortran} Software Package for the Numerical Inversion of the {Laplace} Transform Based on a {Fourier} Series Method", journal = j-TOMS, volume = "25", number = "3", pages = "306--315", month = sep, year = "1999", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Apr 4 16:36:33 MDT 2000", URL = "http://doi.acm.org/10.1145/326147.326149", abstract = "A software package for the numerical inversion of a Laplace Transform function is described. Besides function values of $F(z)$ for complex and real $z$, the user has only to provide the numerical value of the Laplace convergence abscissa or, failing this, an upper bound to this quantity, and the accuracy he or she requires in the computed value of the inverse Transform. The method implemented is based on a Fourier series expansion of the inverse transform, and it is especially suitable when such inverse Laplace Transform is sectionally continuous.", accepted = "10 feb 1999", acknowledgement = ack-nhfb, keywords = "automatic stopping criterion; Fourier series methods; Laplace transform inversion", subject = "Software --- Programming Languages --- Language Classifications (D.3.2): FORTRAN 77; Mathematics of Computing --- Numerical Analysis --- Integral Equations (G.1.9); Mathematics of Computing --- Numerical Analysis --- Approximation (G.1.2): Nonlinear approximation; General Terms: Algorithms", } @Article{Dayde:1999:RBB, author = "Michel J. Dayd{\'e} and Iain S. Duff", title = "The {RISC BLAS}: {A} Blocked Implementation of {Level 3 BLAS} for {RISC} Processors", journal = j-TOMS, volume = "25", number = "3", pages = "316--340", month = sep, year = "1999", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Apr 4 16:36:33 MDT 2000", URL = "http://doi.acm.org/10.1145/326147.326150", abstract = "We describe a version of the Level 3 BLAS which is designed to be efficient on RISC processors. This is an extension of previous studies by the authors and colleagues on a similar approach for efficient serial and parallel implementations on virtual-memory and shared-memory multiprocessors. All our codes are written in Fortran and use loop-unrolling, blocking, and copying to improve the performance. A blocking technique is used to express the BLAS in terms of operations involving triangular blocks and calls to the matrix-matrix multiplication kernel (GEMM). No manufacturer-supplied or assembler code is used. This blocked implementation uses the same blocking ideas as in our implementation for vector machines except that the ordering of loops is designed for efficient reuse of date held in cache and not necessarily for parallelization. All the codes are specifically tuned for RISC processors. The software also includes a tuned version of GEMM. A parameter which controls the blocking allows efficient exploitation of the memory hierarchy on the various target computers. We present results on a range of RISC-based workstations and multiprocessors: CRAY T3D, DEC 8400 5/300, HP 715/64, IBM SP2, MEIKO CS2-HA, SGI Power Challenge 10000, and SUN UltraSPARC-1 model 140. This implementation of the Level 3 BLAS is available on anonymous FTP, and we welcome input from users to improve and extend our BLAS implementation.", accepted = "April 1999", acknowledgement = ack-nhfb, keywords = "blocking; level 3 BLAS; loop-unrolling; matrix-matrix kernels; RISC processors", subject = "Mathematics of Computing --- Mathematical Software (G.4); Theory of Computation --- Analysis of Algorithms and Problem Complexity --- Numerical Algorithms and Problems (F.2.1): Computations on matrices; Mathematics of Computing --- Numerical Analysis --- General (G.1.0): Numerical algorithms; Mathematics of Computing --- Numerical Analysis --- Numerical Linear Algebra (G.1.3): Linear systems (direct and iterative methods); General Terms: Algorithms, Measurement, Performance", } @Article{Ribeiro:1999:AFS, author = "Celso C. Ribeiro and Mauricio G. C. Resende", title = "{Algorithm 797}: {Fortran} subroutines for approximate solution of graph planarization problems using {GRASP}", journal = j-TOMS, volume = "25", number = "3", pages = "341--352", month = sep, year = "1999", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Apr 4 16:36:33 MDT 2000", URL = "http://doi.acm.org/10.1145/326147.326153", abstract = "We describe Fortran subroutines for finding approximate solutions of the maximum planar subgraph problem (graph planarization) using a Greedy Randomized Adaptive Search Procedure (GRASP). The design and implementation of the code are described in detail. Computational results with the subroutines illustrate the quality of solutions found as a function of number of GRASP iterations.", accepted = "5 may 1999", acknowledgement = ack-nhfb, keywords = "GRASP; automatic graph drawing; combinatorial optimization; graph planarization; local search", subject = "Software --- Programming Languages --- Language Classifications (D.3.2): FORTRAN 77; Mathematics of Computing --- Discrete Mathematics --- Combinatorics (G.2.1): Combinatorial algorithms; Mathematics of Computing --- Miscellaneous (G.m); General Terms: Algorithms, Performance", } @Article{Berry:1999:AHD, author = "Michael W. Berry and Karen S. Minser", title = "{Algorithm 798}: High-Dimensional Interpolation Using the Modified {Shepard} Method", journal = j-TOMS, volume = "25", number = "3", pages = "353--366", month = sep, year = "1999", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Apr 4 16:36:33 MDT 2000", URL = "http://doi.acm.org/10.1145/326147.326154", abstract = "A new implementation of the Modified Quadratic Shepard Method for the interpolation of scattered data is presented. QSHEP5D is a C++ translation of the original Fortran-77 program QSHEP3D developed by Renka (for 2-D and 3-D interpolation) which has been upgraded for 5-D interpolation. This software development was motivated by the need for interpolated 5-D hypervolumes of environmental response variables produced by forest growth and production models.", accepted = "3 jun 1999", acknowledgement = ack-nhfb, keywords = "C++ implementation, modified Shepard method, multivariate interpolation, netCDF file format", subject = "G.4 Mathematical Software - Algorithm design and analysis G.1.1 Numerical Analysis - Interpolation", subject = "Mathematics of Computing --- Mathematical Software (G.4): Algorithm design and analysis; Mathematics of Computing --- Numerical Analysis --- Interpolation (G.1.1); General Terms: Algorithms, Measurement, Performance", } @Article{Lecuyer:1999:BLC, author = "Pierre L'Ecuyer and Richard Simard", title = "Beware of Linear Congruential Generators with Multipliers of the Form $a = \pm 2^{q} \pm 2^r$", journal = j-TOMS, volume = "25", number = "3", pages = "367--374", month = sep, year = "1999", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Sep 19 09:42:41 MDT 2000", bibsource = "http://www.acm.org/pubs/toc/", URL = "http://doi.acm.org/10.1145/326147.326156", abstract = "Linear congruential random-number generators with Mersenne prime modulus and multipliers of the form $a = \pm 2^q \pm 2^r$ have been proposed recently. Their main advantage is the availability of a simple and fast implementation algorithm for such multipliers. This note generalizes this algorithm, points out statistical weaknesses of these multipliers when used in a straightforward manner, and suggests in what context they could be used safely.", accepted = "24 Aug 1999", acknowledgement = ack-nhfb, keywords = "correlation test; linear congruential generators; random number generation", subject = "Mathematics of Computing --- Mathematical Software (G.4): {\bf Algorithm design and analysis}; Computing Methodologies --- Simulation and Modeling (I.6); Mathematics of Computing --- Probability and Statistics (G.3): {\bf Random number generation}; General Terms: Algorithms, Experimentation, Measurement, Performance", } @Article{Kees:1999:CIN, author = "Christopher E. Kees and Cass T. Miller", title = "{C++} implementations of numerical methods for solving differential-algebraic equations: design and optimization considerations", journal = j-TOMS, volume = "25", number = "4", pages = "377--403", month = dec, year = "1999", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Sep 19 09:42:41 MDT 2000", bibsource = "http://www.acm.org/pubs/toc/", URL = "http://doi.acm.org/10.1145/332242.334001", abstract = "Object-oriented programming can produce improved implementations of complex numerical methods, but it can also introduce a performance penalty. Since computational simulation often requires intricate and highly efficient codes, the performance penalty of high-level techniques must always be weighed against the improvements they enable. These issues are addressed in a general object-oriented (OO) toolkit for the numerical solution of differential-algebraic equations (DAEs). The toolkit can be configured in several different ways to solve DAE initial-value problems with an adaptive multistep method. It contains a wrapped version of the Fortran 77 code DASPK and a translation of this to C++. Two C++ constructs for assembling the tools are provided, as are two implementations an important DAE test problem. Multiple configurations of the toolkit for DAE test problems are compared in order to assess the performance penalties of C++. The mathematical methods and implementation techniques are discussed in detail in order to provide heuristics for efficient OO scientific programming and to demonstrate the effectiveness of OO techniques in managing complexity and producing better code. The codes were tested on a variety of problems using publicly available Fortran 77 and C++ compilers. Extensive efficiency comparisons are presented in order to isolate computationally inefficient OO techniques. Techniques that caused difficulty in implementation and maintenance are also highlighted. The comparisons demonstrate that the majority of C++'s built-in support for OO programming has a negligible effect on performance, when used at sufficiently high levels, and provides flexible and extensible software for numerical methods.", acknowledgement = ack-nhfb, keywords = "Algorithms, design, experimentation, languages, performance, differential-algebraic equations", subject = "Software --- Programming Languages --- Language Classifications (D.3.2): {\bf C++}; Software --- Programming Languages --- Language Classifications (D.3.2): {\bf FORTRAN 77}; Mathematics of Computing --- Numerical Analysis --- Ordinary Differential Equations (G.1.7): {\bf Differential-algebraic equations}; Software --- Programming Techniques --- Object-oriented Programming (D.1.5); Software --- Software Engineering --- Coding Tools and Techniques (D.2.3): {\bf Object-oriented programming}", } @Article{Duff:1999:FCS, author = "Iain S. Duff and Jennifer A. Scott", title = "A frontal code for the solution of sparse positive-definite symmetric systems arising from finite-element applications", journal = j-TOMS, volume = "25", number = "4", pages = "404--424", month = dec, year = "1999", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Sep 19 09:42:41 MDT 2000", bibsource = "http://www.acm.org/pubs/toc/", URL = "http://doi.acm.org/10.1145/332242.332243", abstract = "We describe the design, implementation, and performance of a frontal code for the solution of large sparse symmetric systems of linear finite-element equations. The code is intended primarily for positive-definite systems, since numerical pivoting is not performed. The resulting software package, MA62, will be included in the Harwell Subroutine Library. We illustrate the performance of our new code on a range of problems arising from real engineering and industrial applications. The performance of the code is compared with that of the Harwell Subroutine Library general frontal solver MA42 and with other positive-definite codes from the Harwell Subroutine Library.", acknowledgement = ack-nhfb, keywords = "Algorithms; finite-element equations; Gaussian elimination; Level 3 BLAS; performance; sparse symmetric linear equations; symmetric frontal method", subject = "Mathematics of Computing --- Numerical Analysis --- General (G.1.0): {\bf Numerical algorithms}; Mathematics of Computing --- Numerical Analysis --- Numerical Linear Algebra (G.1.3); Mathematics of Computing --- Numerical Analysis --- Numerical Linear Algebra (G.1.3): {\bf Sparse, structured, and very large systems (direct and iterative methods)}", } @Article{Dackland:1999:BAS, author = "Krister Dackland and Bo K{\aa}gstr{\"{o}}m", title = "Blocked algorithms and software for reduction of a regular matrix pair to generalized {Schur} form", journal = j-TOMS, volume = "25", number = "4", pages = "425--454", month = dec, year = "1999", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Sep 19 09:42:41 MDT 2000", bibsource = "http://www.acm.org/pubs/toc/", URL = "http://doi.acm.org/10.1145/332242.332244", abstract = "A two-stage blocked algorithm for reduction of a regular matrix pair $(A,B)$ to upper Hessenberg-triangular form is presented. In stage 1 $(A,B)$ is reduced to block upper Hessenberg-triangular form using mainly level 3 (matrix-matrix) operations that permit data reuse in the higher levels of a memory hierarchy. In the second stage all but one of the $r$ subdiagonals of the block Hessenberg $A$-part are set to zero using Givens rotations. The algorithm proceeds in a sequence of supersweeps, each reducing $m$ columns. The updates with respect to row and column rotations are organized to reference consecutive columns of $A$ and $B$. To further improve the data locality, all rotations produced in a supersweep are stored to enable a left-looking reference pattern, i.e., all updates are delayed until they are required for the continuation of the supersweep. Moreover, we present a blocked variant of the single-diagonal double-shift QZ method for computing the generalized Schur form of $(A,B)$ in upper Hessenberg-triangular form. The blocking for improved data locality is done similarly, now by restructuring the reference pattern of the updates associated with the bulge chasing in the QZ iteration. Timing results show that our new blocked variants outperform the current LAPACK routines, including drivers for the generalized eigenvalue problem, by a factor 2--5 for sufficiently large problems.", acknowledgement = ack-nhfb, keywords = "algorithms; blocked algorithms; blocked algorithms; generalized Schur form; Hessenberg-triangular reduction; LAPACK; memory hierarchy; parallelization; performance; QZ-algorithm", subject = "Theory of Computation --- Analysis of Algorithms and Problem Complexity --- Numerical Algorithms and Problems (F.2.1); Mathematics of Computing --- Numerical Analysis --- Numerical Linear Algebra (G.1.3); Mathematics of Computing --- Mathematical Software (G.4): {\bf Certification and testing}; Mathematics of Computing --- Mathematical Software (G.4): {\bf Efficiency}; Mathematics of Computing --- Mathematical Software (G.4): {\bf Portability**}; Mathematics of Computing --- Mathematical Software (G.4): {\bf Reliability and robustness}", } @Article{Edwards:1999:CSC, author = "John A. Edwards", title = "Characteristic Spectra of the Curvature Functional: {A} Numerical Study in Bifurcation", journal = j-TOMS, volume = "25", number = "4", pages = "455--475", month = dec, year = "1999", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Sep 19 09:42:41 MDT 2000", bibsource = "http://www.acm.org/pubs/toc/", URL = "http://doi.acm.org/10.1145/332242.332245", abstract = "A method is described for the eigenvalues of piecewise smooth $C^2$ extremum-energy curves. Typical interpolants are investigated within the framework of their eigensystems, and conclusions are presented concerning their natural modes of vibration, stability state, and limits of existence. In the present discussion the word ``spline'' means exclusively an interpolating elastica.", acknowledgement = ack-nhfb, keywords = "acoustics; algorithms; buckling; catastrophes; degenerate critical points; deterministic chaos; deterministic chaos; dynamical systems; eigenanalysis; elastica; elasticity; energy extrema; generalized coordinates; modal analysis; Morse theory; structural stability; theory; variational methods; vibrations", subject = "Mathematics of Computing --- Numerical Analysis --- Interpolation (G.1.1): {\bf Spline and piecewise polynomial interpolation}; Mathematics of Computing --- Numerical Analysis --- Numerical Linear Algebra (G.1.3): {\bf Determinants**}; Mathematics of Computing --- Numerical Analysis --- Numerical Linear Algebra (G.1.3): {\bf Eigenvalues and eigenvectors (direct and iterative methods)}; Mathematics of Computing --- Numerical Analysis --- Optimization (G.1.6): {\bf Constrained optimization}; Mathematics of Computing --- Numerical Analysis --- Ordinary Differential Equations (G.1.7): {\bf Boundary value problems}; Computing Methodologies --- Symbolic and Algebraic Manipulation --- Algorithms (I.1.2): {\bf Algebraic algorithms}; Computer Applications --- Physical Sciences and Engineering (J.2): {\bf Engineering}; Computer Applications --- Physical Sciences and Engineering (J.2): {\bf Physics}; Computer Applications --- Computer-Aided Engineering (J.6): {\bf Computer-aided design (CAD)}; Computer Applications --- Computer-Aided Engineering (J.6): {\bf Computer-aided manufacturing (CAM)}", } @Article{Ferris:2000:NCS, author = "Michael C. Ferris and Michael P. Mesnier and Jorge J. Mor{\'e}", title = "{NEOS} and {Condor}: solving optimization problems over the {Internet}", journal = j-TOMS, volume = "26", number = "1", pages = "1--18", month = mar, year = "2000", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Sep 19 09:42:41 MDT 2000", bibsource = "http://www.acm.org/pubs/toc/", URL = "http://doi.acm.org/10.1145/347837.347842", abstract = "We discuss the use of Condor, a distributed resource management system, as a provider of computational resources for NEOS, an environment for solving optimization problems over the Internet. We also describe how problems are submitted and processed by NEOS, and then scheduled and solved by Condor on available (idle) workstations", acknowledgement = ack-nhfb, keywords = "automatic differentiation; complementarity problems; computational servers; network computing; resource management", subject = "Mathematics of Computing --- Mathematical Software (G.4); Computer Systems Organization --- Computer-Communication Networks --- General (C.2.0); Software --- Software Engineering --- General (D.2.0)", } @Article{Griewank:2000:ARI, author = "Andreas Griewank and Andrea Walther", title = "{Algorithm 799}: {Revolve}: an implementation of checkpointing for the reverse or adjoint mode of computational differentiation", journal = j-TOMS, volume = "26", number = "1", pages = "19--45", month = mar, year = "2000", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Sep 19 09:42:41 MDT 2000", bibsource = "http://www.acm.org/pubs/toc/", URL = "http://doi.acm.org/10.1145/347837.347846", abstract = "In its basic form, the reverse mode of computational differentiation yields the gradient of a scalar-valued function at a cost that is a small multiple of the computational work needed to evaluate the function itself. However, the corresponding memory requirement is proportional to the run-time of the evaluation program. Therefore, the practical applicability of the reverse mode in its original formulation is limited despite the availability of ever larger memory systems. This observation leads to the development of checkpointing schedules to reduce the storage requirements. This article presents the function {\tt revolve}, which generates checkpointing schedules that are provably optimal with regard to a primary and a secondary criterion. This routine is intended to be used as an explicit ``controller'' for running a time-dependent applications program.", acknowledgement = ack-nhfb, } @Article{deTisi:2000:RAS, author = "Flavia De Tisi and Alba Valtulina", title = "Remark on {Algorithm 761}: scattered-data surface fitting that has the accuracy of a cubic polynomial", journal = j-TOMS, volume = "26", number = "1", pages = "46--48", month = mar, year = "2000", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Sep 19 09:42:41 MDT 2000", bibsource = "http://www.acm.org/pubs/toc/", note = "See \cite{Akima:1996:ASS,Renka:1998:RA}.", URL = "http://doi.acm.org/10.1145/347837.349795", abstract = "Several improvements to the estimation of partial derivatives in Algorithm 761 are presented. The problems corrected are (1) in the calculation of the probability weight in subroutine {\tt SDPD3P} which may result in overflow, (2) in the calculation of final weight in subroutine {\tt SDPD3P} which may result in overflow, (3) in the computation of a determinant in subroutine {\tt SDLEQN} which is not necessary, and (4) in the computation of the condition number of a matrix in subroutine {\tt SDLEQN} which generates very different results for matrices that differ only in row order.", acknowledgement = ack-nhfb, keywords = "bivariate interpolation; interpolation; local interpolation", subject = "Software --- Programming Languages --- Language Classifications (D.3.2): {\bf FORTRAN 77}; Mathematics of Computing --- Numerical Analysis --- Interpolation (G.1.1): {\bf Interpolation formulas}; Mathematics of Computing --- Mathematical Software (G.4)", } @Article{Benner:2000:AFS, author = "Peter Benner and Ralph Byers and Eric Barth", title = "{Algorithm 800}: {Fortran 77} subroutines for computing the eigenvalues of {Hamiltonian} matrices {I}: the square-reduced method", journal = j-TOMS, volume = "26", number = "1", pages = "49--77", month = mar, year = "2000", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Sep 19 09:42:41 MDT 2000", bibsource = "http://www.acm.org/pubs/toc/", URL = "http://doi.acm.org/10.1145/347837.347852", abstract = "This article describes LAPACK-based Fortran 77 subroutines for the reduction of a Hamiltonian matrix to square-reduced form and the approximation of all its eigenvalues using the implicit version of Van Loan's method. The transformation of the Hamiltonian matrix to a square-reduced form transforms a Hamiltonian eigenvalue problem of order $2n$ to a Hessenberg eigenvalue problem of order $n$. The eigenvalues of the Hamiltonian matrix are the square roots of those of the Hessenberg matrix. Symplectic scaling and norm scaling are provided, which, in some cases, improve the accuracy of the computed eigenvalues. We demonstrate the performance of the subroutines for several examples and show how they can be used to solve some control-theoretic problems.", acknowledgement = ack-nhfb, keywords = "algebraic Riccati equation; eigenvalues; Hamiltonian matrix; skew-Hamiltonian matrix; (square-reduced)", subject = "Software --- Programming Languages --- Language Classifications (D.3.2): {\bf FORTRAN 77}; Theory of Computation --- Analysis of Algorithms and Problem Complexity --- Numerical Algorithms and Problems (F.2.1): {\bf Computations on matrices}; Mathematics of Computing --- Numerical Analysis --- Numerical Linear Algebra (G.1.3): {\bf Eigenvalues and eigenvectors (direct and iterative methods)}; Mathematics of Computing --- Mathematical Software (G.4): {\bf Algorithm design and analysis}; Mathematics of Computing --- Mathematical Software (G.4): {\bf Certification and testing}; Mathematics of Computing --- Mathematical Software (G.4): {\bf Documentation}; Mathematics of Computing --- Mathematical Software (G.4): {\bf Efficiency}; Mathematics of Computing --- Mathematical Software (G.4): {\bf Reliability and robustness}", } @Article{Leydold:2000:ASR, author = "Josef Leydold", title = "Automatic Sampling with the Ratio-of-Uniforms Method", journal = j-TOMS, volume = "26", number = "1", pages = "78--98", month = mar, year = "2000", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Sep 19 09:42:41 MDT 2000", bibsource = "http://www.acm.org/pubs/toc/", URL = "http://doi.acm.org/10.1145/347837.347863", abstract = "Applying the ratio-of-uniforms method for generating random variates results in very efficient, fast, and easy-to-implement algorithms. However parameters for every particular type of density must be precalculated analytically. In this article we show, that the ratio-of-uniforms method is also useful for the design of a black-box algorithm suitable for a large class of distributions, including all with log-concave densities. Using polygonal envelopes and squeezes results in an algorithm that is extremely fast. In opposition to any other ratio-of-uniforms algorithm the expected number of uniform random numbers is less than two. Furthermore, we show that this method is in some sense equivalent to transformed density rejection.", acknowledgement = ack-nhfb, keywords = "adaptive method; log-concave; nonuniform; random-number generation; ratio of uniforms; rejection method; T-concave; universal method", subject = "Mathematics of Computing --- Probability and Statistics (G.3): {\bf Random number generation}", } @Article{Hu:2000:HHP, author = "Y. Charlie Hu and Guohua Jin and S. Lennart Johnsson and Dimitris Kehagias and Nadia Shalaby", title = "{HPFBench}: a {High Performance Fortran} benchmark suite", journal = j-TOMS, volume = "26", number = "1", pages = "99--149", month = mar, year = "2000", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Sep 19 09:42:41 MDT 2000", bibsource = "http://www.acm.org/pubs/toc/", URL = "http://doi.acm.org/10.1145/347837.347872", abstract = "The High Performance Fortran (HPF) benchmark suite HPFBench is designed for evaluating the HPF language and compilers on scalable architectures. The functionality of the benchmarks covers scientific software library functions and application kernels that reflect the computational structure and communication patterns in fluid dynamic simulations, fundamental physics, and molecular studies in chemistry and biology. The benchmarks are characterized in terms of FLOP count, memory usage, communication pattern, local memory accesses, array allocation mechanism, as well as operation and communication counts per iteration. The benchmarks output performance evaluation metrics in the form of elapsed times, FLOP rates, and communication time breakdowns. We also provide a benchmark guide to aid the choice of subsets of the benchmarks for evaluating particular aspects of an HPF compiler. Furthermore, we report an evaluation of an industry-leading HPF compiler from the Portland Group Inc. using the HPFBench benchmarks on the distributed-memory IBM SP2", acknowledgement = ack-nhfb, keywords = "benchmarks; compilers; high performance Fortran", subject = "Software --- Programming Languages --- Language Classifications (D.3.2): {\bf Concurrent, distributed, and parallel languages}; Mathematics of Computing --- Numerical Analysis --- Numerical Linear Algebra (G.1.3): {\bf Linear systems (direct and iterative methods)}; Mathematics of Computing --- Mathematical Software (G.4): {\bf Efficiency}; Mathematics of Computing --- Mathematical Software (G.4): {\bf Parallel and vector implementations}; Computing Methodologies --- Simulation and Modeling --- Applications (I.6.3); Computer Applications --- Physical Sciences and Engineering (J.2): {\bf Astronomy}; Computer Applications --- Physical Sciences and Engineering (J.2): {\bf Chemistry}; Computer Applications --- Life and Medical Sciences (J.3): {\bf Biology and genetics}", } @Article{Coleman:2000:AAD, author = "Thomas F. Coleman and Arun Verma", title = "{ADMIT-1}: Automatic Differentiation and {MATLAB} Interface Toolbox", journal = j-TOMS, volume = "26", number = "1", pages = "150--175", month = mar, year = "2000", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Sep 19 09:42:41 MDT 2000", bibsource = "http://www.acm.org/pubs/toc/", URL = "http://doi.acm.org/10.1145/347837.347879", abstract = "ADMIT-1 enables the computation of {\em sparse} Jacobian and Hessian matrices, using automatic differentiation technology, from a MATLAB environment. Given a function to be differentiated, ADMIT-1 will exploit sparsity if present to yield sparse derivative matrices (in sparse MATLAB form). A generic automatic differentiation tool, subject to some functionality requirements, can be plugged into ADMIT-1; examples include ADOL-C (C/C++ target functions) and ADMAT (MATLAB target functions). ADMIT-1 also allows for the calculation of gradients and has several other related functions. This article provides an introduction to the design and usage of ADMIT-1.", acknowledgement = ack-nhfb, keywords = "automatic differentiation; computational differentiation; efficient computation of gradient; graph coloring; Jacobians and Hessians; user interface", subject = "Mathematics of Computing --- Numerical Analysis --- General (G.1.0): {\bf Numerical algorithms}; Mathematics of Computing --- Numerical Analysis --- Roots of Nonlinear Equations (G.1.5): {\bf Systems of equations}; Mathematics of Computing --- Numerical Analysis --- Optimization (G.1.6): {\bf Unconstrained optimization}; Mathematics of Computing --- Mathematical Software (G.4): {\bf MATLAB}", } @Article{Wise:2000:APP, author = "Steven M. Wise and Andrew J. Sommese and Layne T. Watson", title = "{Algorithm 801}: {POLSYS\_PLP}: a partitioned linear product homotopy code for solving polynomial systems of equations", journal = j-TOMS, volume = "26", number = "1", pages = "176--200", month = mar, year = "2000", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Sep 19 09:42:41 MDT 2000", bibsource = "http://www.acm.org/pubs/toc/", URL = "http://doi.acm.org/10.1145/347837.347885", abstract = "Globally convergent, probability-one homotopy methods have proven to be very effective for finding all the isolated solutions to polynomial systems of equations. After many years of development, homotopy path trackers based on probability-one homotopy methods are reliable and fast. Now, theoretical advances reducing the number of homotopy paths that must be tracked, and in the handling of singular solutions, have made probability-one homotopy methods even more practical. POLSYS\_PLP consists of Fortran 90 modules for finding all isolated solutions of a complex coefficient polynomial system of equations. The package is intended to be used in conjunction with HOMPACK90 (Algorithm 777), and makes extensive use of Fortran 90 derived data types to support a partitioned linear product (PLP) polynomial system structure. PLP structure is a generalization of $m$-homogeneous structure, whereby each component of the system can have a different $m$-homogeneous structure. The code requires a PLP structure as input, and although finding the optimal PLP structure is a difficult combinatorial problem, generally physical or engineering intuition about a problem yields a very good structure. POLSYS\_PLP employs a sophisticated power series end game for handling singular solutions, and provides support for problem definition both at a high level and via hand-crafted code. Different PLP structures and their corresponding Bezout numbers can be systematically explored before committing to root finding.", acknowledgement = ack-nhfb, keywords = "Chow-Yorke algorithm; curve tracking; fixed point; globally convergent; homotopy methods; $m$-homogeneous; partitioned linear product; probability-one; zero", subject = "Software --- Programming Languages --- Language Classifications (D.3.2): {\bf Fortran 90}; Mathematics of Computing --- Numerical Analysis --- Roots of Nonlinear Equations (G.1.5): {\bf Continuation (homotopy) methods}; Mathematics of Computing --- Numerical Analysis --- Roots of Nonlinear Equations (G.1.5): {\bf Polynomials, methods for}; Mathematics of Computing --- Numerical Analysis --- Roots of Nonlinear Equations (G.1.5): {\bf Systems of equations}; Mathematics of Computing --- Mathematical Software (G.4)", } @Article{Hormann:2000:AAG, author = "Wolfgang H{\"o}rmann", title = "{Algorithm 802}: an automatic generator for bivariate log-concave distributions", journal = j-TOMS, volume = "26", number = "1", pages = "201--219", month = mar, year = "2000", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Tue Sep 19 09:42:41 MDT 2000", bibsource = "http://www.acm.org/pubs/toc/", URL = "http://doi.acm.org/10.1145/347837.347908", abstract = "Different automatic (also called universal or black-box) methods have been suggested to sample from univariate log-concave distributions. Our new automatic algorithm for bivariate log-concave distributions is based on the method of transformed density rejection. In order to construct a hat function for a rejection algorithm the bivariate density is transformed by the logarithm into a concave function. Then it is possible to construct a dominating function by taking the minimum of several tangent planes, which are by exponentiation transformed back into the original scale. The choice of the points of contact is automated using adaptive rejection sampling. This means that points that are rejected by the rejection algorithm can be used as additional points of contact. The article describes the details how this main idea can be used to construct Algorithm ALC2D that can generate random pairs from all bivariate log-concave distributions with known domain, computable density, and computable partial derivatives.", acknowledgement = ack-nhfb, keywords = "automatic generator; bivariate log-concave distributions; rejection method; universal generator", subject = "Software --- Programming Languages --- Language Classifications (D.3.2); Mathematics of Computing --- Probability and Statistics (G.3): {\bf Random number generation}", } @Article{Boisvert:2000:ESI, author = "Ronald F. Boisvert and Wayne R. Dyksen and Elias N. Houstis", title = "Editorial: special issue in honor of {John Rice}'s 65th birthday", journal = j-TOMS, volume = "26", number = "2", pages = "223--223", month = jun, year = "2000", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Wed Feb 6 16:43:41 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/353474.354094", acknowledgement = ack-nhfb, for = "Special issue dedicated to John Rice on his 65th birthday.", } @Article{Anonymous:2000:JRR, author = "Anonymous", title = "{John R. Rice}: biographical and professional notes", journal = j-TOMS, volume = "26", number = "2", pages = "225--226", month = jun, year = "2000", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Wed Feb 6 16:43:41 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/353474.354105", acknowledgement = ack-nhfb, } @Article{Houstis:2000:PIK, author = "Elias N. Houstis and Ann C. Catlin and John R. Rice and Vassilios S. Verykios and Naren Ramakrishnan and Catherine E. Houstis", title = "{PYTHIA-II}: a knowledge\slash database system for managing performance data and recommending scientific software", journal = j-TOMS, volume = "26", number = "2", pages = "227--253", month = jun, year = "2000", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Wed Feb 6 16:43:41 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/353474.353475", abstract = "Often scientists need to locate appropriate software for their problems and then select from among many alternatives. We have previously proposed an approach for dealing with this task by processing performance data of the targeted software. This approach has been tested using a customized implementation referred to as PYTHIA. This experience made us realize the complexity of the algorithmic discovery of knowledge from performance data and of the management of these data together with the discovered knowledge. To address this issue, we created PYTHIA-II--a modular framework and system which combines a general knowledge discovery in databases (KDD) methodology and recommender system technologies to provide advice about scientific software/hardware artifacts. The functionality and effectiveness of the system is demonstrated for two existing performance studies using sets of software for solving partial differential equations. From the end-user perspective, PYTHIA-II allows users to specify the problem to be solved and their computational objectives. In turn, PYTHIA-II (i) selects the software available for the user's problem (ii) suggests parameter values, and (iii) assesses the recommendation provided. PYTHIA-II provides all the necessary facilities to set up database schemas for testing suites and associated performance data in order to test sets of software. Moreover, it allows easy interfacing of alternative data mining and recommendation facilities. PYTHIA-II is an open-ended system implemented on public domain software and has been used for performance evaluation in several different problem domains.", acknowledgement = ack-nhfb, for = "Special issue dedicated to John Rice on his 65th birthday.", } @Article{Ramakrishnan:2000:MVR, author = "Naren Ramakrishnan and Calvin J. Ribbens", title = "Mining and visualizing recommendation spaces for elliptic {PDEs} with continuous attributes", journal = j-TOMS, volume = "26", number = "2", pages = "254--273", month = jun, year = "2000", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Wed Feb 6 16:43:41 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/353474.353481", abstract = "In this paper we extend previous work in mining recommendation spaces based on symbolic problem features to PDE problems with continuous-valued attributes. We identify the research issues in mining such spaces, present a dynamic programming algorithm form the data-mining literature, and describe how a priori domain metaknowledge can be used to control the complexity of induction. A visualization aid for continuous-valued recommendation spaces is also outlined. Two case studies are presented to illustrate our approach and tools: (i) a comparison of an iterative and a direct linear system solver on nearly singular problems, and (ii) a comparison of two iterative solvers on problems posed on nonrectangular domains. Both case studies involve continuously varying problem and method parameters which strongly influence the choice of best algorithm in particular cases. By mining the results from thousands of PDE solves, we can gain valuable insight into the relative performance of these methods on similar problems.", acknowledgement = ack-nhfb, for = "Special issue dedicated to John Rice on his 65th birthday.", } @Article{Enright:2000:AAS, author = "W. H. Enright", title = "Accurate Approximate Solution of Partial Differential Equations at Off-mesh Points", journal = j-TOMS, volume = "26", number = "2", pages = "274--292", month = jun, year = "2000", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Wed Feb 6 16:43:41 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/353474.353482", abstract = "Numerical methods for partial differential equations often determine approximations that are more accurate at the set of discrete meshpoints than they are at the ``off-mesh'' points in the domain of interest. These methods are generally most effective if they are allowed to adjust the location of the mesh points to match the local behavior of the solution. Different methods will typically generate their respective approximations on incompatible, unstructured meshes, and it can be difficult to evaluate the quality of a particular solution, or to visualize important properties of a solution. In this paper we will introduce a generic approach which can be used to generate approximate solution values at arbitrary points in the domain of interest for any method that determines approximations to the solution and low-order derivatives at meshpoints. This approach is based on associating a set of ``collocation'' points with each mesh element and requiring that the local approximation interpolate the meshpoint data and almost satisfy the partial differential equation at the collocation points. The accuracy associated with this interpolation/collocation approach is consistent with the ``meshpoint accuracy'' of the underlying method. The approach that we develop applies to a large class of methods and problems. It uses local information only and is therefore particularly suitable for implementation in a parallel or network computing environment. Numerical examples are given for some second-order problems in two and three dimensions.", acknowledgement = ack-nhfb, for = "Special issue dedicated to John Rice on his 65th birthday.", } @Article{Grosz:2000:HVA, author = "Lutz Grosz", title = "How to Vectorize the Algebraic Multi-level Iteration", journal = j-TOMS, volume = "26", number = "2", pages = "293--309", month = jun, year = "2000", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Wed Feb 6 16:43:41 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/353474.353483", abstract = "We consider the algebraic multilevel iteration (AMLI) for the solution of systems of linear equations as they arise form a finite-difference discretization on a rectangular grid. Key operation is the matrix-vector product, which can efficiently be executed on vector and parallel-vector computer architectures if the nonzero entries of the matrix are concentrated in a few diagonals. In order to maintain this structure for all matrices on all levels coarsening in alternating directions is used. In some cases it is necessary to introduce additional dummy grid hyperplanes. The data movements in the restriction and prolongation are crucial, as they produce massive memory conflicts on vector architectures. By using a simple performance model the best of the possible vectorization strategies is automatically selected at runtime. Examples show that on a Fujitsu VPP300 the presented implementation of AMLI reaches about 85\% of the useful performance, and scalability with respect to computing time can be achieved.", acknowledgement = ack-nhfb, for = "Special issue dedicated to John Rice on his 65th birthday.", } @Article{Ward:2000:ASM, author = "William A. {Ward, Jr.}", title = "{Algorithm 803}: {A} Simpler Macro Processor", journal = j-TOMS, volume = "26", number = "2", pages = "310--319", month = jun, year = "2000", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Wed Feb 6 16:43:41 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/353474.353484", abstract = "Macro processors have been in the computing tool chest since the late 1950's. Their use, though perhaps not what it was in the heyday of assembly language programming, is still widespread. In the past, producing a full-featured macro processor has required significant effort, similar to that required to implement the front-end to a compiler augmented by appropriate text substitution capabilities. The tool described here adopts a different approach. The text containing macro definitions and substitutions is, in a sense, ``compiled'' to produce a program, and this program must then be executed to produce the final output.", acknowledgement = ack-nhfb, for = "Special issue dedicated to John Rice on his 65th birthday.", } @Article{Enright:2000:SIC, author = "Wayne H. Enright and Ramanan Sivasothinathan", title = "Superconvergent interpolants for collocation methods applied to mixed-order {BVODEs}", journal = j-TOMS, volume = "26", number = "3", pages = "323--351", month = sep, year = "2000", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/358407.358410", accepted = "24 Nov 1999", acknowledgement = ack-nhfb, } @Article{Liepelt:2000:RAN, author = "Michael Liepelt and Klaus Schittkowski", title = "Remark on Algorithm 746: new features of {PCOMP}: {A} {Fortran} Code for Automatic Differentiation", journal = j-TOMS, volume = "26", number = "3", pages = "352--362", month = sep, year = "2000", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/358407.358412", abstract = "The software system PCOMP uses automatic differentiation to calculate derivatives of functions that are defined by the user in a modeling language similar to Fortran. This symbolical representation is converted into an intermediate code, which can be interpreted to calculate function and derivative values at run-time within machine accuracy. Furthermore, it is possible to generate Fortran code for function and gradient evaluation, which has to be compiled and linked separately. The first version of PCOMP was introduced in Dobmann et al. [1995]. In this article, we describe a series of extensions and additional features that have been implemented in the meantime.", accepted = "20 dec 1999", acknowledgement = ack-nhfb, } @Article{Marsaglia:2000:SMG, author = "George Marsaglia and Wai Wan Tsang", title = "A Simple Method for Generating Gamma Variables", journal = j-TOMS, volume = "26", number = "3", pages = "363--372", month = sep, year = "2000", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/358407.358414", accepted = "14 Jan 2000", acknowledgement = ack-nhfb, } @Article{Kearfott:2000:SCV, author = "R. B. Kearfott and G. W. Walster", title = "On Stopping Criteria in Verified Nonlinear Systems or Optimization Algorithms", journal = j-TOMS, volume = "26", number = "3", pages = "373--389", month = sep, year = "2000", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/358407.358418", abstract = "Traditionally, iterative methods for nonlinear systems use heuristic domain and range stopping criteria to determine when accuracy tolerances have been met. However, such heuristics can cause stopping at points far from actual solutions, and can be unreliable due to the effects of roundoff error or inaccuracies in data.\par In verified computations, rigorous determination of when a set of bounds has met a tolerance can be done analogously to the traditional approximate setting. Nonetheless, the range tolerance possibly cannot be met. If the criteria are used to determine when to stop subdivision of $n$-dimensional bounds into subregions, then failure of a range tolerance results in excessive, unnecessary subdivision, and could make the algorithm impractical.\par On the other hand, interval techniques can detect when inaccuracies or roundoff will not permit residual bounds to be narrowed. These techniques can be incorporated into {\it range thickness\/} stopping criteria that complement the range stopping criteria. In this note, the issue is first introduced and illustrated with a simple example. The thickness stopping criterion is then formally introduced and analyzed. Third, inclusion of the criterion within a general verified global optimization algorithm is studied. An industrial example is presented. Finally, consequences and implications are discussed.", accepted = "21 Mar 2000", acknowledgement = ack-nhfb, } @Article{Alhargan:2000:ACA, author = "Fayez A. Alhargan", title = "Algorithms for the Computation of all {Mathieu} Functions of Integer Orders", journal = j-TOMS, volume = "26", number = "3", pages = "390--407", month = sep, year = "2000", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/358407.358420", abstract = "The paper presents methods for the computation of all Mathieu functions of integer order, which cover a large range of $n$ and $h$; previous algorithms were limited to small values of $n$. The algorithms are given in sufficient details to enable straightforward implementation. The algorithms can handle a large range of the order $n$ (0-200) and the parameter $h$ (0-4$n$).", accepted = "19 May 2000", acknowledgement = ack-nhfb, } @Article{Alhargan:2000:ASC, author = "Fayez A. Alhargan", title = "{Algorithm 804}: subroutines for the computation of {Mathieu} functions of integer orders", journal = j-TOMS, volume = "26", number = "3", pages = "408--414", month = sep, year = "2000", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/358407.358422", abstract = "Computer subroutines in C++ for computing Mathieu functions of integer orders are described. The core routines for computing Mathieu characteristic numbers and Mathieu coefficients are described in details, the rest of the subroutines are standard implementation of the series summations for each function. The routines can handle a large range of the order $n$ and the parameter $h$.", accepted = "19 May 2000", acknowledgement = ack-nhfb, } @Article{Kolda:2000:ACU, author = "Tamara G. Kolda and Dianne P. O'Leary", title = "{Algorithm 805}: computation and uses of the semidiscrete matrix decomposition", journal = j-TOMS, volume = "26", number = "3", pages = "415--435", month = sep, year = "2000", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/358407.358424", abstract = "We derive algorithms for computing a semidiscrete approximation to a matrix in the Frobenius and weighted norms. The approximation is formed as a weighted sum of outer products of vectors whose elements are $\pm 1$ or 0, so the storage required by the approximation is quite small. We also present a related algorithm for approximation of a tensor. Applications of the algorithms are presented to data compression, and information retrieval; and software is provided in C and in Matlab.", accepted = "18 May 2000", acknowledgement = ack-nhfb, } @Article{Mascagni:2000:ASS, author = "Michael Mascagni and Ashok Srinivasan", title = "{Algorithm 806}: {SPRNG}: a scalable library for pseudorandom number generation", journal = j-TOMS, volume = "26", number = "3", pages = "436--461", month = sep, year = "2000", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", note = "See correction \cite{Mascagni:2000:CAS}.", URL = "http://doi.acm.org/10.1145/358407.358427", abstract = "In this article we present background, rationale, and a description of the Scalable Parallel Random Number Generators (SPRNG) library. We begin by briefly presenting some methods for parallel pseudorandom number generation. We will focus on methods based on parameterization, meaning that we will not consider splitting methods. We describe parameterized versions of the following pseudorandom number generators: (i) linear congruential generators, (ii) shift-register generators, and (iii) lagged-Fibonacci generators. We briefly describe the methods, detail some advantages and disadvantages of each method and recount results from number theory that impact our understanding of their quality in parallel applications. SPRNG was designed around the uniform implementation of different families of parameterized random number generators. We then present a short description of SPRNG. The description contained within this document is meant only to outline the rationale behind and the capabilities of SPRNG. Much more information, including examples and detailed documentation aimed at helping users with installing and using SPRNG on scalable systems is available at the url http://www.ncsa.uiuc.edu/Apps/SPRNG. In our description of SPRNG we discuss the random number library as well as the suite of tests of randomness that is an integral part of SPRNG. Random number tools for parallel Monte Carlo applications must be subjected to classical as well as new types of empirical tests of randomness to eliminate generators that show defects when used in scalable environments.", accepted = "26 may 2000", acknowledgement = ack-nhfb, } @Article{Weideman:2000:MDM, author = "J. A. C. Weideman and S. C. Reddy", title = "A {MATLAB} Differentiation Matrix Suite", journal = j-TOMS, volume = "26", number = "4", pages = "465--519", month = dec, year = "2000", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/365723.365727", abstract = "A software suite consisting of 17 MATLAB functions for solving differential equations by the spectral collocation (i.e., pseudospectral) method is presented. It includes functions for computing derivatives of arbitrary order corresponding to Chebyshev, Hermite, Laguerre, Fourier, and sinc interpolants. Auxiliary functions are included for incorporating boundary conditions, performing interpolation using barycentric formulas, and computing roots of orthogonal polynomials. It is demonstrated how to use the package for solving eigenvalue, boundary value, and initial value problems arising in the fields of special functions, quantum mechanics, nonlinear waves, and hydrodynamic stability.", accepted = "15 March 2000", acknowledgement = ack-nhfb, } @Article{Kaufman:2000:OBS, author = "Linda Kaufman", title = "An Observation on Bisection Software for the Symmetric Tridiagonal Eigenvalue Problem", journal = j-TOMS, volume = "26", number = "4", pages = "520--526", month = dec, year = "2000", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/365723.365728", abstract = "In this paper we discuss a small modification of the bisection routines in EISPACK and LAPACK for finding a few of the eigenvalues of a symmetric tridiagonal matrix A. When the principal minors of the matrix A yield good approximations to the desired eigenvalues, these modifications can yield about 30 percent reduction in the computation times.", accepted = "27 June 2000", acknowledgement = ack-nhfb, } @Article{Filippone:2000:PLP, author = "Salvatore Filippone and Michele Colajanni", title = "{PSBLAS}: {A} Library for Parallel Linear Algebra Computation on Sparse Matrices", journal = j-TOMS, volume = "26", number = "4", pages = "527--550", month = dec, year = "2000", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/365723.365732", abstract = "Many computationally intensive problems in engineering and science give rise to the solution of large, sparse, linear systems of equations. Fast and efficient methods for their solution are very important because these systems usually occur in the innermost loop of the computational scheme. Parallelization is often necessary to achieve an acceptable level of performance. This paper presents the design, implementation, and interface of a library of Basic Linear Algebra Subroutines for sparse matrices (PSBLAS) which is specifically tailored to distributed memory computers. PSBLAS enables easy, efficient and portable implementations of parallel iterative solvers for linear systems. The interface keeps in view a Single Program Multiple Data programming model on distributed memory machines. However, the architecture of the library does not exclude an implementation in different paradigms, such as those based on the shared memory model.", accepted = "5 July 2000", acknowledgement = ack-nhfb, } @Article{Kaufman:2000:BRA, author = "Linda Kaufman", title = "Band Reduction Algorithms Revisited", journal = j-TOMS, volume = "26", number = "4", pages = "551--567", month = dec, year = "2000", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/365723.365733", abstract = "In this paper we explain some of the changes that have been incorporated in the latest version of the LAPACK subroutine for reducing a symmetric banded matrix to tridiagonal form. These modifications improve the performance for larger-bandwidth problems and reduce the number of operations when accumulating the transformations onto the identity matrix, by taking advantage of the structure of the initial matrix. We show that similar modifications can be made to the LAPACK subroutines for reducing a symmetric positive definite generalized eigenvalue problem to a standard symmetric banded eigenvalue problem and for reducing a general banded matrix to bidiagonal form to facilitate the computation of the singular values of the matrix.", accepted = "3 Aug 2000", acknowledgement = ack-nhfb, } @Article{Ramakrishnan:2000:NGE, author = "Naren Ramakrishnan and Ra{\'u}l E. Vald{\'e}s-P{\'e}rez", title = "Note on Generalization in Experimental Algorithmics", journal = j-TOMS, volume = "26", number = "4", pages = "568--580", month = dec, year = "2000", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/365723.365734", abstract = "A recurring theme in mathematical software evaluation is the generalization of rankings of algorithms on test problems to build knowledge-based recommender systems for algorithm selection. A key issue is to {\em profile} algorithms in terms of the qualitative characteristics of benchmark problems. In this methodological note, we adapt a novel all-pairs algorithm for the profiling task --- Given performance rankings for $m$ algorithms on $n$ problem instances, each described with $p$ features, identify a (minimal) subset of $p$ that is useful for assessing the selective superiority of an algorithm over another, for all pairs of the $m$ algorithms. We show how techniques presented in the mathematical software literature are inadequate for such profiling purposes. In conclusion, we also address various statistical issues underlying the effective application of this technique.", accepted = "3 Aug 2000", acknowledgement = ack-nhfb, } @Article{Bischof:2000:FSB, author = "Christian H. Bischof and Bruno Lang and Xiaobai Sun", title = "A Framework for Symmetric Band Reduction", journal = j-TOMS, volume = "26", number = "4", pages = "581--601", month = dec, year = "2000", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/365723.365735", abstract = "We develop an algorithmic framework for reducing the bandwidth of symmetric matrices via orthogonal similarity transformations. This framework includes the reduction of full matrices to banded or tridiagonal form and the reduction of banded matrices to narrower banded or tridiagonal form, possibly in multiple steps. Our framework leads to algorithms that require fewer floating-point operations than do standard algorithms, if only the eigenvalues are required. In addition, it allows for space--time tradeoffs and enables or increases the use of blocked transformations.", accepted = "29 May 2000", acknowledgement = ack-nhfb, } @Article{Bischof:2000:AST, author = "Christian H. Bischof and Bruno Lang and Xiaobai Sun", title = "{Algorithm 807}: {The SBR Toolbox}---software for successive band reduction", journal = j-TOMS, volume = "26", number = "4", pages = "602--616", month = dec, year = "2000", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/365723.365736", abstract = "We present a software toolbox for symmetric band reduction via orthogonal transformations, together with a testing and timing program. The toolbox contains drivers and computational routines for the reduction of full symmetric matrices to banded form and the reduction of banded matrices to narrower banded or tridiagonal form, with optional accumulation of the orthogonal transformations, as well as repacking routines for storage rearrangement. The functionality and the calling sequences of the routines are described, with a detailed discussion of the ``control'' parameters that allow adaptation of the codes to particular machine and matrix characteristics. We also briefly describe the testing and timing program included in the toolbox.", accepted = "29 May 2000", acknowledgement = ack-nhfb, } @Article{Anderson:2000:RAF, author = "Stuart Anderson", title = "Remark on {Algorithm 723}: {Fresnel} integrals", journal = j-TOMS, volume = "26", number = "4", pages = "617--617", month = dec, year = "2000", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/365723.365737", accepted = "16 October 2000", acknowledgement = ack-nhfb, } @Article{Mascagni:2000:CAS, author = "Michael Mascagni and Ashok Srinivasan", title = "Corrigendum: {Algorithm 806}: {SPRNG}: a scalable library for pseudorandom number generation", journal = j-TOMS, volume = "26", number = "4", pages = "618--619", month = dec, year = "2000", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", note = "See \cite{Mascagni:2000:ASS}.", URL = "http://doi.acm.org/10.1145/365723.365738", abstract = "In this article we present background, rationale, and a description of the Scalable Parallel Random Number Generators (SPRNG) library. We begin by presenting some methods for parallel pseudorandom number generation. We will focus on methods based on parameterization, meaning that we will not consider splitting methods such as the leap-frog or blocking methods. We describe, in detail, parameterized versions of the following pseudorandom number generators: (i) linear congruential generators, (ii) shift-register generators, and (iii) lagged-Fibonacci generators. We briefly describe the methods, detail some advantages and disadvantages of each method, and recount results from number theory that impact our understanding of their quality of parallel applications. SPRNG was designed around the uniform implementation of different families of parameterized random number generators. We then present a short description of SPRNG. The description contained within this document is meant only to outline the rationale behind and the capabilities of SPRNG. Much more information, including examples and detailed documentation aimed at helping users with putting and using SPRNG on scalable systems is available at http://sprng.cs.fsu.edu. In this description of SPRNG we discuss the random-number generator library as well as the suite of tests of randomness that is an integral part of SPRNG. Random-number tools for parallel Monte Carlo applications must be subjected to classical as well as new types of empirical tests of randomness to eliminate generators that show defects when used in scalable environments.", acknowledgement = ack-nhfb, keywords = "Algorithms; Design; Documentation; Experimentation; Performance; Reliability; Standardization; lagged-Fibonacci generator; linear congruential generator; parallel random-number generators; random-number software; random-number tests", subject = "Primary Classification: D. Software D.3 PROGRAMMING LANGUAGES Additional Classification: D. Software D.3 PROGRAMMING LANGUAGES D.3.2 Language Classifications Nouns: FORTRAN; C++ G. Mathematics of Computing G.4 MATHEMATICAL SOFTWARE Subjects: Efficiency; Documentation; Parallel and vector implementations; Algorithm design and analysis; Reliability and robustness", } @Article{Langtangen:2001:SSP, author = "Hans Petter Langtangen and Otto Munthe", title = "Solving Systems of Partial Differential Equations using Object-Oriented Programming Techniques with Coupled Heat and Fluid Flow as Example", journal = j-TOMS, volume = "27", number = "1", pages = "1--26", month = mar, year = "2001", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/382043.382045", abstract = "This paper exploits object-oriented implementation techniques to facilitate the development of computer codes for solving systems of coupled partial differential equations. We show how to build a simulator for equation systems by merging independent solvers for each equation that enters the system. The main goal is to obtain a rapid, robust, and reliable software development process with extensive reuse of implemented code. Coupled heat and fluid flow in pipes is used as example for illustrating the implementation techniques. We also present some results for the particular case of temperature-dependent generalized Newtonian fluid flow between two nonconcentric cylinders. The general applicability of the approach is discussed.", accepted = "5 July 2000", acknowledgement = ack-nhfb, keywords = "Languages, Measurement, Performance, Theory; C++; coupled heat-fluid; diffpack; finite elements; non-Newtonian fluids; object-oriented programming; software development; systems of partial differential equations", subject = "Primary Classification: G. Mathematics of Computing G.1 NUMERICAL ANALYSIS G.1.8 Partial Differential Equations Subjects: Finite element methods Additional Classification: D. Software D.1 PROGRAMMING TECHNIQUES D.3 PROGRAMMING LANGUAGES D.3.2 Language Classifications Nouns: C++ I. Computing Methodologies I.6 SIMULATION AND MODELING K. Computing Milieux K.6 MANAGEMENT OF COMPUTING AND INFORMATION SYSTEMS K.6.3 Software Management Subjects: Software development", } @Article{Neumaier:2001:EPE, author = "Arnold Neumaier and Tapio Schneider", title = "Estimation of Parameters and Eigenmodes of Multivariate Autoregressive Models", journal = j-TOMS, volume = "27", number = "1", pages = "27--57", month = mar, year = "2001", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/382043.382304", abstract = "Dynamical characteristics of a complex system can often be inferred from analyses of a stochastic time series model fitted to observations of the system. Oscillations in geophysical systems, for example, are sometimes characterized by principal oscillation patterns, eigenmodes of estimated autoregressive (AR) models of first order. This paper describes the estimation of eigenmodes of AR models of arbitrary order. AR processes of any order can be decomposed into eigenmodes with characteristic oscillation periods, damping times, and excitations. Estimated eigenmodes and confidence intervals for the eigenmodes and their oscillation periods and damping times can be computed from estimated model parameters. As a computationally efficient method of estimating the parameters of AR models from high-dimensional data, a stepwise least squares algorithm is proposed. This algorithm computes model coefficients and evaluates criteria for the selection of the model order stepwise for AR models of successively decreasing order. Numerical simulations indicate that, with the least squares algorithm, the AR model coefficients and the eigenmodes derived from the coefficients are estimated reliably and that the approximate 95\% confidence intervals for the coefficients and eigenmodes are rough approximations of the confidence intervals inferred from the simulations.", accepted = "10 October 2000", acknowledgement = ack-nhfb, } @Article{Schneider:2001:AAM, author = "Tapio Schneider and Arnold Neumaier", title = "{Algorithm 808}: {ARfit}---a {Matlab} package for the estimation of parameters and eigenmodes of multivariate autoregressive models", journal = j-TOMS, volume = "27", number = "1", pages = "58--65", month = mar, year = "2001", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/382043.382316", abstract = "{\sc ARfit} is a collection of Matlab modules for modeling and analyzing multivariate time series with autoregressive (AR) models. {\sc ARfit} contains modules for fitting AR models to given time series data, for analyzing eigenmodes of a fitted model, and for simulating AR processes. {\sc ARfit} estimates the parameters of AR models from given time series data with a stepwise least squares algorithm that is computationally efficient, in particular when the data are high-dimensional. {\sc ARfit} modules construct approximate confidence intervals for the estimated parameters and compute statistics with which the adequacy of a fitted model can be assessed. Dynamical characteristics of the modeled time series can be examined by means of a decomposition of a fitted AR model into eigenmodes and associated oscillation periods, damping times, and excitations. The {\sc ARfit} module that performs the eigendecomposition of a fitted model also constructs approximate confidence intervals for the eigenmodes and their oscillation periods and damping times.", accepted = "10 October 2000", acknowledgement = ack-nhfb, } @Article{Leydold:2001:SUG, author = "Josef Leydold", title = "A simple universal generator for continuous and discrete univariate {$T$}-concave distributions", journal = j-TOMS, volume = "27", number = "1", pages = "66--82", month = mar, year = "2001", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/382043.382322", accepted = "27 November 2000", acknowledgement = ack-nhfb, } @Article{Morales:2001:APF, author = "Jos{\'e} Luis Morales and Jorge Nocedal", title = "{Algorithm 809}: {PREQN}: {Fortran 77} subroutines for preconditioning the conjugate gradient method", journal = j-TOMS, volume = "27", number = "1", pages = "83--91", month = mar, year = "2001", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/382043.382343", abstract = "PREQN is a package of Fortran 77 subroutines for automatically generating preconditioners for the conjugate gradient method. It is designed for solving a sequence of linear systems $A_i x=b_i, \,\, i=1,\dots,t$, where the coefficient matrices $A_i$ are symmetric and positive definite and vary slowly. The preconditioners are based on limited memory quasi-Newton updating and are recommended for problems in which: (i) the coefficient matrices are not explicitly known and only matrix-vector products of the form $A_i v$ can be computed; or (ii) the coefficient matrices are not sparse. PREQN is written so that a single call from a conjugate gradient routine performs the preconditioning operation and stores information needed for the generation of a new preconditioner.", accepted = "26 October 2000", acknowledgement = ack-nhfb, } @Article{Verdonk:2001:PRIa, author = "Brigitte Verdonk and Annie Cuyt and Dennis Verschaeren", title = "A precision- and range-independent tool for testing floating-point arithmetic {I}: basic operations, square root, and remainder", journal = j-TOMS, volume = "27", number = "1", pages = "92--118", month = mar, year = "2001", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/382043.382404", abstract = "This paper introduces a precision- and range-independent tool for testing the compliance of hardware or software implementations of (multiprecision) floating-point arithmetic with the principles of the IEEE standards 754 and 854. The tool consists of a driver program, offering many options to test only specific aspects of the IEEE standards, and a large set of test vectors, encoded in a precision-independent syntax to allow the testing of basic and extended hardware formats as well as multiprecision floating-point implementations. The suite of test vectors stems on one hand from the integration and fully precision- and range-independent generalization of existing hardware test sets, and on the other hand from the systematic testing of exact rounding for all combinations of round and sticky bits that can occur. The former constitutes only 50\% of the resulting test set. In the latter we especially focus on hard-to-round cases. In addition, the test suite implicitly tests properties of floating-point operations, following the idea of Paranoia, and it reports which of the three IEEE-compliant underflow mechanisms is used by the floating-point implementation under consideration. We also check whether that underflow mechanism is used consistently. The tool is backward compatible with the UCBTEST package and with Coonen's test syntax.", accepted = "23 February 2001", acknowledgement = ack-nhfb, keywords = "Verification; IEEE floating-point standard; arithmetic; floating-point; multiprecision; validation", subject = "Primary Classification: G. Mathematics of Computing G.1 NUMERICAL ANALYSIS G.1.0 General Subjects: Computer arithmetic Additional Classification: D. Software D.3 PROGRAMMING LANGUAGES D.3.0 General Subjects: Standards", } @Article{Verdonk:2001:PRIb, author = "Brigitte Verdonk and Annie Cuyt and Dennis Verschaeren", title = "A precision- and range-independent tool for testing floating-point arithmetic {II}: conversions", journal = j-TOMS, volume = "27", number = "1", pages = "119--140", month = mar, year = "2001", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/382043.382405", abstract = "The IEEE 754 and 854 standards for floating-point arithmetic are essentially a specification of a programming environment, encompassing aspects from computer hardware, operating systems and compilers to programming languages (see especially section 8). Part I and II of this paper together describe a tool to test floating-point implementations of arbitrary precision and exponent range (hardware as well as software) for compliance with the principles outlined in the IEEE standards. The tool consists of a driver program, together with a very large set of test vectors encoded in a precision independent syntax.\par In Part I we have covered the testing of the basic operations +, -, x, /, the square root and remainder functions. In Part II we describe the extension of the test tool to deal with conversions between floating-point formats, conversions between floating-point and integer formats, the rounding of floating-point numbers to integral values and last but not least binary-decimal conversions. Conversions can now be tested from a floating-point format of arbitrary precision and exponent range to another arbitrary smaller (larger) floating-point format as well as to and from fixed hardware integer formats. Conversions between the bases 2 and 10 can be tested for a number of precisions ranging from single (24 bits), double (53 bits), long double or extended (64 bits) to quadruple (113 bits) precision and a proper multiprecision (240 bits) format.\par We conclude Part II with some applications of our test tool and report on the results of testing various floating-point implementations, meaning various language-compiler-hardware combinations as well as multiprecision libraries.", accepted = "23 February 2001", acknowledgement = ack-nhfb, } @Article{Bailey:2001:ASS, author = "P. B. Bailey and W. N. Everitt and A. Zettl", title = "{Algorithm 810}: The {SLEIGN2 Sturm--Liouville} Code", journal = j-TOMS, volume = "27", number = "2", pages = "143--192", month = jun, year = "2001", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/383738.383739", abstract = "The SLEIGN2 code is based on the ideas and methods of the original SLEIGN code of 1979. The main purpose of the SLEIGN2 code is to compute eigenvalues and eigenfunctions of regular and singular Sturm-Liouville problems, with both separated and coupled boundary conditions, and to approximate the continuous spectrum in the singular case. The code uses a number of different algorithms, some of which are new, and has a user-friendly interface. In this paper the algorithms and their implementation are discussed, and the class of problems to which each algorithm applies is identified.", accepted = "14 February 2001", acknowledgement = ack-nhfb, } @Article{Luksan:2001:ANA, author = "Ladislav Luk{\v{s}}an and Jan Vl{\v{c}}ek", title = "{Algorithm 811}: {NDA}: algorithms for nondifferentiable optimization", journal = j-TOMS, volume = "27", number = "2", pages = "193--213", month = jun, year = "2001", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/383738.383740", abstract = "We present four basic Fortran subroutines for nondifferentiable optimization with simple bounds and general linear constraints. Subroutine PMIN, intended for minimax optimization, is based on a sequential quadratic programming variable metric algorithm. Subroutine PBUN and PNEW, intended for general non-smooth problems, are based on bundle type methods. Subroutine PVAR is based on special nonsmooth variable metric methods. Besides the description of methods and codes, we propose computational experiments which demonstrate the efficiency of this approach.", accepted = "14 February 2001", acknowledgement = ack-nhfb, keywords = "minimax optimization, discrete Chebychev approximation, sequential quadratic programming methods, variable metric methods, general linear constraints", } @Article{Andersen:2001:RFC, author = "Bjarne S. Andersen and Jerzy Wa{\'s}niewski and Fred G. Gustavson", title = "A recursive formulation of {Cholesky} factorization of a matrix in packed storage", journal = j-TOMS, volume = "27", number = "2", pages = "214--244", month = jun, year = "2001", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/383738.383741", abstract = "A new compact way to store a symmetric or triangular matrix called RPF for Recursive Packed Format is fully described. Novel ways to transform RPF to and from standard packed format are included. A new algorithm, called RPC for Recursive Packed Cholesky, that operates on the RPG format is presented. Algorithm RPC is basd on level-3 BLAS and requires variants of algorithms TRSM and SYRK that work on RPF. We call these RP\_TRSM and RP\_SYRK and find that they do most of their work by calling GEMM. It follows that most of the execution time of RPC lies in GEMM. The advantage of this storage scheme compared to traditional packed and full storage is demonstrated. First, the RPC storage format uses the minimal amount of storage for the symmetric or triangular matrix. Second, RPC gives a level-3 implementation of Cholesky factorization whereas standard packed implementations are only level 2. Hence, the performance of our RPC implementation is decidedly superior. Third, unlike fixed block size algorithms, RPC, requires no block size tuning parameter. We present performance measurements on several current architectures that demonstrate improvements over the traditional packed routines. Also MSP parallel computations on the IBM SMP computer are made. The graphs that are attached in Section 7 show that the RPC algorithms are superior by a factor between 1.6 and 7.4 for order around 1000, and between 1.9 and 10.3 for order around 3000 over the traditional packed algorithms. For some architectures, the RPC performance results are almost the same or even better than the traditional full-storage algorithms results.", accepted = "15 March 2001", acknowledgement = ack-nhfb, } @Article{Cash:2001:ACS, author = "J. R. Cash and G. Moore and R. W. Wright", title = "An automatic continuation strategy for the solution of singularly perturbed nonlinear boundary value problems", journal = j-TOMS, volume = "27", number = "2", pages = "245--266", month = jun, year = "2001", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/383738.383742", abstract = "In a recent paper, the present authors derived an automatic continuation algorithm for the solution of linear singular perturbation problems. The algorithm was incorporated into two general-purpose codes for solving boundary value problems, and it was shown to deal effectively with a large test set of linear problems. The present paper describes how the continuation algorithm for linear problems can be extended to deal with the nonlinear case. The results of extensive numerical testing on a set of nonlinear singular perturbation problems are given, and these clearly demonstrate the efficacy of continuation for solving such problems.", accepted = "9 April 2001", acknowledgement = ack-nhfb, } @Article{Tsai:2001:ABO, author = "Yi-Feng Tsai and Rida T. Farouki", title = "{Algorithm 812}: {BPOLY}: {An} object-oriented library of numerical algorithms for polynomials in {Bernstein} form", journal = j-TOMS, volume = "27", number = "2", pages = "267--296", month = jun, year = "2001", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/383738.383743", abstract = "The design, implementation, and testing of a C++ software library for univariate polynomials in Bernstein form is described. By invoking the class environment and operator overloading, each polynomial in an expression is interpreted as an object compatible with the arithmetic operations and other common functions (subdivision, degree elevation, differentiation and integration, composition, greatest common divisor, real-root solving, etc.) for polynomials in Bernstein form. The library allows compact and intuitive implementation of lengthy manipulations of Bernstein-form polynomials, which often arise in computer graphics and computer-aided design and manufacturing applications. A series of empirical tests indicate that the library functions are typically very accurate and reliable, even for polynomials of surprisingly high degree.", accepted = "4 May 2001", acknowledgement = ack-nhfb, } @Article{Kierzenka:2001:BSB, author = "Jacek Kierzenka and Lawrence F. Shampine", title = "A {BVP} solver based on residual control and the {Matlab PSE}", journal = j-TOMS, volume = "27", number = "3", pages = "299--316", month = sep, year = "2001", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/502800.502801", abstract = "Our goal was to make it as easy as possible to solve a large class of boundary value problems (BVPs) for ordinary differential equations in the Matlab problem solving environment (PSE). We present here theoretical and software developments resulting in bvp4c, a capable BVP solver that is exceptionally easy to use.", accepted = "1 May 2001", acknowledgement = ack-nhfb, } @Article{Yang:2001:CPD, author = "Dow-Yung Yang and Ananth Grama and Vivek Sarin and Naren Ramakrishnan", title = "Compression of particle data from hierarchical approximate methods", journal = j-TOMS, volume = "27", number = "3", pages = "317--339", month = sep, year = "2001", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/502800.502802", abstract = "This article presents an analytical and computational framework for the compression of particle data resulting from hierarchical approximate treecodes such as the {\em Barnes--Hut} and {\em Fast Multipole Methods}. Due to approximations introduced by hierarchical methods, various parameters (such as position, velocity, acceleration, potential) associated with a particle can be bounded by distortion radii. Using this distortion radii, we develop storage schemes that guarantee error bounds while maximizing compression. Our schemes make extensive use of spatial and temporal coherence of particle behavior and yield compression ratios higher than 12:1 over raw data, and 6:1 over gzipped (LZ) raw data for selected simulation instances. We demonstrate that for uniform distributions with 2M particles, storage requirements can be reduced from 24 MB to about 1.8 MB (about 7 bits per particle per timestep) for storing particle positions. This is significant because it enables faster storage/retrieval, better temporal resolution, and improved analysis. Our results are shown to scale from small systems (2K particles) to much larger systems (over 2M particles). The associated algorithm is asymptotically optimal in computation time ($O(n)$) with a small constant. Our implementations are demonstrated to run extremely fast---much faster than the time it takes to compute a single time-step advance. In addition, our compression framework relies on a natural hierarchical representation upon which other analysis tasks such as segmented and window retrieval can be built.", accepted = "23 July 2001", acknowledgement = ack-nhfb, keywords = "Astrophysics; Barnes--Hut; Fast Multipole Method; data compression and analysis; materials simulation; molecular dynamics; particle dynamics", } @Article{Birgin:2001:ASS, author = "Ernesto G. Birgin and Jos{\'e} Mario Mart{\'\i}nez and Marcos Raydan", title = "{Algorithm 813}: {SPG}---Software for {Convex-Constrained Optimization}", journal = j-TOMS, volume = "27", number = "3", pages = "340--349", month = sep, year = "2001", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/502800.502803", abstract = "Fortran 77 software implementing the SPG method is introduced. SPG is a nonmonotone projected gradient algorithm for solving large-scale convex-constrained optimization problems. It combines the classical projected gradient method with the spectral gradient choice of steplength and a nonmonotone line-search strategy. The user provides objective function and gradient values, and projections onto the feasible set. Some recent numerical tests are reported on very large location problems, indicating that SPG is substantially more efficient than existing general-purpose software on problems for which projections can be computed efficiently.", accepted = "6 July 2001", acknowledgement = ack-nhfb, keywords = "algorithms; Bound constrained problems; large-scale problems; nonmonotone line search; projected gradients; spectral gradient method", subject = "Primary Classification: D. Software D.3 PROGRAMMING LANGUAGES D.3.2 Language Classifications Additional Classification: G. Mathematics of Computing G.1 NUMERICAL ANALYSIS G.1.6 Optimization Subjects: Gradient methods G.4 MATHEMATICAL SOFTWARE", } @Article{Azulay:2001:RSM, author = "David-Olivier Azulay and Jean-Fran{\c{c}}ois Pique", title = "A revised simplex method with integer {$Q$}-matrices", journal = j-TOMS, volume = "27", number = "3", pages = "350--360", month = sep, year = "2001", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/502800.502804", abstract = "We describe a modification of the simplex formulas in which Q-matrices are used to implement exact computations with an integer multiprecision library. Our motivation comes from the need for efficient and exact incremental solvers in the implementation of constraint solving languages such as Prolog. We explain how to reformulate the problem and the different steps of the simplex algorithm. We compare some measurements obtained with integer and rational computations.", accepted = "26 July 2001", acknowledgement = ack-nhfb, } @Article{Benson:2001:CSP, author = "Steven J. Benson and Lois Curfman McInnes and Jorge J. Mor{\'e}", title = "A case study in the performance and scalability of optimization algorithms", journal = j-TOMS, volume = "27", number = "3", pages = "361--376", month = sep, year = "2001", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Wed Feb 6 16:43:42 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/502800.502805", abstract = "We analyze the performance and scalabilty of algorithms for the solution of large optimization problems on high-performance parallel architectures. Our case study uses the GPCG (gradient projection, conjugate gradient) algorithm for solving bound-constrained convex quadratic problems. Our implementation of the GPCG algorithm within the Toolkit for Advanced Optimization (TAO) is available for a wide range of high-performance architectures and has been tested on problems with over 2.5 million variables. We analyze the performance as a function of the number of variables, the number of free variables, and the preconditioner. In addition, we discuss how the software design facilitates algorithmic comparisons.", accepted = "10 August 2001", acknowledgement = ack-nhfb, } @Article{Smith:2001:AFS, author = "David M. Smith", title = "{Algorithm 814}: {Fortran 90} software for floating-point multiple precision arithmetic, gamma and related functions", journal = j-TOMS, volume = "27", number = "4", pages = "377--387", month = dec, year = "2001", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Wed Mar 13 08:49:29 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/504210.504211", abstract = "A collection of Fortran 90 routines for evaluating the Gamma function and related functions using the FM multiple-precision arithmetic package.", acknowledgement = ack-nhfb, } @Article{Amestoy:2001:ACT, author = "Patrick R. Amestoy and Iain S. Duff and Jean-Yves L'Excellent and Xiaoye S. Li", title = "Analysis and Comparison of Two General Sparse Solvers for Distributed Memory Computers", journal = j-TOMS, volume = "27", number = "4", pages = "388--421", month = dec, year = "2001", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Wed Mar 13 08:49:29 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/504210.504212", abstract = "This paper provides a comprehensive study and comparison of two state-of-the-art direct solvers for large sparse sets of linear equations on large-scale distributed-memory computers. One is a multifrontal solver called MUMPS, the other is a supernodal solver called superLU. We describe the main algorithmic features of the two solvers and compare their performance characteristics with respect to uniprocessor speed, interprocessor communication, and memory requirements. For both solvers, preorderings for numerical stability and sparsity play an important role in achieving high parallel efficiency. We analyse the results with various ordering algorithms. Our performance analysis is based on data obtained from runs on a 512-processor Cray T3E using a set of matrices from real applications. We also use regular 3D grid problems to study the scalability of the two solvers.", acknowledgement = ack-nhfb, } @Article{Gunnels:2001:FFL, author = "John A. Gunnels and Fred G. Gustavson and Greg M. Henry and Robert A. van de Geijn", title = "{FLAME}: {Formal Linear Algebra Methods Environment}", journal = j-TOMS, volume = "27", number = "4", pages = "422--455", month = dec, year = "2001", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Wed Mar 13 08:49:29 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/504210.504213", abstract = "Since the advent of high-performance distributed-memory parallel computing, the need for intelligible code has become ever greater. The development and maintenance of libraries for these architectures is simply too complex to be amenable to conventional approaches to implementation. Attempts to employ traditional methodology have led, in our opinion, to the production of an abundance of anfractuous code that is difficult to maintain and almost impossible to upgrade.Having struggled with these issues for more than a decade, we have concluded that a solution is to apply a technique from theoretical computer science, formal derivation, to the development of high-performance linear algebra libraries. We think the resulting approach results in aesthetically pleasing, coherent code that greatly facilitates intelligent modularity and high performance while enhancing confidence in its correctness. Since the technique is language-independent, it lends itself equally well to a wide spectrum of programming languages (and paradigms) ranging from C and Fortran to C++ and Java. In this paper, we illustrate our observations by looking at the Formal Linear Algebra Methods Environment (FLAME), a framework that facilitates the derivation and implementation of linear algebra algorithms on sequential architectures. This environment demonstrates that lessons learned in the distributed-memory world can guide us toward better approaches even in the sequential world. We present performance experiments on the Intel (R) Pentium (R) III processor that demonstrate that high performance can be attained by coding at a high level of abstraction.", acknowledgement = ack-nhfb, } @Article{Festa:2001:AFS, author = "Paola Festa and Panos M. Pardalos and Mauricio G. C. Resende", title = "{Algorithm 815}: {FORTRAN} subroutines for computing approximate solutions of feedback set problems using {GRASP}", journal = j-TOMS, volume = "27", number = "4", pages = "456--464", month = dec, year = "2001", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Wed Mar 13 08:49:29 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/504210.504214", abstract = "We propose FORTRAN subroutines for approximately solving the feedback vertex and arc set problems on directed graphs using a Greedy Randomized Adaptive Search Procedure (GRASP). Implementation and usage of the package is outlined and computational experiments are reported illustrating solution quality as a function of running time.", acknowledgement = ack-nhfb, keywords = "Algorithms; Performance; Combinatorial optimization; FORTRAN subroutines; GRASP; feedback set problems; graph bipartization; local search", subject = "Primary Classification: G. Mathematics of Computing G.1 NUMERICAL ANALYSIS G.1.6 Optimization Subjects: Integer programming Additional Classification: G. Mathematics of Computing G.2 DISCRETE MATHEMATICS G.2.1 Combinatorics Subjects: Combinatorial algorithms G.m MISCELLANEOUS", } @Article{Engelborghs:2002:NBA, author = "K. Engelborghs and T. Luzyanina and D. Roose", title = "Numerical bifurcation analysis of delay differential equations using {DDE-BIFTOOL}", journal = j-TOMS, volume = "28", number = "1", pages = "1--21", month = mar, year = "2002", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Nov 9 11:16:50 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/513001.513002", abstract = "We describe {\DDEBIFCODE}, a Matlab package for numerical bifurcation analysis of systems of delay differential equations with several fixed, discrete delays. The package implements continuation of steady state solutions and periodic solutions and their stability analysis. It also computes and continues steady state fold and Hopf bifurcations and, from the latter, it can switch to the emanating branch of periodic solutions. We describe the numerical methods upon which the package is based and illustrate its usage and capabilities through analysing three examples: two models of coupled neurons with delayed feedback and a model of two oscillators coupled with delay.", acknowledgement = ack-nhfb, } @Article{Gockenbach:2002:EAI, author = "Mark S. Gockenbach and Daniel R. Reynolds and Peng Shen and William W. Symes", title = "Efficient and automatic implementation of the adjoint state method", journal = j-TOMS, volume = "28", number = "1", pages = "22--44", month = mar, year = "2002", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Nov 9 11:16:50 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/513001.513003", abstract = "Combination of object-oriented programming with automatic differentiation techniques facilitates the solution of data fitting, control, and design problems driven by explicit time stepping schemes for initial-boundary value problems. The C++ class fdtd takes a complete specification of a single step, along with some associated code, and assembles from it a complete simulator, along with the linearized and adjoint simulations. The result is a (nonlinear) operator in the sense of the Hilbert Class Library (HCL), a C++ software package for optimization. The HCL operator so produced links directly with any of the HCL optimization algorithms. Moreover, the performance of simulators constructed in this way is equivalent to that of optimized Fortran implementations.", acknowledgement = ack-nhfb, } @Article{Gansterer:2002:EDC, author = "Wilfried N. Gansterer and Robert C. Ward and Richard P. Muller", title = "An Extension of the Divide-and-Conquer Method for a Class of Symmetric Block-Tridiagonal Eigenproblems", journal = j-TOMS, volume = "28", number = "1", pages = "45--58", month = mar, year = "2002", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Nov 9 11:16:50 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/513001.513004", abstract = "A divide-and-conquer method for computing eigenvalues and eigenvectors of a block-tridiagonal matrix with rank-one off-diagonal blocks is presented. The implications of unbalanced merging operations due to unequal block sizes are analyzed and illustrated with numerical examples. It is shown that an unfavorable order for merging blocks in the synthesis phase of the algorithm may lead to a significant increase of the arithmetic complexity. A strategy to determine a good merging order which is at least close to optimal in all cases is given. The method has been implemented and applied to test problems from a Quantum Chemistry application.", acknowledgement = ack-nhfb, } @Article{Hopkins:2002:RCA, author = "Tim Hopkins", title = "Renovating the {Collected Algorithms from ACM}", journal = j-TOMS, volume = "28", number = "1", pages = "59--74", month = mar, year = "2002", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Nov 9 11:16:50 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/513001.513005", abstract = "Since 1960 the Association for Computing Machinery has published a series of refereed algorithm implementations known as the Collected Algorithms of the ACM (CALGO). Most of those published since 1975 are mathematical algorithms, and many of them remain useful today. In this paper we describe measures that have been taken to bring some 400 of these latter codes to an up-to-date and consistent state.", acknowledgement = ack-nhfb, } @Article{Robinson:2002:ARA, author = "Ian Robinson and Michael Hill", title = "{Algorithm 816}: {\em r2d2lri\/}: an algorithm for automatic two-dimensional cubature", journal = j-TOMS, volume = "28", number = "1", pages = "75--100", month = mar, year = "2002", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Nov 9 11:16:50 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/513001.513006", abstract = "{\em r2d2lri} is a non-adaptive algorithm implemented in C++ for performing automatic cubature over a wide variety of finite and non-finite two-dimensional domains. The core integrator uses a sixth-order Sidi transformation applied to a sequence of embedded lattice rules in such a fashion as to incur virtually no computational overhead. Even for integrals over non-finite domains, for which several non-finite to finite transformations may be attempted, the algorithm remains very fast. Performance data is presented which demonstrates both the effectiveness and efficiency of {\em r2d2lri}, taking into account the number of function evaluations needed and the execution speed.", acknowledgement = ack-nhfb, } @Article{Bertolazzi:2002:APG, author = "Enrico Bertolazzi and Gianmarco Manzini", title = "{Algorithm 817}: {P2MESH}: generic object-oriented interface between {$2$-D} unstructured meshes and {FEM\slash FVM}-based {PDE} solvers", journal = j-TOMS, volume = "28", number = "1", pages = "101--132", month = mar, year = "2002", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Nov 9 11:16:50 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/513001.513007", abstract = "The software interface P2MESH is a collection of C++ class templates suitable for developing prototypes of high-performance PDE solvers on unstructured 2-D meshes. P2MESH supports several discretization methods on triangles and quadrilaterals, such as Finite Volumes or Finite Elements. The design philosophy of P2MESH does not consider neither specific model problems nor built-in approximation algorithms. The software package is of general purpose and it may also be used as a building block in the implementation of numerical both for engineering applications and mathematical problems.", accepted = "21 March 2002", acknowledgement = ack-nhfb, } @Article{Boisvert:2002:PSI, author = "Ronald F. Boisvert and Jack J. Dongarra", title = "Preface to the special issue on the {Basic Linear Algebra Subprograms (BLAS)}", journal = j-TOMS, volume = "28", number = "2", pages = "133--134", month = jun, year = "2002", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Nov 9 11:16:50 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/567806.567812", acknowledgement = ack-nhfb, } @Article{Blackford:2002:USB, author = "L. Susan Blackford and James Demmel and Jack Dongarra and Iain Duff and Sven Hammarling and Greg Henry and Michael Heroux and Linda Kaufman and Andrew Lumsdaine and Antoine Petitet and Roldan Pozo and Karin Remington and R. Clint Whaley", title = "An updated set of {Basic Linear Algebra Subprograms (BLAS)}", journal = j-TOMS, volume = "28", number = "2", pages = "135--151", month = jun, year = "2002", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Nov 9 11:16:50 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/567806.567807", abstract = "This paper expands the specification of a set of kernel routines for linear algebra, historically called the Basic Linear Algebra Subprograms and commonly known as the BLAS.\par Numerical linear algebra, particularly the solution of linear systems of equations, linear least squares problems, eigenvalue problems and singular value problems, is fundamental to most calculations in scientific computing, and is often the computationally intense part of such calculations. Designers of computer programs involving linear algebraic operations have frequently chosen to implement certain low level operations, such as the dot product or the matrix vector product, as separate subprograms. This may be observed both in many published codes and in codes written for specific applications at many computer installations.\par A major aim of the standards defined in this paper is to enable linear algebra libraries (both public domain and commercial) to interoperate efficiently, reliably and easily.", acknowledgement = ack-nhfb, } @Article{Li:2002:DIT, author = "Xiaoye S. Li and James W. Demmel and David H. Bailey and Greg Henry and Yozo Hida and Jimmy Iskandar and William Kahan and Suh Y. Kang and Anil Kapur and Michael C. Martin and Brandon J. Thompson and Teresa Tung and Daniel J. Yoo", title = "Design, implementation and testing of extended and mixed precision {BLAS}", journal = j-TOMS, volume = "28", number = "2", pages = "152--205", month = jun, year = "2002", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Nov 9 11:16:50 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/567806.567808", abstract = "This paper describes the design rationale, a C implementation, and conformance testing of a subset of the new Standard for the BLAS (Basic Linear Algebra Subroutines): Extended and Mixed Precision BLAS. Permitting higher internal precision and mixed input\slash output types and precisions allows us to implement some algorithms that are simpler, more accurate, and sometimes faster than possible without these features. The new BLAS are challenging to implement and test because there are many more subroutines than in the existing Standard, and because we must be able to assess whether a higher precision is used for internal computations than is used for either input or output variables. We have therefore developed an automated process of generating and systematically testing these routines. Our methodology is applicable to languages besides C. In particular, our algorithms used in the testing code will be valuable to all other BLAS implementors. Our extra precision routines achieve excellent performance---close to half of the machine peak Megaflop rate even for the Level 2 BLAS, when the data access is stride one.", acknowledgement = ack-nhfb, } @Article{Bindel:2002:CGR, author = "David Bindel and James Demmel and William Kahan and Osni Marques", title = "On computing {Givens} rotations reliably and efficiently", journal = j-TOMS, volume = "28", number = "2", pages = "206--238", month = jun, year = "2002", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Nov 9 11:16:50 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/567806.567809", abstract = "We consider the efficient and accurate computation of Givens rotations. When $f$ and $g$ are positive real numbers, this simply amounts to computing the values of $c = f/\sqrt{f^2+g^2}$, $s = g/\sqrt{f^2+g^2}$, and $r = \sqrt{f^2+g^2}$. This apparently trivial computation merits closer consideration for the following three reasons. First, while the definitions of $c$, $s$ and $r$ seem obvious in the case of two nonnegative arguments $f$ and $g$, there is enough freedom of choice when one or more of $f$ and $g$ are negative, zero or complex that LAPACK auxiliary routines SLARTG, CLARTG, SLARGV and CLARGV can compute rather different values of $c$, $s$ and $r$ for mathematically identical values of $f$ and $g$. To eliminate this unnecessary ambiguity, the BLAS Technical Forum chose a single consistent definition of Givens rotations that we will justify here. Second, computing accurate values of $c$, $s$ and $r$ as efficiently as possible and reliably despite over/underflow is surprisingly complicated. For complex Givens rotations, the most efficient formulas require only one real square root and one real divide (as well as several much cheaper additions and multiplications), but a reliable implementation using only working precision has a number of cases. On a Sun Ultra-10, the new implementation is slightly faster than the previous LAPACK implementation in the most common case, and 2.7 to 4.6 times faster than the corresponding vendor, reference or ATLAS routines. It is also more reliable; all previous codes occasionally suffer from large inaccuracies due to over/underflow. For real Givens rotations there are also improvements in speed and accuracy, though not as striking. Third, the design process that led to this reliable implementation is quite systematic, and could be applied to the design of similarly reliable subroutines.", acknowledgement = ack-nhfb, } @Article{Duff:2002:OSB, author = "Iain S. Duff and Michael A. Heroux and Roldan Pozo", title = "An overview of the {Sparse Basic Linear Algebra Subprograms}: {The} new standard from the {BLAS Technical Forum}", journal = j-TOMS, volume = "28", number = "2", pages = "239--267", month = jun, year = "2002", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Nov 9 11:16:50 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/567806.567810", abstract = "We discuss the interface design for the Sparse Basic Linear Algebra Subprograms (BLAS), the kernels in the recent standard from the BLAS Technical Forum that are concerned with unstructured sparse matrices. The motivation for such a standard is to encourage portable programming while allowing for library-specific optimizations. In particular, we show how this interface can shield one from concern over the specific storage scheme for the sparse matrix. This design makes it easy to add further functionality to the sparse BLAS in the future.We illustrate the use of the Sparse BLAS with examples in the three supported programming languages, Fortran 95, Fortran 77, and C.", acknowledgement = ack-nhfb, } @Article{Duff:2002:ARM, author = "Iain S. Duff and Christof V{\"o}mel", title = "{Algorithm 818}: {A} reference model implementation of the {Sparse BLAS} in {Fortran 95}", journal = j-TOMS, volume = "28", number = "2", pages = "268--283", month = jun, year = "2002", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Nov 9 11:16:50 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/567806.567811", abstract = "The Basic Linear Algebra Subprograms for sparse matrices (Sparse BLAS) as defined by the blas technical forum are a set of routines providing basic operations for sparse matrices and vectors. A principal goal for the Sparse BLAS standard is to aid in the development of iterative solvers for large sparse systems by specifying on the one hand interfaces for a high-level description of vector and matrix operations for the algorithm developer and on the other hand leaving enough freedom for vendors to provide the most efficient implementation of the underlying algorithms for their specific architectures.\par The Sparse BLAS standard defines interfaces and bindings for the three target languages: C, Fortran 77 and Fortran 95. We describe here our Fortran 95 implementation intended as a reference model for the Sparse BLAS. We identify the underlying complex issues of the representation and the handling of sparse matrices and give suggestions to other implementors of how to address them.", acknowledgement = ack-nhfb, } @Article{Hopkins:2002:CPT, author = "Tim Hopkins", title = "A comment on the presentation and testing of {CALGO} codes and a remark on {Algorithm 639}: {To} integrate some infinite oscillating tails", journal = j-TOMS, volume = "28", number = "3", pages = "285--300", month = sep, year = "2002", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Nov 9 11:16:50 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/569147.569148", abstract = "We report on a number of coding problems that occur frequently in published CALGO software and are still appearing in new algorithm submissions. Using Algorithm 639 as an extended example, we describe how these types of faults may be almost entirely eliminated using available commercial compilers and software tools. We consider the levels of testing required to instill confidence that code performs reliably. Finally, we look at how the source code may be re-engineered, and thus made more maintainable, by taking account of advances in hardware and language development.", acknowledgement = ack-nhfb, } @Article{Gupta:2002:RAD, author = "Anshul Gupta", title = "Recent Advances in Direct Methods for Solving Unsymmetric Sparse Systems of Linear Equations", journal = j-TOMS, volume = "28", number = "3", pages = "301--324", month = sep, year = "2002", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Mar 28 11:26:40 2003", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/569147.569149", abstract = "During the past few years, algorithmic improvements alone have reduced the time required for the direct solution of unsymmetric sparse systems of linear equations by almost an order of magnitude. This paper compares the performance of some well-known software packages for solving general sparse systems. In particular, it demonstrates the consistently high level of performance achieved by WSMP---the most recent of such solvers. It compares the various algorithmic components of these solvers and discusses their impact on solver performance. Our experiments show that the algorithmic choices made in WSMP enable it to run more than twice as fast as the best among similar solvers and that WSMP can factor some of the largest sparse matrices available from real applications in only a few seconds on a 4-CPU workstation. Thus, the combination of advances in hardware and algorithms makes it possible to solve those general sparse linear systems quickly and easily that might have been considered too large until recently.", acknowledgement = ack-nhfb, keywords = "Algorithms, Performance; Multifrontal Method; Parallel Sparse Solvers; Sparse LU Decomposition; Sparse Matrix Factorization", subject = "Primary Classification: G. Mathematics of Computing G.1 NUMERICAL ANALYSIS G.1.3 Numerical Linear Algebra", } @Article{Gil:2002:AAB, author = "Amparo Gil and Javier Segura and Nico M. Temme", title = "{Algorithm 819}: {AIZ}, {BIZ}: two {Fortran 77} routines for the computation of complex {Airy} functions", journal = j-TOMS, volume = "28", number = "3", pages = "325--336", month = sep, year = "2002", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Nov 9 11:16:50 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/569147.569150", abstract = "Two Fortran 77 routines for the evaluation of Airy functions of complex arguments $Ai(z)$, $Bi(z)$ and their derivatives are presented. The routines are based on the use of Gaussian quadrature, Maclaurin series and asymptotic expansions. Comparison with a previous code by E. Amos (ACM TOMS 12 (1986)) is provided.", acknowledgement = ack-nhfb, } @Article{Ferrando:2002:AFI, author = "Sebastian E. Ferrando and Lawrence A. Kolasa and Natasha Kova{\v{c}}evi{\'c}", title = "{Algorithm 820}: {A} flexible implementation of matching pursuit for {Gabor} functions on the interval", journal = j-TOMS, volume = "28", number = "3", pages = "337--353", month = sep, year = "2002", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Nov 9 11:16:50 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/569147.569151", abstract = "The matching pursuit algorithm of Mallat et.~al.~is discussed in the context of discretized Gabor functions on an interval. Results from frame theory are used to introduce corresponding finite dictionaries. We then proceed to describe two software implementations based on these dictionaries. One implementation allows for users to have great flexibility in the Gabor dictionary to be used. This is a useful improvement over other implementations which only allow for a fixed dictionary. The other implementation takes advantage of the FFT algorithm and is faster. These implementations are written in C++, and can be used in many practical situations given its flexibility and generality.", acknowledgement = ack-nhfb, } @Article{Hanson:2002:AFI, author = "Richard J. Hanson and Clay P. Breshears and Henry A. Gabb", title = "{Algorithm 821}: {A} {Fortran} interface to {POSIX} threads", journal = j-TOMS, volume = "28", number = "3", pages = "354--371", month = sep, year = "2002", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Nov 9 11:16:50 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/569147.569152", abstract = "Pthreads is the library of POSIX standard functions for concurrent, multithreaded programming. The POSIX standard only defines an application programming interface (API) to the C programming language, not to Fortran. Many scientific and engineering applications are written in Fortran. Also, many of these applications exhibit functional, or task-level, concurrency. They would benefit from multithreading, especially on symmetric multiprocessors (SMP). We present here an interface to that part of the Pthreads library that is compatible with standard Fortran. The contribution consists of two primary source files: a Fortran module and a collection of C wrappers to Pthreads functions. The Fortran module defines the data structures, interface and initialization routines used to manage threads. The stability and portability of the Fortran API to Pthreads is demonstrated using common mathematical computations on three different systems.", acknowledgement = ack-nhfb, } @Article{Hopkins:2002:RAF, author = "Tim Hopkins", title = "Remark on {Algorithm 705}: {A} {Fortran-77} software package for solving the {Sylvester} matrix equation {$AXB^T + CXD^T = E$}", journal = j-TOMS, volume = "28", number = "3", pages = "372--375", month = sep, year = "2002", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Sat Nov 9 11:16:50 MST 2002", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", note = "See \cite{Gardiner:1992:AFS}.", URL = "http://doi.acm.org/10.1145/569147.569153", abstract = "We present a number of corrections to Algorithm 705 [Gardiner et al. 1992].", acknowledgement = ack-nhfb, } @Article{Reid:2002:IHE, author = "John K. Reid and Jennifer A. Scott", title = "Implementing {Hager}'s exchange methods for matrix profile reduction", journal = j-TOMS, volume = "28", number = "4", pages = "377--391", month = dec, year = "2002", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Mar 28 08:17:55 MST 2003", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/592843.592844", abstract = "Hager recently introduced down and up exchange methods for reducing the profile of a sparse matrix with a symmetric sparsity pattern. The methods are particularly useful for refining orderings that have been obtained using a standard profile reduction algorithm, such as the Sloan method. The running times for the exchange algorithms reported by Hager suggested their cost could be prohibitive for practical applications. We examine how to implement the exchange algorithms efficiently. For a range of real test problems, it is shown that the cost of running our new implementation does not add a prohibitive overhead to the cost of the original reordering.", acknowledgement = ack-nhfb, } @Article{Jonsson:2002:RBAa, author = "Isak Jonsson and Bo K{\aa}gstr{\"o}m", title = "Recursive blocked algorithms for solving triangular systems: {Part I}: one-sided and coupled {Sylvester}-type matrix equations", journal = j-TOMS, volume = "28", number = "4", pages = "392--415", month = dec, year = "2002", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Mar 28 08:17:55 MST 2003", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/592843.592845", abstract = "Triangular matrix equations appear naturally in estimating the condition numbers of matrix equations and different eigenspace computations, including block-diagonalization of matrices and matrix pairs and computation of functions of matrices. To solve a triangular matrix equation is also a major step in the classical Bartels--Stewart method for solving the standard continuous-time Sylvester equation ($AX - XB = C$). We present novel recursive blocked algorithms for solving one-sided triangular matrix equations, including the continuous- time Sylvester and Lyapunov equations, and a generalized coupled Sylvester equation. The main parts of the computations are performed as level-3 general matrix multiply and add (GEMM) operations. In contrast to explicit standard blocking techniques, our recursive approach leads to an automatic variable blocking that has the potential of matching the memory hierarchies of today's HPC systems. Different implementation issues are discussed, including when to terminate the recursion, the design of new optimized superscalar kernels for solving leaf-node triangular matrix equations efficiently, and how parallelism is utilized in our implementations. Uniprocessor and SMP parallel performance results of our recursive blocked algorithms and corresponding routines in the state-of-the-art libraries LAPACK and SLICOT are presented. The performance improvements of our recursive algorithms are remarkable, including 10-fold speedups compared to standard algorithms.", acknowledgement = ack-nhfb, keywords = "Algorithms; automatic blocking; GEMM-based; generalized coupled Sylvester; LAPACK; level-3 BLAS; Matrix equations; Performance; recursion; SLICOT; SMP parallelization; standard Sylvester and Lyapunov; superscalar", subject = "Primary Classification: G. Mathematics of Computing G.4 MATHEMATICAL SOFTWARE Subjects: Algorithm design and analysis Additional Classification: F. Theory of Computation F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY F.2.1 Numerical Algorithms and Problems Subjects: Computations on matrices G. Mathematics of Computing G.1 NUMERICAL ANALYSIS G.1.3 Numerical Linear Algebra Subjects: Conditioning; Linear systems (direct and iterative methods) G.4 MATHEMATICAL SOFTWARE Subjects: Parallel and vector implementations; Efficiency; Reliability and robustness", } @Article{Jonsson:2002:RBAb, author = "Isak Jonsson and Bo K{\aa}gstr{\"o}m", title = "Recursive Blocked Algorithms for Solving Triangular Systems: {Part II}: Two-Sided and Generalized {Sylvester} and {Lyapunov} Matrix Equations", journal = j-TOMS, volume = "28", number = "4", pages = "416--435", month = dec, year = "2002", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Mar 28 08:17:55 MST 2003", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/592843.592846", abstract = "We continue our study of high-performance algorithms for solving triangular matrix equations. They appear naturally in different condition estimation problems for matrix equations and various eigenspace computations, and as reduced systems in standard algorithms. Building on our successful recursive approach applied to one-sided matrix equations (Part I), we now present novel recursive blocked algorithms for two-sided matrix equations, which include matrix product terms such as AXBT. Examples are the discrete-time standard and generalized Sylvester and Lyapunov equations. The means for achieving high performance is the recursive variable blocking, which has the potential of matching the memory hierarchies of today's high-performance computing systems, and level-3 computations which mainly are performed as GEMM operations. Different implementation issues are discussed, including the design of efficient new algorithms for two-sided matrix products. We present uniprocessor and SMP parallel performance results of recursive blocked algorithms and routines in the state-of-the-art SLICOT library. Although our recursive algorithms with optimized kernels for the two-sided matrix equations perform more operations, the performance improvements are remarkable, including 10-fold speedups or more, compared to standard algorithms.", acknowledgement = ack-nhfb, keywords = "Algorithms; automatic blocking; Design; generalized Sylvester and Lyapunov; LAPACK; level-3 BLAS; Matrix equations; Performance GEMM-based; recursion; SLICOT; SMP parallelization; standard discrete-time Sylvester and Lyapunov; superscalar", subject = "Primary Classification: G. Mathematics of Computing G.4 MATHEMATICAL SOFTWARE Subjects: Algorithm design and analysis Additional Classification: F. Theory of Computation F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY F.2.1 Numerical Algorithms and Problems Subjects: Computations on matrices G. Mathematics of Computing G.1 NUMERICAL ANALYSIS G.1.3 Numerical Linear Algebra Subjects: Linear systems (direct and iterative methods); Conditioning G.4 MATHEMATICAL SOFTWARE Subjects: Parallel and vector implementations; Reliability and robustness; Efficiency", } @Article{Gil:2002:AGH, author = "Amparo Gil and Javier Segura and Nico M. Temme", title = "{Algorithm 822}: {GIZ}, {HIZ}: two {Fortran} 77 routines for the computation of complex {Scorer} functions", journal = j-TOMS, volume = "28", number = "4", pages = "436--447", month = dec, year = "2002", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Mar 28 08:17:55 MST 2003", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/592843.592847", abstract = "Two Fortran 77 routines for the evaluation of Scorer functions of complex arguments $Gi(z)$, $Hi(z)$ and their derivatives are presented. The routines are based on the use of quadrature, Maclaurin series and asymptotic expansions. For real $z$ comparison with a previous code by A. J. Macleod (J. Comput. Appl. Math. 53 (1994)) is provided.", acknowledgement = ack-nhfb, } @Article{Edlund:2002:SPS, author = "Ove Edlund", title = "A software package for sparse orthogonal factorization and updating", journal = j-TOMS, volume = "28", number = "4", pages = "448--482", month = dec, year = "2002", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Mar 28 08:17:55 MST 2003", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/592843.592848", abstract = "Though there is good software for sparse QR factorization, there is little support for updating and downdating---something that is absolutely essential in some linear programming algorithms, for example. This paper describes an implementation of sparse LQ factorization, including block triangularization, approximate minimum degree ordering, symbolic factorization, multifrontal factorization, {\em and\/} updating and downdating. The factor $Q$ is not retained. The updating algorithm expands the nonzero pattern of the factor $L$, which is reflected in the dynamic representation of $L$. The block triangularization is used as an ``ordering for sparsity'' rather than as a prerequisite for block backward substitution. In the symbolic factorization, something called ``element counters'' is introduced to reduce the overestimation of the number of nonzeros that the commonly used methods do. Both the approximate minimum degree ordering and the symbolic factorization are done without explicitly forming the nonzero pattern of the symmetric matrix in the corresponding normal equations.\par Tests show that the average time used for a single update or downdate is essentially the same as the time used for a single forward or backward substitution. Other parts of the implementation show the same range of performance as existing code, but cannot be replaced because of the special character of the systems that are solved.", acknowledgement = ack-nhfb, } @Article{Soderlind:2003:DFA, author = "Gustaf S{\"o}derlind", title = "Digital filters in adaptive time-stepping", journal = j-TOMS, volume = "29", number = "1", pages = "1--26", month = mar, year = "2003", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Mar 28 08:17:55 MST 2003", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/641876.641877", abstract = "Adaptive time-stepping based on linear digital control theory has several advantages: the algorithms can be analyzed in terms of stability and adaptivity, and they can be designed to produce smoother stepsize sequences resulting in significantly improved regularity and computational stability. Here, we extend this approach by viewing the closed-loop transfer map Hϕ: logϕ ↦ log h as a digital filter, processing the signal logϕ (the principal error function) in the frequency domain, in order to produce a smooth stepsize sequence log h. The theory covers all previously considered control structures and offers new possibilities to construct stepsize selection algorithms in the asymptotic stepsize-error regime. Without incurring extra computational costs, the controllers can be designed for special purposes such as higher order of adaptivity (for smooth ODE problems) or a stronger ability to suppress high-frequency error components (nonsmooth problems, stochastic ODEs). Simulations verify the controllers' ability to produce stepsize sequences resulting in improved regularity and computational stability.", acknowledgement = ack-nhfb, keywords = "Adaptivity; algorithm analysis; control theory; digital filters; error control; mathematical software; stepsize control; algorithms; theory", subject = "G. Mathematics of Computing G.1 NUMERICAL ANALYSIS G.1.7 Ordinary Differential Equations Subjects: Initial value problems", } @Article{Nievergelt:2003:SFM, author = "Yves Nievergelt", title = "Scalar fused multiply-add instructions produce floating-point matrix arithmetic provably accurate to the penultimate digit", journal = j-TOMS, volume = "29", number = "1", pages = "27--48", month = mar, year = "2003", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Mar 28 08:17:55 MST 2003", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/641876.641878", abstract = "Combined with doubly compensated summation, scalar fused multiply-add instructions redefine the concept of floating-point arithmetic, because they allow for the computation of sums of real or complex matrix products accurate to the penultimate digit. Particular cases include complex arithmetic, dot products, cross products, residuals of linear systems, determinants of small matrices, discriminants of quadratic, cubic, or quartic equations, and polynomials.", acknowledgement = ack-nhfb, keywords = "algorithms; design; languages; standardization; theory; doubly compensated summation; floating-point arithmetic; fused multiply-add instruction; matrix arithmetic; provable accuracy; rounding error", subject = "Primary Classification: B. Hardware, B.2 ARITHMETIC AND LOGIC STRUCTURES, B.2.0 General; Additional Classification: B. Hardware, B.7 INTEGRATED CIRCUITS B.7.1 Types and Design Styles Subjects: Algorithms implemented in hardware B.8 Performance and Reliability B.8.2 Performance Analysis and Design Aids C. Computer Systems Organization C.0 GENERAL Subjects: Instruction set design (e.g., RISC, CISC, VLIW) F. Theory of Computation F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY F.2.1 Numerical Algorithms and Problems Subjects: Computations on matrices G. Mathematics of Computing G.1 NUMERICAL ANALYSIS G.1.0 General Subjects: Computer arithmetic; Multiple precision arithmetic; Numerical algorithms; Error analysis G.4 MATHEMATICAL SOFTWARE Subjects: Algorithm design and analysis; Certification and testing; Reliability and robustness", } @Article{Joe:2003:RAI, author = "Stephen Joe and Frances Y. Kuo", title = "Remark on {Algorithm 659}: {Implementing} {Sobol}'s quasirandom sequence generator", journal = j-TOMS, volume = "29", number = "1", pages = "49--57", month = mar, year = "2003", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Mar 28 08:17:55 MST 2003", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/641876.641879", abstract = "An algorithm to generate Sobol' sequences to approximate integrals in up to 40 dimensions has been previously given by Bratley and Fox in Algorithm 659. Here, we provide more primitive polynomials and ``direction numbers'' so as to allow the generation of Sobol' sequences to approximate integrals in up to 1111 dimensions. The direction numbers given generate Sobol' sequences that satisfy Sobol's so-called Property A.", acknowledgement = ack-nhfb, keywords = "Low-discrepancy sequences; Sobol' sequences; primitive polynomials; quasirandom sequences; algorithms", subject = "G. Mathematics of Computing G.1 NUMERICAL ANALYSIS G.1.4 Quadrature and Numerical Differentiation Subjects: Multidimensional (multiple) quadrature", } @Article{Gertz:2003:OOS, author = "E. Michael Gertz and Stephen J. Wright", title = "Object-oriented software for quadratic programming", journal = j-TOMS, volume = "29", number = "1", pages = "58--81", month = mar, year = "2003", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Mar 28 08:17:55 MST 2003", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/641876.641880", abstract = "The object-oriented software package OOQP for solving convex quadratic programming problems (QP) is described. The primal-dual interior point algorithms supplied by OOQP are implemented in a way that is largely independent of the problem structure. Users may exploit problem structure by supplying linear algebra, problem data, and variable classes that are customized to their particular applications. The OOQP distribution contains default implementations that solve several important QP problem types, including general sparse and dense QPs, bound-constrained QPs, and QPs arising from support vector machines and Huber regression. The implementations supplied with the OOQP distribution are based on such well known linear algebra packages as MA27/57, LAPACK, and PETSc. OOQP demonstrates the usefulness of object-oriented design in optimization software development, and establishes standards that can be followed in the design of software packages for other classes of optimization problems. A number of the classes in OOQP may also be reusable directly in other codes.", acknowledgement = ack-nhfb, keywords = "Algorithms; Design; Interior-Point Methods; Object-Oriented Software; Quadratic Programming", subject = "Primary Classification: D. Software D.2 SOFTWARE ENGINEERING D.2.2 Design Tools and Techniques Additional Classification: G. Mathematics of Computing G.1 NUMERICAL ANALYSIS G.1.6 Optimization Subjects: Quadratic programming methods G.4 MATHEMATICAL SOFTWARE Subjects: Algorithm design and analysis", } @Article{Wenzel:2003:IWD, author = "Lothar Wenzel and Ram Rajagopal and Dinesh Nair", title = "Induced well-distributed sets in {Riemannian} spaces", journal = j-TOMS, volume = "29", number = "1", pages = "82--94", month = mar, year = "2003", CODEN = "ACMSCU", ISSN = "0098-3500", bibdate = "Fri Mar 28 08:17:55 MST 2003", bibsource = "http://www.acm.org/pubs/contents/journals/toms/", URL = "http://doi.acm.org/10.1145/641876.641881", abstract = "The concept of Riemannian geometries is used to construct induced homogeneous point sets on manifolds that are based on well-distributed point sets in unit cubes of an appropriately chosen Euclidean space. These well-distributed point sets in unit cubes are based on standard low-discrepancy sequences. The approach is algorithmic, that is, the methods developed in this article have been implemented and tested. Applications in image processing, graph theory and measurement-based exploration are presented.", acknowledgement = ack-nhfb, keywords = "Algorithms; Measurement; Theory; Riemannian geometry; image processing; low-discrepancy sequences; well-distributed point sets", subject = "J. Computer Applications J.2 PHYSICAL SCIENCES AND ENGINEERING", } @Article{Hong:2003:AIS, author = "Hee Sun Hong and Fred J. Hickernell", title = "Algorithm 823: Implementing Scrambled Digital Sequences", journal = j-TOMS, volume = "29", number = "2", pages = "95--109", month = jun, year = "2003", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/779359.779360", abstract = "Random scrambling of deterministic (t,m,s)-nets and (t,s)-sequences eliminates their inherent bias while retaining their low discrepency properties. This article describes an implementation of two types of random scrambling, one proposed by Owen and another proposal by Faure and Tezuka. The four different constructions of digital sequences implemented are those proposed by Sobol, Faure, Niederreiter, and Niederreiter and Xing. Because the random scrambling involves manipulating all digits of each point, the code must be written carefully to minimize the execution time. Computed root mean square discrepencies of the scrambled sequences are compared to known theoretical results. Furthermore, the performances of the sequences on various test problems are discussed.", } @Article{Li:2003:SSD, author = "Xiaoye S. Li and James W. Demmel", title = "SuperLU-DIST: A Scalable Distributed-Memory Sparse Direct Solver for Unsymmetric Linear Systems", journal = j-TOMS, volume = "29", number = "2", pages = "110--140", month = jun, year = "2003", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/779359.779361", abstract = "In this paper we present the main algorithmic features in the software package SuperLU_DIST, a distributed-memory sparse direct solver for large sets of linear equations. We give in detail our parallelization strategies, with focus on scalability issues, and demonstrate its parallel performance and scalability on current machines. The solver is based on sparse Gaussian elimination, with an innovative static pivoting strayegy proposed earlier by the authors. The main advantage of static pivoting over classical partial pivoting is that it permits a priori determination of data structures and communication patterns, which lets us exploit techniques used in parallel sparse Choelesky algorithms to better parallelize both LU decomposition and triangular solve on large scale distributed machines.", } @Article{Dhooge:2003:MMP, author = "A. Dhooge, W. Govaerts, and Yu. A. Kuznetsov", title = "{MATCONT}: A {MATLAB} Package for Numerical Bifurcation Analysis of ODEs", journal = j-TOMS, volume = "29", number = "2", pages = "141--164", month = jun, year = "2003", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/779359.779362", abstract = "MATCONT is a graphical MATLAB software package for the interactive numerical study of dynamical systems. It allows to compute curves of equilibria, limit points, Hopf points, limit cycles, period doubling bifurcation points of limit cycles and fold bifurcation points of limit cycles. All curves are computed by the same function that implements a prediction-correction continuation algorithm based on the Moore-Penrose matrix pseudo-inverse. The continuation of bifurcation points of equilibria and limit cycles is based on bordering methods and minimally extended systems. Hence no additional unknowns such as singular vectors and eigenvectors are used and no artificial sparsity in the systems is created. The sparsity of the discretized systems for the computation of limit cycles and their bifurcation points is exploited by using the standard MATLAB sparse matrix methods. The {\sc matlab} environment makes the standard MATLAB ODE Suite interactively available and provides computational and visualization tools; it also eliminates the compilation stage and so makes installation straightforward. Compared to other packages such as AUTO and CONTENT, adding a new type of curves is easy in the MATLAB environment. We illustrate this by a detailed description of the limit point curve type.", } @Article{Henrion:2003:GGO, author = "Didier Henrion and Jean-Bernard Lasserre", title = "{GloptiPoly}: Global Optimization over Polynomials with {Matlab} and {SeDuMi}", journal = j-TOMS, volume = "29", number = "2", pages = "165--194", month = jun, year = "2003", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/779359.779363", abstract = "GloptiPoly is a Matlab/SeDuMi add-on to build and solve convex linear matrix inequality relaxations of the (generally non-convex) global optimization problem of minimizing a multivariable polynomial function subject to polynomial inequality, equality or integer constraints. It generates a series of lower bounds monotonically converging to the global optimum without any problem splitting. Global optimality is detected and isolated optimal solutions are extracted automatically. Numerical experiments show that for most of the small-scale problems described in the literature, the global optimum is reached at low computational cost.", } @Article{Sarra:2003:SSP, author = "Scott A. Sarra", title = "The Spectral Signal Processing Suite", journal = j-TOMS, volume = "29", number = "2", pages = "195--217", month = jun, year = "2003", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/779359.779364", abstract = "A software suite written in the Java programming language for the postprocessing of Chebyshev approximations to discontinuous functions is presented. It is demonstrated how to use the package to remove the effects of the Gibbs-Wilbraham phenomenon from Chebyshev approximations of discontinuous functions. Additionally, the package is used to postprocess Chebyshev collocation and Chebyshev super spectral viscosity approximations of hyperbolic partial differential equations. The postprocessing method is the Gegenbauer reconstruction procedure. The Spectral Signal Processing Suite is the first publicly available package that implements the procedure. State of the art techniques are used to implement the algorithms with efficiency while reducing round-off error.", } @Article{Quintana-Orti:2003:FDA, author = "Enrique S. Quintana-Ort\'{i} and Robert A. van de Geijn", title = "Formal Derivation of Algorithms: The Triangular {Sylvester} Equation", journal = j-TOMS, volume = "29", number = "2", pages = "218--243", month = jun, year = "2003", CODEN = "ACMSCU", ISSN = "0098-3500", URL = "http://doi.acm.org/10.1145/779359.779365", abstract = "In this paper we apply a formal approach for the derivation of dense linear algebra algorithms to the triangular Sylvester equation. The result is a large family of provably correct algorithms. By using a coding style that reflects the algorithms as they are naturally presented, the correctness of the algorithms carries through to the correctness of the implementations. Analytically motivated heuristics are used to subsequently choose members from the family that can be expected to yield high performance. Finally, we report performance on the Intel (R) Pentium (R) III processor that is competitive with that of recursive algorithms reported previously in the literature for this operation.", } @Article{Martins:2003:CSD, author = "Joaquim R. R. A. Martins and Peter Sturdza and Juan J. Alonso", title = "The Complex-Step Derivative Approximation", journal = j-TOMS, volume = "29", number = "3", pages = "245--262", month = sep, year = "2003", URL = "http://doi.acm.org/10.1145/838250.838251", abstract = "The complex-step derivative approximation and its application to numerical algorithms are presented. Improvements to the basic method are suggested that further increase its accuracy and robustness and unveil the connection to algorithmic differentiation theory. A general procedure for the implementation of the complex-step method is described in detail and a script is developed that automates its implementation. Automatic implementations of the complex-step method for Fortran and C/C++ are presented and compared to existing algorithmic differentiation tools. The complex-step method is tested in two large multidisciplinary solvers and the resulting sensitivities are compared to results given by finite differences. The resulting sensitivities are shown to be as accurate as the analyses. Accuracy, robustness, ease of implementation and maintainability make these complex-step derivative approximation tools very attractive options for sensitivity analysis.", } @Article{Eble:2003:ASP, author = "Ingo Eble and Markus Neher", title = "ACETAF: A Software Package for Computing Validated Bounds for {Taylor} Coefficients of Analytic Functions", journal = j-TOMS, volume = "29", number = "3", pages = "263--286", month = sep, year = "2003", URL = "http://doi.acm.org/10.1145/838250.838252", abstract = "This paper presents methods for practical computation of verified bounds for Taylor coefficients of analytic functions. These bounds are constructed from Cauchy's estimate and from some of its modifications. Interval arithmetic is used to obtain rigorous results.", } @Article{Cools:2003:ACP, author = "Ronald Cools and Ann Haegemans", title = "Algorithm 824: CUBPACK: A Package for Automatic Cubature; Framework Description", journal = j-TOMS, volume = "29", number = "3", pages = "287--296", month = sep, year = "2003", URL = "http://doi.acm.org/10.1145/838250.838253", abstract = "The aim of CUBPACK is to offer a collection of re-usable code for automatic n-dimensional ($n \ge 1$) numerical integration of functions over a collection of regions, i.e., quadrature and cubature. The current version allows that this region consists of a union of n-simplices and n-parellellepids. In this text the framework of CUBPACK is described as well as its user interface. The functionality of several well known routines is embedded. New features include integration algorithms using the epsilon-algorithm for extrapolation for regions other than triangles and the implementation of a new type of subdivision for 3-cubes.", } @Article{Genz:2003:ANC, author = "Alan Genz and Ronald Cools", title = "An Adaptive Cubature Algorithm for Simplices", journal = j-TOMS, volume = "29", number = "3", pages = "297--308", month = sep, year = "2003", URL = "http://doi.acm.org/10.1145/838250.838254", abstract = "A globally adaptive algorithm for numerical multiple cubature of a vector of functions over a collection of n-dimensional simplices is described. The algorithm is based on a subdivision strategy that chooses for subdivision at each stage the subregion (of the input simplices) with the largest estimated error. This subregion is divided into two, three or four equal volume subregions by cutting selected edges. These edges are selected using information about the smoothness of the integrands in the edge directions. The algorithm allows a choice from several imbedded cubature rule sequences for approximate integration and error estimation. A Fortran 90 implementation as part of CUBPACK is also discussed. Testing of the algorithm is described.", } @Article{Shellman:2003:ADC, author = "Spenser Shellman and K. Sikorski", title = "Algorithm 825: A Deep-Cut Bisection Envelope Algorithm for Fixed Points", journal = j-TOMS, volume = "29", number = "3", pages = "309--325", month = sep, year = "2003", URL = "http://doi.acm.org/10.1145/838250.838255", abstract = "We present the BEDFix (Bisection Envelope Deep-cut Fixed point) algorithm for the problem of approximating a fixed point of a function on a two-dimensional domain. The function is assumed Lipschitz continuous with respect to the infinity norm, with constant 1. The computed approximation satisfies a residual criterion given a specified tolerance. The BEDFix algorithm improves the BEFix algorithm presented in [Shellman and Sikorski 2001] by utilizing ``deep cuts'', that is, eliminating additional segments of the feasible domain which cannot contain a fixed point. The upper bound on the number of required function evaluations is the same for BEDFix and BEFix, but our numerical tests indicate that BEDFix significantly improves the average-case performance. In addition we show how BEDFix may be used to solve the absolute criterion fixed point problem with significantly better performance than the simple iteration method, when the Lipschitz constant is less than but close to 1.", } @Article{Fahey:2003:APE, author = "Mark R. Fahey", title = "Algorithm 826: A Parallel Eigenvalue Routine for Complex {Hessenberg} Matrices", journal = j-TOMS, volume = "29", number = "3", pages = "326--336", month = sep, year = "2003", URL = "http://doi.acm.org/10.1145/838250.838256", abstract = "A code for computing the eigenvalues of a complex Hessenberg matrix is presented. This code computes the Schur decomposition of a complex Hessenberg matrix. Together with existing ScaLAPACK routines, the eigenvalues of dense complex matrices can be directly computed using a parallel QR algorithm.This parallel complex Schur decomposition routine was developed to fill a void in the ScaLAPACK library and was based on the parallel real Schur decomposition routine already in ScaLAPACK. The real-arithmetic version was appropriately modified to make it work with complex arithmetic and implement a complex multiple bulge QR algorithm. This also required the development of new auxiliary routines that perform essential operations for the complex Schur decomposition, and that will provide additional linear algebra computation capability to the parallel numerical library community.", } @Article{Baglama:2003:AIM, author = "J. Baglama and D. Calvetti and L. Reichel", title = "Algorithm 827: irbleigs: A {MATLAB} Program for Computing a Few Eigenpairs of a Large Sparse {Hermitian} Matrix", journal = j-TOMS, volume = "29", number = "3", pages = "337--348", month = sep, year = "2003", URL = "http://doi.acm.org/10.1145/838250.838257", abstract = "irbleigs is a MATLAB program for computing a few eigenvalues and associated eigenvectors of a sparse Hermitian matrix of large order $n$. The matrix is accessed only through the evaluation of matrix-vector products. Working space of only a few $n$-vectors is required. The program implements a restarted block-Lanczos method. Judicious choices of acceleration polynomials make it possible to compute approximations of a few of the largest eigenvalues, a few of the smallest eigenvalues, or a few eigenvalues in the vicinity of a user-specified point on the real axis. irbleigs also can be applied to certain large generalized eigenproblems as well as to the computation of a few nearby singular values and associated right and left singular vectors of a large general matrix.", } @Article{Hopkins:2003:RAS, author = "Tim Hopkins", title = "Remark on Algorithm 769: {Fortran} Subroutines for Approximate Solution of Sparse Quadratic Assignment Problems Using {GRASP}", journal = j-TOMS, volume = "29", number = "3", pages = "349--351", month = sep, year = "2003", URL = "http://doi.acm.org/10.1145/838250.838258", abstract = "We present a number of corrections and improvements to Algorithm 769.", } @Article{Gould:2003:GLT, author = "Nicholas I. M. Gould and Dominique Orban and Philippe L. Toint", title = "{GALAHAD}, a Library of Thread-safe {Fortran} 90 Packages for Large-Scale Nonlinear Optimization", journal = j-TOMS, volume = "29", number = "4", month = dec, year = "2003", pages = "353--372", URL = "http://doi.acm.org/10.1145/962437.962438", abstract = "We describe the design of version 1.0 of GALAHAD, a library of Fortran 90 packages for large-scale nonlinear optimization. The library particularly addresses quadratic programming problems, containing both interior point and active set algorithms, as well as tools for preprocessing problems prior to solution. It also contains an updated version of the venerable nonlinear programming package LANCELOT", } @Article{Gould:2003:CSC, author = "Nicholas I. M. Gould and Dominique Orban and Philippe L. Toint", title = "{CUTEr} and {SifDec}: A Constrained and Unconstrained Testing Environment, revisited", journal = j-TOMS, volume = "29", number = "4", month = dec, year = "2003", pages = "373--394", URL = "http://doi.acm.org/10.1145/962437.962439", abstract = "The initial release of CUTE, a widely used testing environment for optimization software, was described by Bongartz, {\em et al.} in~1995. A new version, now known as CUTEr, is presented. Features include reorganisation of the environment to allow simultaneous multi-platform installation, new tools for, and interfaces to, optimization packages, and a considerably simplified and entirely automated installation procedure for UNIX systems. The environment is fully backward compatible with its predecessor, and offers support for Fortran~90/95 and a general C++ Application Programming Interface. The SIF decoder, formerly a part of CUTE, has become a separate tool, easily callable by various packages. It features simple extensions to the SIF test problem format and the generation of files suited to automatic differentiation packages.", } @Article{Scott:2003:PFS, author = "Jennifer A. Scott", title = "Parallel Frontal Solvers for Large Sparse Linear Systems", journal = j-TOMS, volume = "29", number = "4", month = dec, year = "2003", pages = "395--417", URL = "http://doi.acm.org/10.1145/962437.962440", abstract = "Many applications in science and engineering give rise to large sparse linear systems of equations that need to be solved as efficiently as possible. As the size of the problems of interest increases, it can become necessary to consider exploiting multiprocessors to solve these systems. We report on the design and development of parallel frontal solvers for the numerical solution of large sparse linear systems. Three codes have been developed for the mathematical software library HSL (www.cse.clrc.ac.uk/Activity/HSL). The first is for unsymmetric finite-element problems; the second is for symmetric positive definite finite-element problems; and the third is for highly unsymmetric linear systems such as those that arise in chemical process engineering. In each case, the problem is subdivided into a small number of loosely connected subproblems and a frontal method is then applied to each of the subproblems in parallel. We discuss how our software is designed to achieve the goals of portability, ease of use, efficiency, and flexibility, and illustrate the performance using problems arising from real applications.", } @Article{Bradbury:2003:FCS, author = "Emma L. Bradbury and Wayne H. Enright", title = "Fast Contouring of Solutions to Partial Differential Equations", journal = j-TOMS, volume = "29", number = "4", month = dec, year = "2003", pages = "418--439", URL = "http://doi.acm.org/10.1145/962437.962441", abstract = "The application of Differential Equation Interpolants (DEIs) to the visualization of the solutions to Partial Differential Equations (PDEs) is investigated. In particular, we describe how a DEI can be used to generate a fine mesh approximation from a coarse mesh approximation; this fine mesh approximation can then be used by a standard contouring function to render an accurate contour plot of the surface. However, the standard approach has a time complexity equivalent to that of rendering a surface plot, $O(fm^2)$ for each element of the coarse mesh, (where $fm$ is the ratio of the width of the coarse mesh to the fine mesh). To address this concern three fast contouring algorithms are proposed that compute accurate contour lines directly from the DEI, and have time complexity at most $O(fm)$ for each coarse mesh element.", } @Article{Buecker:2003:MPI, author = "H. Martin B\"{u}cker and Arno Rasch", title = "Modeling the Performance of Interface Contraction", journal = j-TOMS, volume = "29", number = "4", month = dec, year = "2003", pages = "440--457", URL = "http://doi.acm.org/10.1145/962437.962442", abstract = "Automatic differentiation is a technique used to transform a computer code implementing some mathematical function into another program capable of evaluating the function and its derivatives. Compared to numerical differentiation, the derivatives obtained from applying automatic differentiation are free from truncation error, and their computation often requires less time. To increase the efficiency of a black box approach of automatic differentiation, a technique called interface contraction may be used. Interface contraction exploits the local structure of a code to temporarily reduce the global number of derivatives propagated through the code. Two performance models are introduced to predict the potential improvement in the execution time of a program making use of interface contraction compared to a program generated by a black box approach of automatic differentiation. The performance models are validated by numerical experiments carried out on different computing platforms. The computer codes used in the experiments stem from the application areas of neutron scattering and biostatistics.", } @Article{Renka:2003:ADD, author = "Robert J. Renka", title = "Algorithm 828: {DNSPLIN1}: Discrete Nonlinear Spline Interpolation", journal = j-TOMS, volume = "29", number = "4", month = dec, year = "2003", pages = "458--468", URL = "http://doi.acm.org/10.1145/962437.962443", abstract = "We describe a new method and a Fortran-77 code for constructing discrete approximations to nonparametric interpolating nonlinear spline curves. Our approach consists of minimizing the discretized strain energy by a descent method with a Sobolev gradient in place of the standard gradient. It serves as a demonstration of the Sobolev gradient method which is much more generally applicable. The effectiveness of the method in rapidly producing smooth interpolatory curves is demonstrated by test results for several challenging data sets.", } @Article{Gaviano:2003:ASG, author = "Marco Gaviano and Dmitri E. Kvasov and Daniela Lera and Yaroslav D. Sergeyev", title = "Algorithm 829: Software for Generation of Classes of Test Functions with Known Local and Global Minima for Global Optimization", journal = j-TOMS, volume = "29", number = "4", month = dec, year = "2003", pages = "469--480", URL = "http://doi.acm.org/10.1145/962437.962444", abstract = "A procedure for generating non-differentiable, continuously differentiable, and twice continuously differentiable classes of test functions for multiextremal multidimensional box-constrained global optimization is presented. Each test class consists of 100 functions. Test functions are generated by defining a convex quadratic function systematically distorted by polynomials in order to introduce local minima. To determine a class, the user defines the following parameters: (i)~problem dimension, (ii)~number of local minima, (iii)~value of the global minimum, (iv)~radius of the attraction region of the global minimizer, (v)~distance from the global minimizer to the vertex of the quadratic function. Then, all other necessary parameters are generated randomly for all 100 functions of the class. Full information about each test function including locations and values of all local minima is supplied to the user. Partial derivatives are also generated where possible.", } @Article{Gonzalez-Pinto:2004:TSE, author = "S. Gonz\'{a}lez-Pinto and J.I. Montijano and S. P\'{e}rez-Rodr\'{i}guez", title = "Two-Step Error Estimators for Implicit {Runge-Kutta} Methods Applied to Stiff Systems", journal = j-TOMS, volume = "30", number = "1", month = mar, year = "2004", pages = "1--18", URL = "http://doi.acm.org/10.1145/974781.974782", abstract = "This paper is concerned with local error estimation in the numerical integration of stiff systems of ordinary differential equations by means of Runge-Kutta methods. With implicit Runge-Kutta methods it is often difficult to embed a local error estimate with the appropriate order and stability properties. In this paper local error estimation based on the information from the last two integration steps (that are supposed to have the same steplength) is proposed. It is shown that this technique, applied to Radau IIA methods, let us get estimators with proper order and stability properties. Numerical examples showing that the proposed estimate improves the efficiency of the integration codes are presented.", } @Article{Rotkin:2004:DIN, author = "Vladimir Rotkin and Sivan Toledo", title = "The Design and Implementation of a New Out-of-Core Sparse {Cholesky} Factorization Method", journal = j-TOMS, volume = "30", number = "1", month = mar, year = "2004", pages = "19--46", URL = "http://doi.acm.org/10.1145/974781.974783", abstract = "We describe a new out-of-core sparse Cholesky factorization method. The new method uses the elimination tree to partition the matrix, uses an advanced subtree-scheduling algorithm, and utilizes both right-looking and left-looking updates. The implementation of the new method is efficient and robust. On a 2~GHz personal computer with 768~MB of main memory, the code can easily factor matrices with factors of up to 48~GB, usually at rates above 1~Gflop/s. For example, the code can factor \textsc{audikw}, currenly the largest matrix in any matrix collection (factor size over 10~GB), in a little over an hour, and can factor a matrix whose graph is a 140-by-140-by-140 mesh in about 12 hours (factor size around 27~GB).", } @Article{Vaz:2004:ASS, author = "A. Ismael F. Vaz and Edite M. G. P. Fernandez and M. Paula S. F. Gomez", title = "{SIPAMPL}: Semi-Infinite Programming with {AMPL}", journal = j-TOMS, volume = "30", number = "1", month = mar, year = "2004", pages = "47--61", URL = "http://doi.acm.org/10.1145/974781.974784", abstract = "SIPAMPL is an environment for coding semi-infinite programming (SIP) problems. This environment includes a database containing a set of SIP problems that have been collected from the literature and a set of routines. It allows users to code their own SIP problems in AMPL, to use any problem already in the database, and to develop and test any SIP solver. The SIPAMPL routines support the interface between a potential SIP solver and test problems coded in AMPL. SIPAMPL also provides a tool that allows the selection of problems from the database with specified characteristics. As a concept demonstration, we show how MATLAB can use SIPAMPL to solve the problems in the database. The Linux and Microsoft Windows versions together with the database of coded problems are freely available via the web.", } @Article{Bartlett:2004:VRT, author = "Roscoe A. Bartlett and Bart G. Van Bloemen Waanders and Michael A. Heroux", title = "Vector Reduction/Transformation Operators", journal = j-TOMS, volume = "30", number = "1", month = mar, year = "2004", pages = "62--85", URL = "http://doi.acm.org/10.1145/974781.974785", abstract = "Development of flexible linear algebra interfaces is an increasingly critical issue. Efficient and expressive interfaces are well established for some linear algebra abstractions, but not for vectors. Vectors differ from other abstractions in the diversity of necessary operations, sometimes requiring dozens for a given algorithm (e.g. interior-point methods for optimization). We discuss a new approach based on operator objects that are transported to the underlying data by the linear algebra library implementation, allowing developers of abstract numerical algorithms to easily extend the functionality regardless of computer architecture, application or data locality/organization. Numerical experiments demonstrate efficient implementation.", } @Article{Hanson:2004:AAV, author = "R. J. Hanson and Tim Hopkins", title = "Algorithm 830: Another Visit with Standard and Modified {Givens} Transformations and a Remark on {Algorithm} 539 ", journal = j-TOMS, volume = "30", number = "1", month = mar, year = "2004", pages = "86--94", URL = "http://doi.acm.org/10.1145/974781.974786", abstract = "First we report on a correction and improvement to the Level 1 Blas routine {\tt srotmg} for computing the Modified Givens Transformation (MG). We then, in the light of the performance of the code on modern compiler/hardware combinations, reconsider the strategy of supplying separate routines to compute and apply the transformation. Finally, we show that the apparent savings in multiplies obtained by using MG rather than the Standard Givens Transformation (SG) do not always translate into reductions in execution time.", } @Article{Scott:2004:PDS, author = "Jennifer A. Scott and Iain S. Duff", title = "A Parallel Direct Solver for Large Sparse Highly Unsymmetric Linear Systems", journal = j-TOMS, volume = "30", number = "2", month = jun, year = "2004", pages = "95--117", URL = "http://doi.acm.org/10.1145/992200.992201", abstract = "The need to solve large sparse linear systems of equations efficiently lies at the heart of many applications in computational science and engineering. For very large systems when using direct factorization methods of solution, it can be beneficial and sometimes necessary to use multiple processors, because of increased memory availability as well as reduced factorization time. We report on the development of a new parallel code that is designed to solve linear systems with a highly unsymmetric sparsity structure using a modest number of processors (typically up to about 16). The problem is first subdivided into a number of loosely connected subproblems and a variant of sparse Gaussian elimination is then applied to each of the subproblems in parallel. An interface problem in the variables on the boundaries of the subproblems must also be factorized. We discuss how our software is designed to achieve the goals of portability, ease of use, fficiency, and flexibility, and illustrate its performance on an SGI Origin 2000, a Cray T3E, and a 2-processor Compaq DS20, using problems arising from real applications.", } @Article{Duff:2004:MCS, author = "Iain S. Duff", title = "MA57 --- A Code for the Solution of Sparse Symmetric Definite and Indefinite Systems", journal = j-TOMS, volume = "30", number = "2", month = jun, year = "2004", pages = "118--144", URL = "http://doi.acm.org/10.1145/992200.992202", abstract = "We introduce a new code for the direct solution of sparse symmetric linear equations that solves indefinite systems with $2 \times 2$ pivoting for stability. This code, called {\tt MA57}, is in HSL 2002 and supersedes the well used HSL code {\tt MA27}. We describe some of the implementation details and emphasize the novel features of {\tt MA57}. These include restart facilities, matrix modification, partial solution for matrix factors, solution of multiple right-hand sides, and iterative refinement and error analysis. The code is written in Fortran 77, but there are additional facilities within a Fortran 90 implementation that include the ability to identify and change pivots. Several of these facilities have been developed particularly to support optimization applications, and we illustrate the performance of the code on problems arising therefrom.", } @Article{Gil:2004:CSM, author = "Amparo Gil and Javier Segura and Nico M. Temme", title = "Computing Solutions of the Modified {Bessel} Differential Equation for Imaginary Orders and Positive Arguments", journal = j-TOMS, volume = "30", number = "2", month = jun, year = "2004", pages = "145--158", URL = "http://doi.acm.org/10.1145/992200.992203", abstract = " We describe a variety of methods to compute the functions $K_{ia}(x)$, $L_{ia}(x)$ and their derivatives for real $a$ and positive $x$. These functions are numerically satisfactory independent solutions of the differential equation $x^2 w'' + xw' + (a^2 - x^2)w = 0$. In the accompanying paper [Gil et al. 2004], we describe the implementation of these methods in Fortran 77 codes.", } @Article{Gil:2004:AMB, author = "Amparo Gil and Javier Segura and Nico M. Temme", title = "Algorithm 831: Modified {Bessel} Functions of Imaginary Order and Positive Argument", journal = j-TOMS, volume = "30", number = "2", month = jun, year = "2004", pages = "159--164", URL = "http://doi.acm.org/10.1145/992200.992204", abstract = "Fortran 77 programs for the computation of modified Bessel functions of purely imaginary order are presented. The codes compute the functions $K_{ia}(x)$, $L_{ia}(x)$ and their derivatives for real $a$ and positive $x$; these functions are independent solutions of the differential equation $x^2w'' + xw' + (a^2 - x^2)w = 0$. The code also computes exponentially scaled functions. The range of computation is $(x, a) \in (0,1500] \cross [1500, 1500]$ when scaled functions are considered and it is larger than $(0,500] \cross [400, 400]$ for standard IEEE double precision arithmetic. The relative accuracy is better than $10^{-13}$ in the range $(0,200] \cross [200, 200]$ and close to $10^{-12} in $(0, 1500] \cross [1500, 1500]$.", } @Article{Davis:2004:CPS, author = "Timothy A. Davis", title = "A Column Pre-Ordering Strategy for the Unsymmetric-Pattern Multifrontal Method", journal = j-TOMS, volume = "30", number = "2", month = jun, year = "2004", pages = "165--195", URL = "http://doi.acm.org/10.1145/992200.992205", abstract = "A new method for sparse LU factorization is presented that combines a column pre-ordering strategy with a right-looking unsymmetric-pattern multifrontal numerical factorization. The column ordering is selected to give a good a priori upper bound on fill-in and then refined during numerical factorization (while preserving the bound). Pivot rows are selected to maintain numerical stability and to preserve sparsity. The method analyzes the matrix and automatically selects one of three pre-ordering and pivoting strategies. The number of nonzeros in the LU factors computed by the method is typically less than or equal to those found by a wide range of unsymmetric sparse LU factorization methods, including left-looking methods and prior multifrontal methods.", } @Article{Davis:2004:AUU, author = "Timothy A. Davis", title = "Algorithm 832: UMFPACK --- an Unsymmetric-Pattern Multifrontal Method", journal = j-TOMS, volume = "30", number = "2", month = jun, year = "2004", pages = "196--199", URL = "http://doi.acm.org/10.1145/992200.992206", abstract = "An ANSI C code for sparse LU factorization is presented that combines a column pre-ordering strategy with a right-looking unsymmetric-pattern multifrontal numerical factorization. The pre-ordering and symbolic analysis phase computes an upper bound on fill-in, work, and memory usage during the subsequent numerical factorization. User-callable routines are provided for ordering and analyzing a sparse matrix, computing the numerical factorization, solving a system with the LU factors, transposing and permuting a sparse matrix, and converting between sparse matrix representations. The simple user interface shields the user from the details of the complex sparse factorization data structures by returning simple handles to opaque objects. Additional user-callable routines are provided for printing and extracting the contents of these opaque objects. An even simpler way to use the package is through its MATLAB interface. UMFPACK is incorporated as a built-in operator in MATLAB 6.5 as {\tt x = A}$\backslash${\tt b} when {\tt A} is sparse and unsymmetric.", } @Article{Renka:2004:ACI, author = "Robert J. Renka", title = "Algorithm 833: {CSRFPACK} --- Interpolation of Scattered Data with a $C^1$ Convexity-preserving Surface", journal = j-TOMS, volume = "30", number = "2", month = jun, year = "2004", pages = "200--211", URL = "http://doi.acm.org/10.1145/992200.992207", abstract = "We describe a Fortran-77 software package for constructing a $C^1$ convex surface that interpolates a convex data set consisting of data values at arbitrarily distributed points in the plane (nodes) such that there exists a triangulation of the nodes for which the triangle-based piecewise linear interpolant is convex. The method consists of constructing this data-dependent triangulation, computing a set of nodal gradients for which there exists a convex piecewise linear Hermite interpolant $H$ of the nodal values and gradients, and applying convolution smoothing to $H$.", } @Article{Renka:2004:AGI, author = "Robert J. Renka", title = "Algorithm 834: glsurf --- An Interactive Surface Plotting Program using {OpenGL}", journal = j-TOMS, volume = "30", number = "2", month = jun, year = "2004", pages = "212--217", URL = "http://doi.acm.org/10.1145/992200.992208", abstract = "We describe an interactive surface visualization tool implemented in C, OpenGL, and GLUT. The surface is represented by a set of triangles in Euclidean 3-space, thus allowing for unrestricted topology. Capabilities include color-filled contour plots (for the graph of a bivariate function) and surface perspective plots with lighting and smooth shading. Interactive zooms and axis rotations are executed with a single keypress or mouse motion. The advantage of this code over the many alternatives is that it is small, simple, portable, easy to install and use, and the source code is available if the user wishes to change defaults, add light sources, or whatever.", } @Article{Zeng:2004:AMM, author = "Zhonggang Zeng", title = "Algorithm 835: MultRoot --- A {Matlab} Package for Computing Polynomial Roots and Multiplicities", journal = j-TOMS, volume = "30", number = "2", month = jun, year = "2004", pages = "218--236", URL = "http://doi.acm.org/10.1145/992200.992209", abstract = "MultRoot is a collection of Matlab modules for accurate computation of polynomial roots, especially roots with non-trivial multiplicities. As a blackbox-type software, MultRoot requires the polynomial coe cients as the only input, and outputs the computed roots, multiplicities, backward error, estimated forward error, as well as the structure preserving condition number. The most significant features of MultRoot are the multiplicity identification capability and high accuracy on multiple roots without using the multiprecision arithmetic, even if the polynomial coefficients are inexact. A comprehensive test suite of polynomials that are collected from the literature is included for numerical experiments and performance comparison.", } @Article{Matthey:2004:POF, author = "Thierry Matthey and Trevor Cickovski and Scott Hampton and Alice Ko and Qun Ma and Matthew Nyerges and Troy Raeder and Thomas Slabach and Jes\'{u}s A. Izaguirre ", title = "ProtoMol, an Object-Oriented Framework for Prototyping Novel Algorithms for Molecular Dynamics", journal = j-TOMS, volume = "30", number = "3", month = sep, year = "2004", pages = "237--265", URL = "http://doi.acm.org/10.1145/1024074.1024075", abstract = "ProtoMol is a high-performance framework in C++ for rapid prototyping of novel algorithms for molecular dynamics and related applications. Its flexibility is achieved primarily through the use of inheritance and design patterns (object-oriented programming). Performance is obtained by using templates that enable generation of efficient code for sections critical to performance (generic programming). The framework encapsulates important optimizations that can be used by developers, such as parallelism in the force computation. Its design is based on domain analysis of numerical integrators for molecular dynamics (MD) and of fast solvers for the force computation, particularly due to electrostatic interactions. Several new and efficient algorithms are implemented in ProtoMol. Finally, it is shown that ProtoMol's sequential performance is excellent when compared to a leading MD program, and that it scales well for moderate number of processors. Binaries and source codes for Windows, Linux, Solaris, IRIX, HP-UX, and AIX platforms are available under open source license at \texttt{\scriptsize http://protomol.sourceforge.net}.", } @Article{Forth:2004:JCG, author = "Shaun A. Forth and Mohamed Tadjouddine and John D. Pryce and John K. Reid", title = "Jacobian Code Generated by Source Transformation and Vertex Elimination can be as Efficient as Hand-Coding", journal = j-TOMS, volume = "30", number = "3", month = sep, year = "2004", pages = "266--299", URL = "http://doi.acm.org/10.1145/1024074.1024076", abstract = "This paper presents the first extended set of results from EliAD, a source-transformation implementation of the vertex-elimination Automatic Differentiation approach to calculating the Jacobians of functions defined by Fortran code (Griewank and Reese, Automatic Differentiation of Algorithms: Theory, Implementation, and Application, 1991, pp. 126-135). We introduce the necessary theory in terms of well known algorithms of numerical linear algebra applied to the linear, extended Jacobian system that prescribes their relationship between the derivatives of all variables in the function code. Using an example, we highlight the potential for numerical instability in vertex-elimination. We describe the source transformation implementation of our tool EliAD and present results from 5 test cases, 4 of which are taken from the MINPACK-2 collection (Averick et al, Report ANL/MCS-TM-150, 1992) and for which hand-coded Jacobian codes are available. On 5 computer/compiler platforms, we show that the Jacobian code obtained by EliAD is as efficient as hand-coded Jacobian code. It is also between 2 to 20 times more efficient than that produced by current, state of the art, Automatic Differentiation tools even when such tools make use of sophisticated techniques such as sparse Jacobian compression. We demonstrate the effectiveness of reverse-ordered pre-elimination from the (successively updated) extended Jacobian system of all intermediate variables used once. Thereafter, the monotonic forward/reverse ordered eliminations of all other intermediates is shown to be very efficient. On only one test case were orderings determined by the Markowitz or related VLR heuristics found superior. A re-ordering of the statements of the Jacobian code, with the aim of reducing reads and writes of data from cache to registers, was found to have mixed effects but could be very beneficial.", } @Article{Gould:2004:NEH, author = "Nicholas I. M. Gould and Jennifer A. Scott", title = "A Numerical Evaluation of {HSL} Packages for the Direct Solution of Large Sparse, Symmetric Linear Systems of Equations", journal = j-TOMS, volume = "30", number = "3", month = sep, year = "2004", pages = "300--325", URL = "http://doi.acm.org/10.1145/1024074.1024077", abstract = "In recent years a number of new direct solvers for the solution of large sparse, symmetric linear systems of equations have been added to the mathematical software library HSL. These include solvers that are designed for the solution of positive-definite systems as well as solvers that are principally intended for solving indefinite problems. The available choice can make it difficult for users to know which solver is the most appropriate for their use. In this study, we use performance profiles as a tool for evaluating and comparing the performance of the HSL solvers on an extensive set of test problems taken from a range of practical applications.", } @Article{Bai:2004:BTE, author = "Yihua Bai and Wilfried N. Gansterer and Robert C. Ward", title = "Block Tridiagonalization of ``Effectively'' Sparse Symmetric Matrices", journal = j-TOMS, volume = "30", number = "3", month = sep, year = "2004", pages = "326--352", URL = "http://doi.acm.org/10.1145/1024074.1024078", abstract = "A block tridiagonalization algorithm is proposed for transforming a sparse (or effectively sparse) symmetric matrix into a related block tridiagonal matrix, such that the eigenvalue error remains bounded by some prescribed accuracy tolerance. It is based on a heuristic for imposing a block tridiagonal structure on matrices with a large percentage of zero or effectively zero (with respect to the given accuracy tolerance) elements. In the light of a recently developed block tridiagonal divide-and-conquer eigensolver [Gansterer, Ward, Muller, and Goddard, III, SIAM J. Sci. Comput. 25 (2003), pp. 65-85], for which block tridiagonalization may be needed as a preprocessing step, the algorithm also provides an option for attempting to produce at least a few very small diagonal blocks in the block tridiagonal matrix. This leads to low time complexity of the last merging operation in the block divide-and-conquer method. Numerical experiments are presented and various block tridiagonalization strategies are compared.", } @Article{Davis:2004:CAM, author = "Timothy A. Davis and John R. Gilbert and Stefan I. Larimore and Esmond G. Ng", title = "A Column Approximate Minimum Degree Ordering Algorithm", journal = j-TOMS, volume = "30", number = "3", month = sep, year = "2004", pages = "353--376", URL = "http://doi.acm.org/10.1145/1024074.1024079", abstract = "Sparse Gaussian elimination with partial pivoting computes the factorization $\m{PAQ}=\m{LU}$ of a sparse matrix $\m{A}$, where the row ordering $\m{P}$ is selected during factorization using standard partial pivoting with row interchanges. The goal is to select a column preordering, $\m{Q}$, based solely on the nonzero pattern of $\m{A}$, that limits the worst-case number of nonzeros in the factorization. The fill-in also depends on $\m{P}$, but $\m{Q}$ is selected to reduce an upper bound on the fill-in for any subsequent choice of $\m{P}$. The choice of $\m{Q}$ can have a dramatic impact on the number of nonzeros in $\m{L}$ and $\m{U}$. One scheme for determining a good column ordering for $\m{A}$ is to compute a symmetric ordering that reduces fill-in in the Cholesky factorization of $\m{A}\tr\m{A}$. A conventional minimum degree ordering algorithm would require the sparsity structure of $\m{A}\tr\m{A}$ to be computed, which can be expensive both in terms of space and time since $\m{A}\tr\m{A}$ may be much denser than $\m{A}$. An alternative is to compute $\m{Q}$ directly from the sparsity structure of $\m{A}$; this strategy is used by MATLAB's COLMMD preordering algorithm. A new ordering algorithm, COLAMD, is presented. It is based on the same strategy but uses a better ordering heuristic. COLAMD is faster and computes better orderings, with fewer nonzeros in the factors of the matrix.", } @Article{Davis:2004:ACC, author = "Timothy A. Davis and John R. Gilbert and Stefan I. Larimore and Esmond G. Ng", title = "Algorithm 836: {COLAMD}, a Column Approximate Minimum Degree Ordering Algorithm", journal = j-TOMS, volume = "30", number = "3", month = sep, year = "2004", pages = "377--380", URL = "http://doi.acm.org/10.1145/1024074.1024080", abstract = "Two codes are discussed, COLAMD and SYMAMD, that compute approximate minimum degree orderings for sparse matrices in two contexts: (1) sparse partial pivoting, which requires a sparsity preserving column pre-ordering prior to numerical factorization, and (2) sparse Cholesky factorization, which requires a symmetric permutation of both the rows and columns of the matrix being factorized. These orderings are computed by COLAMD and SYMAMD, respectively. The ordering from COLAMD is also suitable for sparse QR factorization, and the factorization of matrices of the form $\m{A}\tr\m{A}$ and $\m{AA}\tr$, such as those that arise in least-squares problems and interior point methods for linear programming problems. The two routines are available both in MATLAB and C-callable forms. They appear as built-in routines in MATLAB Version 6.0.", } @Article{Amestoy:2004:AAA, author = "Patrick Amestoy and Timothy Davis and Iain Duff", title = "Algorithm 837: {AMD}, an Approximate Minimum Degree Ordering Algorithm", journal = j-TOMS, volume = "30", number = "3", month = sep, year = "2004", pages = "381--388", URL = "http://doi.acm.org/10.1145/1024074.1024081", abstract = "AMD is a set of routines that implements the approximate minimum degree ordering algorithm to permute sparse matrices prior to numerical factorization. There are versions written in both C and Fortran 77. A MATLAB interface is included.", } @Article{Priest:2004:ISC, author = "Douglas M. Priest", title = "Efficient Scaling for Complex Division", journal = j-TOMS, volume = "30", number = "4", month = dec, pages = "389--401", year = "2004", URL = "http://doi.acm.org/10.1145/1039813.1039814", abstract = "We develop a simple method for scaling to avoid overflow and harmful underflow in complex division. The method guarantees that no overflow will occur unless at least one component of the quotient must overflow, and otherwise the normwise error in the computed result is at most a few units in the last place. Moreover, the scaling requires only four floating point multiplications and a small amount of integer arithmetic to compute the scale factor. Thus, on many modern CPUs, our method is both safer and faster than Smith's widely used algorithm.", } @Article{Nievergelt:2004:AAP, author = "Yves Nievergelt", title = "Analysis and Applications of Priest's Distillation", journal = j-TOMS, volume = "30", number = "4", month = dec, year = "2004", pages = "402--433", URL = "http://doi.acm.org/10.1145/1039813.1039815", abstract = "Correcting an infinite loop in Douglas M.Priest's renormalization algorithm, the theory proved here supports streamlined algorithms to resolve the tablemaker's dilemma for the floating point computation of real and complex sums and dot products, properly rounded to the ultimate digit. Applications include computations of areas, volumes, and intersections.", } @Article{Whittle:2004:AIK, author = "Jon Whittle and Johann Schumann", title = "Automating the Implementation of {Kalman} Filter Algorithms", journal = j-TOMS, volume = "30", number = "4", month = dec, pages = "434--453", year = "2004", URL = "http://doi.acm.org/10.1145/1039813.1039816", abstract = "{\sc autofilter} is a tool that generates implementations that solve state estimation problems using Kalman filters. From a high-level, mathematics-based description of a state estimation problem, {\sc autofilter} automatically generates code that computes a statistically optimal estimate using one or more of a number of well-known variants of the Kalman filter algorithm. The problem description may be given in terms of continuous or discrete, linear or nonlinear process and measurement dynamics. From this description, {\sc autofilter} automates many common solution methods (e.g., linearization, discretization) and generates C or Matlab code fully automatically. {\sc autofilter} surpasses toolkit-based programming approaches for Kalman filters because it requires no low-level programming skills (e.g., to ``glue'' together library function calls). {\sc autofilter} raises the level of discourse to the mathematics of the problem at hand rather than the details of what algorithms, data structures, optimizations etc. are required to implement it. An overview of {\sc autofilter} is given along with an example of its practical application to deep space attitude estimation.", } @Article{Wang:2004:BAC, author = "R. Wang and P. Keast and P. Muir", title = "{BACOL}: {B-spline Adaptive COLlocation} Software for 1-D Parabolic {PDEs}", journal = j-TOMS, volume = "30", number = "4", month = dec, year = "2004", pages = "454--470", URL = "http://doi.acm.org/10.1145/1039813.1039817", abstract = "BACOL is a new, high quality, robust software package in Fortran 77 for solving one-dimensional parabolic PDEs, which has been shown to be significantly more efficient than any other widely available software package of the same class (to our knowledge), especially for problems with solutions exhibiting rapid spatial variation. A novel feature of this package is that it employs high order, adaptive methods in both time and space, controlling and balancing both spatial and temporal error estimates. The software implements a spline collocation method at Gaussian points, with a B-spline basis, for the spatial discretization. The time integration is performed using a modification of the popular DAE solver, DASSL. Based on the computation of a second, higher order, global solution, a high quality {\em a posteriori} spatial error estimate is obtained after each successful time step. The spatial error is controlled by a sophisticated new mesh selection algorithm based on an equidistribution principle. In this paper we describe the overall structure of the BACOL package, and in particular the modifications to the DASSL package that improve its performance within BACOL. An example is provided in the Appendix to illustrate the use of the package.", } @Article{Fabijonas:2004:CCA, author = "B. R. Fabijonas and D. W. Lozier and F. W. J. Olver", title = "Computation of Complex {Airy} Functions and their Zeros using Asymptotics and the Differential Equation", journal = j-TOMS, volume = "30", number = "4", month = dec, year = "2004", pages = "471--490", URL = "http://doi.acm.org/10.1145/1039813.1039818", abstract = "We describe a method by which one can compute the solutions of Airy's differential equation, and their derivatives, both on the real line and in the complex plane. The computational methods are numerical integration of the differential equation and summation of asymptotic expansions for large argument. We give details involved in obtaining all of the parameter values, and we control the truncation errors rigorously. Using the same computational methods, we describe an algorithm which computes the zeros and associated values of the Airy functions and their derivatives, and the modulus and phase functions on the negative real axis.", } @Article{Fabijonas:2004:AAF, author = "B. R. Fabijonas", title = "Algorithm 838: {Airy} Functions", journal = j-TOMS, volume = "30", number = "4", month = dec, year = "2004", pages = "491--501", URL = "http://doi.acm.org/10.1145/1039813.1039819", abstract = "We present a Fortran 90 module which computes the solutions and their derivatives of Airy's differential equation, both on the real line and in the complex plane. The module also computes the zeros and associated values of the solutions and their derivatives, and the modulus and phase functions on the negative real axis. The computational methods are numerical integration of the differential equation and summation of asymptotic expansions for large argument. These methods were chosen because they are simple, adaptable to any precision, and amenable to rigorous error analysis. The module can be used to validate other codes or as a component in programs that require Airy functions.", } @Article{Kirby:2004:AFN, author = "Robert C. Kirby", title = "Algorithm 839: {FIAT}, A New Paradigm for Computing Finite Element Basis Functions", journal = j-TOMS, volume = "30", number = "4", month = dec, year = "2004", pages = "502--516", URL = "http://doi.acm.org/10.1145/1039813.1039820", abstract = "Much of finite element computation is constrained by the diffculty of evaluating high-order nodal basis functions. While most codes rely on explicit formulae for these basis functions, we present a new approach that allows us to construct a general class of finite element basis functions from orthonormal polynomials and evaluate and differentiate them at any points. This approach relies on fundamental ideas from linear algebra and is implemented in Python using several object-oriented and functional programming techniques.", } @Article{Bientinesi:2005:SDD, author = "Paolo Bientinesi and John A. Gunnels and Margaret E. Myers and Enrique S. Quintana-Ort\'{i} and Robert A. van de Geijn", title = "The Science of Deriving Dense Linear Algebra Algorithms", journal = j-TOMS, volume = "31", number = "1", month = mar, year = "2005", pages = "1--26", URL = "http://doi.acm.org/10.1145/1055531.1055532", abstract = "In this paper we present a systematic approach to the derivation of families of high-performance algorithms for a large set of frequently encountered dense linear algebra operations. As part of the derivation a constructive proof of the correctness of the algorithm is generated. The paper is structured so that it can be used as a tutorial for novices. However, the method has been shown to yield new, high-performance algorithms for well-studied linear algebra operations and should also be of interest to those who wish to produce best-in-class high-performance codes. ", } @Article{Bientinesi:2005:RLA, author = "Paolo Bientinesi and Enrique S. Quintana-Ort\'{i} and Robert A. van de Geijn", title = "Representing Linear Algebra Algorithms in Code: The {FLAME} Application Programming Interfaces", journal = j-TOMS, volume = "31", number = "1", month = mar, year = "2005", pages = "27--59", URL = "http://doi.acm.org/10.1145/1055531.1055533", abstract = "In this paper, we present a number of Application Program Interfaces (APIs) for coding linear algebra algorithms. On the surface, these APIs for the MATLAB M-script and C programming languages appear to be simple, almost trivial, extensions of those languages. Yet with them, the task of programming and maintaining families of algorithms for a broad spectrum of linear algebra operations is greatly simplified. In combination with our Formal Linear Algebra Methods Environment (FLAME) approach to deriving such families of algorithms, dozens of algorithms for a single linear algebra operation can be derived, verified to be correct, implemented, and tested, often in a matter of minutes per algorithm. Since the algorithms are expressed in code much like they are explained in a classroom setting, these APIs become not just a tool for implementing libraries, but also a valuable tool for teaching the algorithms that are incorporated in the libraries. In combination with an extension of the Parallel Linear Algebra Package (PLAPACK) API, the approach presents a migratory path from algorithm to MATLAB implementation to high-performance sequential implementation to parallel implementation. Finally, the APIs are being used to create a repository of algorithms and implementations for linear algebra operations, the FLAME Interface REpository (FIRE), which already features hundreds of algorithms for dozens of commonly encountered linear algebra operations.", } @Article{Gunter:2005:POC, author = "Brian C. Gunter and Robert A. van de Geijn", title = "Parallel Out-of-Core Computation and Updating the {QR} Factorization", journal = j-TOMS, volume = "31", number = "1", month = mar, year = "2005", pages = "60--78", URL = "http://doi.acm.org/10.1145/1055531.1055534", abstract = "This paper discusses the high-performance parallel implementation of the computation and updating of QR factorizations of dense matrices, including problems large enough to require out-of-core computation, where the matrix is stored on disk. The algorithms presented here are scalable both in problem size and as the number of processors increases. Implementation using the Parallel Linear Algebra Package (PLAPACK) and the Parallel Out-of-Core Linear Algebra Package (POOCLAPACK) is discussed. The methods are shown to attain excellent performance, in some cases attaining roughly 80 percent of the realizable peak of the architectures on which the experiments were performed.", } @Article{Shampine:2005:UAS, author = "L. F. Shampine and Robert Ketzscher and Shaun A. Forth", title = "Using {AD} to Solve BVPs in {Matlab}", journal = j-TOMS, volume = "31", number = "1", month = mar, year = "2005", pages = "79--94", URL = "http://doi.acm.org/10.1145/1055531.1055535", abstract = "The Matlab program {\tt bvp4c} solves two--point boundary value problems (BVPs) of considerable generality. The numerical method requires partial derivatives of several kinds. To make solving BVPs as easy as possible, the default in {\tt bvp4c} is to approximate these derivatives with finite differences. The solver is more robust and efficient if analytical derivatives are supplied. In this paper we investigate how to use automatic differentiation (AD) to obtain the advantages of analytical derivatives without giving up the convenience of finite differences. In {\tt bvp4cAD} we have approached this ideal by a careful use of the MAD AD tool and some modification of {\tt bvp4c}.", } @Article{Dercole:2005:SAD, author = "Fabio Dercole and Yuri A. Kuznetsov", title = "{SlideCont}: An {Auto97} Driver for Bifurcation Analysis of {Filippov} Systems", journal = j-TOMS, volume = "31", number = "1", month = mar, year = "2005", pages = "95--119", URL = "http://doi.acm.org/10.1145/1055531.1055536", abstract = "SlideCont, an Auto97 driver for sliding bifurcation analysis of discontinuous piecewise-smooth autonomous systems, known as Filippov systems, is described in detail. Sliding bifurcations are those in which some sliding on the discontinuity boundary is critically involved. The software allows for detection and continuation of codimension-1 sliding bifurcations as well as detection of some codimension-2 singularities, with special attention to planar systems ($n=2$). Some bifurcations are also supported for $n$-dimensional systems. This paper gives a brief introduction to Filippov systems, describes the structure of SlideCont and all computations supported by SlideCont 2.0. Several examples, which are distributed together with the source code of SlideCont, are presented.", } @Article{Jin:2005:CFE, author = "Guohua Jin and John Mellor-Crummey", title = "SFCGen: An Framework for Efficient Generation of Multi-dimensional Space-filling Curves", journal = j-TOMS, volume = "31", number = "1", month = mar, year = "2005", pages = "120--148", URL = "http://doi.acm.org/10.1145/1055531.1055537", abstract = "Because they are continuous and self-similar, space-filling curves have been widely used in mathematics to transform multi-dimensional problems into one-dimensional forms. For scientific applications, reordering computation by certain space-filling curves can significantly improve data reuse because of the locality properties of these curves. However, when space-filling curves are used in programs for reordering data, traversal or indexing of the curves must be efficient. To address this problem, we present the table-driven framework SFCGen to efficiently generate multi-dimensional space-filling curves on the fly. The framework is general and easy enough to be used in any application that can be partitioned recursively in multiple dimensions. We describe a movement specification table, a universal turtle algorithm to enumerate points along a space-filling curve, a table-based indexing algorithm to transform coordinates of a point into its position along the curve and an algorithm to pre-generate the table automatically. As examples, we show how high-dimensional Hilbert, Morton, and Peano curves and a two-dimensional Sierpi\'{n}ski curve can be generated with our algorithms. We present performance results for Hilbert, Morton, and Peano curves and compare the efficiency of our curve generation algorithm with the most recent work on generating Hilbert curves. Our experimental results on three modern microprocessor-based platforms show that SFCGen performs up to 63\% faster than the most recent recursive algorithm on 2D curve generation and up to a factor of 132 faster than two previous byte-oriented non-recursive implementations. On curve indexing, SFCGen performs as much as a factor of three faster than the byte-oriented implementation. Our results on 4D space-filling curves also show that SFCGen scales very well with curve level for higher dimensional spaces.", } @Article{Boyd:2005:ACG, author = "John P. Boyd", title = "Algorithm 840: Computation of Grid Points, Quadrature Weights and Derivatives for Spectral Element Methods Using Prolate Spheroidal Wave Functions --- Prolate Elements", journal = j-TOMS, volume = "31", number = "1", month = mar, year = "2005", pages = "149--165", URL = "http://doi.acm.org/10.1145/1055531.1055538", abstract = "High order domain decomposition methods using a basis of Legendre polynomials, known variously as ``spectral elements'' or ``p-type finite elements'', have become very popular. Recent studies suggest that accuracy and efficiency can be improved by replacing Legendre polynomials by prolate spheroidal wave functions of zeroth order. In this article, we explain the practicalities of computing all the numbers needed to switch bases: the grid points $x_j$, the quadrature weights $w_j$, and the values of the prolate functions and their derivatives at the grid points. The prolate functions themselves are computed by a Legendre-Galerkin discretization of the prolate differential equation;this yields a symmetric tridiagonal matrix. The prolate functions are then de ned by Legendre series whose coefficients are the eigenfunctions of the matrix eigenproblem. The grid points and weights are found simultaneously through a Newton iteration. For large $N$ and $c$, the iteration diverges from a first guess of the Legendre-Lobatto points and weights. Fortunately, the variations of the $x_j$ and $w_j$ with $c$ are well-approximated by a symmetric parabola over the whole range of interest. This makes it possible to bypass the continuation procedures of earlier authors. The software is encapsulated in a Matlab library.", } @Article{Howell:2005:ABG, author = "Gary W. Howell and Nadia Diaa", title = "Algorithm 841: {BHESS}: {Gaussian} Reduction to a Similar Banded {Hessenberg} Form", journal = j-TOMS, volume = "31", number = "1", month = mar, year = "2005", pages = "166--185", URL = "http://doi.acm.org/10.1145/1055531.1055539", abstract = "BHESS uses Gaussian similarity transformations to reduce a general real square matrix to similar upper Hessenberg form. Multipliers are bounded in root mean square by a user-supplied parameter. If the input matrix is not highly nonnormal and the user-supplied tolerance on multipliers is of a size greater than ten, the returned matrix usually has small upper bandwidth. In such a case, eigenvalues of the returned matrix can be determined by the bulge-chasing BR iteration or by Rayleigh quotient iteration. BHESS followed by BR iteration determines a complete spectrum in about one-fifth the time required for orthogonal reduction to Hessenberg form followed by QR iterations. The FORTRAN 77 code provided for BHESS runs efficiently on a cache-based architecture.", } @Article{Xin:2005:IHB, author = "Jianguo Xin and Katia Pinchedez and Joseph E. Flaherty", title = "Implementation of Hierarchical Bases in {Femlab} for Simplicial Elements", journal = j-TOMS, volume = "31", number = "2", month = jun, year = "2005", pages = "187--200", URL = " http://doi.acm.org/10.1145/1067967.1067968", abstract = "We present the implementation of a well-conditioned hierarchical bases for one-dimensional, triangular and tetrahedral elements in finite element Femlab software. Using the domain mesh information provided by Femlab, we found an easy way to maintain the continuity of solutions across the inter-element boundaries. The conditionings of the global stiffness matrices of several standard problems are compared with Lagrange bases and are smaller for all cases.", } @Article{Andersen:2005:FPH, author = "Bjarne S. Andersen and John A. Gunnels and Fred G. Gustavson and John K. Reid and Jerzy Wa\'{s}niewski", title = "A Fully Portable High Performance Minimal Storage Hybrid {Cholesky} Algorithm", journal = j-TOMS, volume = "31", number = "2", month = jun, year = "2005", pages = "201--227", URL = " http://doi.acm.org/10.1145/1067967.1067969", abstract = "We consider the efficient implementation of the Cholesky solution of symmetric positive-definite dense linear systems of equations using packed storage. We take the same starting point as that of LINPACK and LAPACK, with the upper (or lower) triangular part of the matrix being stored by columns. Following LINPACK and LAPACK, we overwrite the given matrix by its Cholesky factor. We consider the use of a hybrid format in which blocks of the matrices are held contiguously and compare this to the present LAPACK code. Code based on this format has the storage advantages of the present code, but substantially outperforms it. Furthermore, it compares favourably to using conventional full format (LAPACK) and using the recursive format of Andersen, Gustavson, and Wa\'{s}niewski.", } @Article{Fraysse:2005:ASG, author = "Val\'{e}rie Frayss\'{e} and Luc Giraud and Serge Gratton and Julien Langou", title = "Algorithm 842: A Set of {GMRES} Routines for Real and Complex Arithmetics on High Performance Computers", journal = j-TOMS, volume = "31", number = "2", month = jun, year = "2005", pages = "228--238", URL = " http://doi.acm.org/10.1145/1067967.1067970", abstract = "In this paper we describe our implementations of the GMRES algorithm for both real and complex, single and double precision arithmetics suitable for serial, shared memory and distributed memory computers. For the sake of portability, simplicity, flexibility and effciency the GMRES solvers have been implemented in Fortran 77 using the reverse communication mechanism for the matrix-vector product, the preconditioning and the dot product computations. For distributed memory computation, several orthogonalization procedures have been implemented to reduce the cost of the dot product calculation, that is a well-known bottleneck of effciency for the Krylov methods. Either implicit or explicit calculation of the residual at restart are possible depending on the actual cost of the matrix-vector product. Finally the implemented stopping criterion is based on a normwise backward error.", } @Article{Driscoll:2005:AIS, author = "Tobin A. Driscoll", title = "Algorithm 843: Improvements to the {Schwarz-Christoffel Toolbox} for {MATLAB}", journal = j-TOMS, volume = "31", number = "2", month = jun, year = "2005", pages = "239--251", URL = " http://doi.acm.org/10.1145/1067967.1067971", abstract = "The Schwarz-Christoffel Toolbox (SC Toolbox) for MATLAB, first released in 1994, made possible the interactive creation and visualization of conformal maps to regions bounded by polygons. The most recent release supports new features, including an object-oriented command-line interface model, new algorithms for multiply elongated and multiple-sheeted regions, and a module for solving Laplace's equation on a polygon with Dirichlet and homogeneous Neumann conditions. Brief examples are given to demonstrate the new capabilities.", } @Article{Berry:2005:ACS, author = "Michael W. Berry and Shakhina A. Pulatova and G. W. Stewart", title = "Algorithm 844: Computing Sparse Reduced-Rank Approximations to Sparse Matrices", journal = j-TOMS, volume = "31", number = "2", month = jun, year = "2005", pages = "252--269", URL = " http://doi.acm.org/10.1145/1067967.1067972", abstract = "In many applications --- latent semantic indexing, for example --- it is required to obtain a reduced rank approximation to a sparse matrix $A$. Unfortunately, the approximations based on traditional decompositions, like the singular value and QR decompositions, are not in general sparse. Stewart [{\it Numer. Math.} 83 (1999) 313--323] has shown how to use a variant of the classical Gram--Schmidt algorithm, called the quasi--Gram-Schmidt--algorithm, to obtain two kinds of low-rank approximations. The first, the SPQR, approximation, is a pivoted, Q-less QR approximation of the form $(XR_{11}^{-1})(R_{11} R_{12})$, where $X$ consists of columns of A. The second, the SCR approximation, is of the form the form $A \cong XTY^{\rm T}$, where $X$ and $Y$ consist of columns and rows $A$ and $T$ is small. In this paper we treat the computational details of these algorithms and describe a Matlab implementations.", } @Article{Money:2005:AEM, author = "James H. Money and Qiang Ye", title = "Algorithm 845: {EIGIFP}: A {MATLAB} Program for Solving Large Symmetric Generalized Eigenvalue Problems", journal = j-TOMS, volume = "31", number = "2", month = jun, year = "2005", pages = "270--279", URL = " http://doi.acm.org/10.1145/1067967.1067973", abstract = "eigifp is a MATLAB program for computing a few extreme eigenvalues and eigenvectors of the large symmetric generalized eigenvalue problem Ax = \lambda¸Bx. It is a black-box implementation of an inverse free preconditioned Krylov subspace projection method developed by Golub and Ye (2002). It has some important features that allow it to solve some difficult problems without any input from users. It is particularly suitable for problems where preconditioning by the standard shift-and-invert transformation is not feasible.", } @Article{Boisvert:2005:ISI, author = "Ronald F. Boisvert and L. A. Drummond and Osni A. Marques", title = "Introduction to the Special Issue on the {Advanced CompuTational Software (ACTS) Collection}", journal = j-TOMS, volume = "31", number = "3", month = sep, year = "2005", pages = "281", URL = "http://doi.acm.org/10.1145/1089014.1089015", abstract = "", } @Article{Drummond:2005:OAC, author = "L. A. Drummond and O. A. Marques", title = "An Overview of the {Advanced CompuTational Software (ACTS) Collection}", journal = j-TOMS, volume = "31", number = "3", month = sep, year = "2005", pages = "282--301", URL = "http://doi.acm.org/10.1145/1089014.1089016", abstract = "The ACTS Collection brings together a number of general-purpose computational tools that were developed by independent research projects mostly funded and supported by the U.S. Department of Energy. These tools tackle a number of common computational issues found in many applications, mainly implementation of numerical algorithms, and support for code development, execution and optimization. In this article, we introduce the numerical tools in the collection and their functionalities, present a model for developing more complex computational applications on top of ACTS tools, and summarize applications that use these tools. Lastly, we present a vision of the ACTS project for deployment of the ACTS Collection by the computational sciences community.", } @Article{Li:2005:OSA, author = "Xiaoye S. Li", title = "An Overview of {SuperLU}: Algorithms, Implementation, and User Interface", journal = j-TOMS, volume = "31", number = "3", month = sep, year = "2005", pages = "302--325", URL = "http://doi.acm.org/10.1145/1089014.1089017", abstract = "We give an overview of the algorithms, design philosophy, and implementation techniques in the software SuperLU, for solving sparse unsymmetric linear systems. In particular, we highlight the differences between the sequential SuperLU (including its multithreaded extension) and parallel SuperLU_DIST. These include the numerical pivoting strategy, the ordering strategy for preserving sparsity, the ordering in which the updating tasks are performed, the numerical kernel, and the parallelization strategy. Because of the scalability concern, the parallel code is drastically different from the sequential one. We describe the user interfaces of the libraries, and illustrate how to use the libraries most efficiently depending on some matrix characteristics. Finally, we give some examples of how the solver has been used in large-scale scientific applications, and the performance.", } @Article{Falgout:2005:PSH, author = "Robert D. Falgout and Jim E. Jones and Ulrike Meier Yang", title = "Pursuing Scalability for {\it hypre}'s Conceptual Interfaces", journal = j-TOMS, volume = "31", number = "3", month = sep, year = "2005", pages = "326--350", URL = "http://doi.acm.org/10.1145/1089014.1089018", abstract = "The software library {\it hypre} provides high performance preconditioners and solvers for the solution of large, sparse linear systems on massively parallel computers as well as conceptual interfaces that allow users to access the library in the way they naturally think about their problems. These interfaces include a stencil-based structured interface (Struct); a semi-structured interface (semiStruct), which is appropriate for applications that are mostly structured, e.g. block structured grids, composite grids in structured adaptive mesh refinement applications, and overset grids; a finite element interface (FEI) for unstructured problems, as well as a conventional linear-algebraic interface (IJ). It is extremely important to provide an efficient, scalable implementation of these interfaces in order to support the scalable solvers of the library, especially when using tens of thousands of processors. This paper describes the data structures, parallel implementation and resulting performance of the IJ, Struct and semiStruct interfaces. It investigates their scalability, presents successes as well as pitfalls of some of the approaches and suggests ways of dealing with them.", } @Article{Hernandez:2005:SSF, author = "Vicente Hernandez and Jose E. Roman and Vicente Vidal", title = "SLEPc: A Scalable and Flexible Toolkit for the Solution of Eigenvalue Problems", journal = j-TOMS, volume = "31", number = "3", month = sep, year = "2005", pages = "351--362", URL = "http://doi.acm.org/10.1145/1089014.1089019", abstract = "The Scalable Library for Eigenvalue Problem Computations (SLEPc) is a software library for computing a few eigenvalues and associated eigenvectors of a large sparse matrix or matrix pencil. It has been developed on top of PETsc and enforces the same programming paradigm. The emphasis of the software is on methods and techniques appropriate for problems in which the associated matrices are sparse, for example, those arising after the discretization of partial differential equations. Therefore, most of the methods offered by the library are projection methods such as Arnoldi or Lanczos, or other methods with similar properties. SLEPc provides basic methods as well as more sophisticated algorithms. It also provides built-in support for spectral transformations such as the shift-and-invert technique. SLEPc is a general library in the sense that it covers standard and generalized eigenvalue problems, both Hermitian and non-Hermitian, with either real or complex arithmetic. SLEPc can be easily applied to real world problems. To illustrate this, several case studies arising from real applications are presented and solved with SLEPc with little programming effort. The addressed problems include a matrix-free standard problem, a complex generalized problem and a singular value decomposition. The implemented codes exhibit good properties regarding flexibility as well as parallel performance.", } @Article{Hindmarsh:2005:SSN, author = "Alan C. Hindmarsh and Peter N. Brown and Keith E. Grant and Steven L. Lee and Radu Serban and Dan E. Shumaker and Carol S. Woodward", title = "{SUNDIALS}: Suite of Nonlinear and Differential/Algebraic Equation Solvers", journal = j-TOMS, volume = "31", number = "3", month = sep, year = "2005", pages = "363--396", URL = "http://doi.acm.org/10.1145/1089014.1089020", abstract = "SUNDIALS is a suite of advanced computational codes for solving large-scale problems that can be modeled as a system of nonlinear algebraic equations, or as initial-value problems in ordinary differential or differential-algebraic equations. The basic versions of these codes are called KINSOL, CVODE, and IDA, respectively. The codes are written in ANSI standard C and are suitable for either serial or parallel machine environments. Common and notable features of these codes include: inexact Newton-Krylov methods for solving large-scale nonlinear systems; linear multistep methods for time-dependent problems; a highly modular structure to allow incorporation of different preconditioning and/or linear solver methods; and clear interfaces allowing for users to provide their own data structures underneath the solvers. We describe the current capabilities of the codes, along with some of the algorithms and heuristics used to achieve efficiency and robustness. We also describe how the codes stem from previous and widely used Fortran 77 solvers, and how the codes have been augmented with forward and adjoint methods for carrying out first-order sensitivity analysis with respect to model parameters or initial conditions.", } @Article{Heroux:2005:OTP, author = "Michael A. Heroux and Roscoe A. Bartlett and Vicki E. Howle and Robert J. Hoekstra and Jonathan J. Hu and Tamara G. Kolda and Richard B. Lehoucq and Kevin R. Long and Roger P. Pawlowski and Eric T. Phipps and Andrew G. Salinger and Heidi K. Thornquist and Ray S. Tuminaro and James M. Willenbring and Alan Williams and Kendall S. Stanley", title = "An Overview of the Trilinos Project", journal = j-TOMS, volume = "31", number = "3", month = sep, year = "2005", pages = "397--423", URL = "http://doi.acm.org/10.1145/1089014.1089021", abstract = "The Trilinos Project is an effort to facilitate the design, development, integration and ongoing support of mathematical software libraries within an object-oriented framework for the solution of large-scale, complex multi-physics engineering and scienti c problems. Trilinos addresses two fundamental issues of developing software for these problems: (i) Providing a streamlined process and set of tools for development of new algorithmic implementations and (ii) promoting interoperability of independently developed software. \par Trilinos uses a two-level software structure designed around collections of packages. A Trilinos package is an integral unit usually developed by a small team of experts in a particular algorithms area such as algebraic preconditioners, nonlinear solvers, etc. Packages exist underneath the Trilinos top level, which provides a common look-and-feel, including configuration, documentation, licensing, and bug-tracking. \par Here we present the overall Trilinos design, describing our use of abstract interfaces and default concrete implementations. We discuss the services that Trilinos provides to a prospective package and how these services are used by various packages. We also illustrate how packages can be combined to rapidly develop new algorithms. Finally, we discuss how Trilinos facilitates highquality software engineering practices that are increasingly required from simulation software.", } @Article{Castillo:2005:FOO, author = "Paul Castillo and Robert Rieben and Daniel White", title = "FEMSTER: An Object Oriented Class Library of High-Order Discrete Differential Forms", journal = j-TOMS, volume = "31", number = "4", month = dec, year = "2005", pages = "425--457", URL = "http://doi.acm.org/10.1145/1114268.1114269", abstract = "FEMSTER is a modular finite element class library for solving three-dimensional problems arising in electromagnetism. The library was designed using a modern geometrical approach based on differential forms (or p-forms) and can be used for high-order spatial discretizations of well known H(div) and H(curl) --- conforming finite element methods. The software consists of a set of abstract interfaces and concrete classes, providing a framework in which the user is able to add new schemes by reusing the existing classes or by incorporating new user-defined data types.", } @Article{Naumann:2005:DEF, author = "Uwe Naumann and Jan Riehme", title = "A Differentiation-Enabled {Fortran} 95 Compiler", journal = j-TOMS, volume = "31", number = "4", month = dec, year = "2005", pages = "458--474", URL = "http://doi.acm.org/10.1145/1114268.1114270", abstract = "The availability of first derivatives of vector functions is crucial for the robustness and effciency of a large number of numerical algorithms. An upcoming new version of the differentiation-enabled NAGWare Fortran 95 compiler is described that uses programming language extensions and a semantic code transformation known as automatic differentiation to provide Jacobians of numerical programs with machine accuracy. We describe a new user interface as well as the relevant algorithmic details. In particular, we focus on the source transformation approach that generates locally optimal gradient code for single assignments by vertex elimination in the linearized computational graph. Extensive tests show the superiority of this method over the current overloading-based approach. The robustness and convenience of the new compiler-feature is illustrated by various case studies.", } @Article{Tang:2005:DNI, author = "Ping Tak Peter Tang", title = "DFTI -- A New Interface for Fast {Fourier} Transform Libraries", journal = j-TOMS, volume = "31", number = "4", month = dec, year = "2005", pages = "475--507", URL = "http://doi.acm.org/10.1145/1114268.1114271", abstract = "The Fast Fourier Transform (FFT) algorithm that calculates the Discrete Fourier Transform (DFT) is one of the major breakthroughs in scientific computing and is now an indispensable tool in a vast number of fields. Unfortunately, software that provide fast computation of DFT via FFT differ vastly in functionality and lack uniformity. A widely accepted Applications Programmer Interface (API) for DFT would advance the field of scientific computing significantly. In this paper, we present the specification of DFTI, a new interface that combines functionality with ease of use. This API is our strawman proposal towards a common interface for DFT calculations.", } @Article{Mu:2005:PNP, author = "Mo Mu", title = "PDE.Mart: A Network-based Problem-solving Environment for {PDEs}", journal = j-TOMS, volume = "31", number = "4", month = dec, year = "2005", pages = "508--531", URL = "http://doi.acm.org/10.1145/1114268.1114272", abstract = "PDE.Mart is a network-based problem-solving environment (PSE) for solving partial differential equations (PDEs) in numerical simulations, academic research, as well as educational settings. The client-server protocol consists of a web-browser-enabled graphical user interface, PDE-GUI, that runs on client machines to manage the server connection, geometric and model specifications, computational method selection, and postprocessing; a server system, PDE-Server, to build computational engines and provide PDE solution services on the host machine; and a library, PDE-LIB, that contains building blocks for developing network-based and PDE-oriented PSEs.", } @Article{Ledoux:2006:MMP, author = "V. Ledoux and M. Van Daele and G. Vanden Berghe", title = "MATSLISE: A {MATLAB} Package for the Numerical Solution of {Sturm-Liouville} and {Schr\"{o}dinger Equations", journal = j-TOMS, volume = "31", number = "4", month = dec, year = "2005", pages = "532--554", URL = "http://doi.acm.org/10.1145/1114268.1114273", abstract = "MATSLISE is a graphical MATLAB software package for the interactive numerical study of regular Sturm-Liouville problems, one-dimensional Schr\"{o}odinger equations and radial Schr\"{o}odinger equations with a distorted Coulomb potential. It allows the fast and accurate computation of the eigenvalues and the visualization of the corresponding eigenfunctions. This is realized by making use of the power of high order piecewise constant perturbation methods, a technique described by Ixaru. For a well-outlined class of problems, the implemented algorithms are more efficient than the well-established SL-solvers SL02F, SLEDGE, SLEIGN and SLEIGN2 which are included by Pryce in the SLDRIVER code that has been built on top of SLTSTPAK.", } @Article{Gao:2005:AMS, author = "Tangan Gao and T. Y. Li and Mengnien Wu", title = "Algorithm 846: {MixedVol}: A Software Package for Mixed Volume Computation", journal = j-TOMS, volume = "31", number = "4", month = dec, year = "2005", pages = "555--560", URL = "http://doi.acm.org/10.1145/1114268.1114274", abstract = "MixedVol is a C++ software package that computes the mixed volume of $n$ finite subsets of $Z^n$ or the support of a system of $n$ polynomials in $n$ variables. The software produces the mixed volume as well as the mixed cells. The mixed cells are crucial for solving polynomial systems by the polyhedral homotopy continuation method. The software leads existing codes for mixed volume computation in speed by a substantial margin and its memory requirement is very low.", } @Article{Klimke:2005:ASP, author = "Andreas Klimke and Barbara Wohlmuth", title = "Algorithm 847: {spinterp}: Piecewise Multilinear Hierarchical Sparse Grid Interpolation in {MATLAB}", journal = j-TOMS, volume = "31", number = "4", month = dec, year = "2005", pages = "561--579", URL = "http://doi.acm.org/10.1145/1114268.1114275", abstract = "To recover or approximate smooth multivariate functions, sparse grids are superior to full grids due to a significant reduction of the required support nodes. The order of the convergence rate in the maximum norm is preserved up to a logarithmic factor. We describe three possible piecewise multilinear hierarchical interpolation schemes in detail and conduct a numerical comparison. Furthermore, we document the features of our sparse grid interpolation software package spinterp for MATLAB", } @Article{Shellman:2005:ARF, author = "Spencer Shellman and K. Sikorski", title = "Algorithm 848: A Recursive Fixed Point Algorithm for the Infinity-Norm Case", journal = j-TOMS, volume = "31", number = "4", month = dec, year = "2005", pages = "580--586", URL = "http://doi.acm.org/10.1145/1114268.1114276", abstract = "We present the PFix algorithm for approximating a fixed point of a function f that has arbitrary dimensionality, is defined on a rectangular domain, and is Lipschitz continuous with respect to the infinity norm with constant 1. PFix has applications in economics, game theory, and solution of partial differential equations. PFix computes an approximation that satisfies the residual error criterion, and can also compute an approximation satisfying the absolute error criterion when the Lipschitz constant is less than 1. For functions defined on all rectangular domains, the worst-case complexity of PFix has order equal to the logarithm of the reciprocal of the tolerance, raised to the power of the dimension. Dividing this order expression by the factorial of the dimension yields the order of the worst-case bound for the case of the unit hypercube. PFix is a recursive algorithm, in that it uses solutions to a d-dimensional problem to compute a solution to a (d+1)-dimensional problem.", } @Article{Davis:2005:ACS, author = "Timothy A. Davis", title = "Algorithm 849: A Concise Sparse {Cholesky} Factorization Package", journal = j-TOMS, volume = "31", number = "4", month = dec, year = "2005", pages = "587--591", URL = "http://doi.acm.org/10.1145/1114268.1114277", abstract = "The LDL software package is a set of short, concise routines for factorizing symmetric positive-definite sparse matrices, with some applicability to symmetric indefinite matrices. Its primary purpose is to illustrate much of the basic theory of sparse matrix algorithms in as concise a code as possible, including an elegant method of sparse symmetric factorization that computes the factorization row-by-row but stores it column-by-column. The entire symbolic and numeric factorization consists of less than 50 lines of code. The package is written in C, and includes a MATLAB interface.", } @Article{Panneton:2006:ILP, author = "Fran{\c{c}}ois Panneton and Pierre L'Ecuyer and Makoto Matsumoto", title = "Improved long-period generators based on linear recurrences modulo $2$", journal = j-TOMS, volume = "32", number = "1", pages = "1--16", month = mar, year = "2006", URL = "http://doi.acm.org/10.1145/1132973.1132974", abstract = "Fast uniform random number generators with extremely long periods have been defined and implemented based on linear recurrences modulo $2$. The twisted GFSR and the Mersenne twister are famous recent examples. Besides the period length, the statistical quality of these generators is usually assessed via their equidistribution properties. The huge-period generators proposed so far are not quite optimal in this respect. In this article, we propose new generators of that form with better equidistribution and ``bit-mixing'' properties for equivalent period length and speed. The state of our new generators evolves in a more chaotic way than for the Mersenne twister. We illustrate how this can reduce the impact of persistent dependencies among successive output values, which can be observed in certain parts of the period of gigantic generators such as the Mersenne twister.", } @Article{Guermouche:2006:CMM, author = "Abdou Guermouche and Jean-Yves L'Excellent", title = "Constructing memory-minimizing schedules for multifrontal methods", journal = j-TOMS, volume = "32", number = "1", pages = "17--32", month = mar, year = "2006", URL = "http://doi.acm.org/10.1145/1132973.1132975", abstract = "We are interested in the memory usage of multifrontal methods. Starting from the algorithms introduced by Liu, we propose new schedules to allocate and process tasks that improve memory usage. This generalizes two existing factorization and memory-allocation schedules by allowing a more flexible task allocation together with a specific tree traversal. We present optimal algorithms for this new class of schedules, and demonstrate experimentally their benefit for some real-world matrices from sparse matrix collections where either the active memory or the total memory is minimized.", } @Article{Koyuturk:2006:NDB, author = "Mehmet Koyut{\"u}rk and Ananth Grama and Naren Ramakrishnan", title = "Nonorthogonal decomposition of binary matrices for bounded-error data compression and analysis", journal = j-TOMS, volume = "32", number = "1", pages = "33--69", month = mar, year = "2006", URL = "http://doi.acm.org/10.1145/1132973.1132976", abstract = "This article presents the design and implementation of a software tool, PROXIMUS, for error-bounded approximation of high-dimensional binary attributed datasets based on nonorthogonal decomposition of binary matrices. This tool can be used for analyzing data arising in a variety of domains ranging from commercial to scientific applications. Using a combination of innovative algorithms, novel data structures, and efficient implementation, PROXIMUS demonstrates excellent accuracy, performance, and scalability to large datasets. We experimentally demonstrate these on diverse applications in association rule mining and DNA microarray analysis. In limited beta release, PROXIMUS currently has over 300 installations in over 10 countries.", } @Article{Gil:2006:CRP, author = "Amparo Gil and Javier Segura and Nico M. Temme", title = "Computing the real parabolic cylinder functions {$U(a,x)$, $V(a,x)$}", journal = j-TOMS, volume = "32", number = "1", pages = "70--101", month = mar, year = "2006", URL = "http://doi.acm.org/10.1145/1132973.1132977", abstract = "Methods for the computation of real parabolic cylinder functions $U(a, x)$, and $V(a, x)$ and their derivatives are described. We give details on power series, asymptotic series, recursion and quadrature. A combination of these methods can be used for computing parabolic cylinder functions for unrestricted values of the order $a$ and the variable $x$ except for the overflow\slash underflow limitations. By factoring the dominant exponential factor, scaled functions can be computed without practical overflow\slash underflow limitations. In an accompanying article we describe the precise domains for these methods and we present the Fortran 90 codes for the computation of these functions.", } @Article{Gil:2006:ARP, author = "Amparo Gil and Javier Segura and Nico M. Temme", title = "{Algorithm 850}: {Real} parabolic cylinder functions {$U(a,x)$, $V(a,x)$}", journal = j-TOMS, volume = "32", number = "1", pages = "102--112", month = mar, year = "2006", URL = "http://doi.acm.org/10.1145/1132973.1132978", abstract = "Fortran 90 programs for the computation of real parabolic cylinder functions are presented. The code computes the functions $U(a, x)$, $V(a, x)$ and their derivatives for real $a$ and $x ($x \geq 0)$. The code also computes scaled functions. The range of computation for scaled PCFs is practically unrestricted. The aimed relative accuracy for scaled functions is better than $5 \times 10^{14}$. Exceptions to this accuracy are the evaluation of the functions near their zeros and the error caused by the evaluation of trigonometric functions of large arguments when $|a| > x$. The routines always give values for which the Wronskian relation for scaled functions is verified with a relative accuracy better than $5 \times 10^{14}$. The accuracy of the unscaled functions is also better than $5 \times 10^{14}$ for moderate values of $x$ and $a$ (except close to the zeros), while for large $x$ and $a$ the error is dominated by exponential and trigonometric function evaluations. For IEEE standard double precision arithmetic, the accuracy is better than $5 \times 10^{13}$ in the computable range of unscaled PCFs (except close to the zeros).", } @Article{Hager:2006:ACD, author = "William W. Hager and Hongchao Zhang", title = "{Algorithm 851}: {CG\_DESCENT}, a conjugate gradient method with guaranteed descent", journal = j-TOMS, volume = "32", number = "1", pages = "113--137", month = mar, year = "2006", URL = "http://doi.acm.org/10.1145/1132973.1132979", abstract = "Recently, a new nonlinear conjugate gradient scheme was developed which satisfies the descent condition $g^T_k d_k \leq -7/8 ||g_k||^2$ and which is globally convergent whenever the line search fulfills the Wolfe conditions. This article studies the convergence behavior of the algorithm; extensive numerical tests and comparisons with other methods for large-scale unconstrained optimization are given.", } @Article{Granvilliers:2006:ARI, author = "Laurent Granvilliers and Fr{\'e}d{\'e}ric Benhamou", title = "{Algorithm 852}: {RealPaver}: an interval solver using constraint satisfaction techniques", journal = j-TOMS, volume = "32", number = "1", pages = "138--156", month = mar, year = "2006", URL = "http://doi.acm.org/10.1145/1132973.1132980", abstract = "RealPaver is an interval software for modeling and solving nonlinear systems. Reliable approximations of continuous or discrete solution sets are computed using Cartesian products of intervals. Systems are given by sets of equations or inequality constraints over integer and real variables. Moreover, they may have different natures, being square or nonsquare, sparse or dense, linear, polynomial, or involving transcendental functions.The modeling language permits stating constraint models and tuning parameters of solving algorithms which efficiently combine interval methods and constraint satisfaction techniques. Several consistency techniques (box, hull, and 3B) are implemented. The distribution includes C sources, executables for different machine architectures, documentation, and benchmarks. The portability is ensured by the GNU C compiler.", } @Article{Foster:2006:AEA, author = "Leslie Foster and Rajesh Kommu", title = "{Algorithm 853}: {An} efficient algorithm for solving rank-deficient least squares problems", journal = j-TOMS, volume = "32", number = "1", pages = "157--165", month = mar, year = "2006", URL = "http://doi.acm.org/10.1145/1132973.1132981", abstract = "Existing routines, such as xGELSY or xGELSD in LAPACK, for solving rank-deficient least squares problems require {$O(m n^2)$} operations to solve $\min ||b - Ax||$ where $A$ is an $m$ by $n$ matrix. We present a modification of the LAPACK routine xGELSY that requires $O(m n k)$ operations where $k$ is the effective numerical rank of the matrix $A$. For low rank matrices the modification is an order of magnitude faster than the LAPACK code.", } @Article{Hasselman:2006:RAF, author = "Berend Hasselman", title = "Remark on {Algorithm 815}: {FORTRAN} subroutines for computing approximate solutions of feedback set problems using {GRASP}", journal = j-TOMS, volume = "32", number = "1", pages = "166--168", month = mar, year = "2006", URL = "http://doi.acm.org/10.1145/1132973.1132982", abstract = "We show that the Fortran source code for Algorithm 815 contains an error and we propose a correction. The error may cause the algorithm to generate incorrect results. We also show that the performance of the corrected algorithm can be improved by a minor adjustment in the code.", } @Article{Joffrain:2006:AHT, author = "Thierry Joffrain and Tze Meng Low and Enrique S. Quintana-Ort\'{i} and Robert van de Geijn and Field Van Zee", title = "Accumulating {Householder} Transformations, Revisited", journal = j-TOMS, volume = "32", number = "2", pages = "169--179", month = jun, year = "2006", URL = "http://doi.acm.org/10.1145/1141885.1141886", abstract = "A theorem related to the accumulation of Householder transformations into a single orthogonal transformation, known as the compact WY transform, is presented. It provides a simple characterization of the computation of this transformation and suggests an alternative algorithm for computing it. It also suggests an alternative transformation, the UT transform, with the same utility as the compact WY Transform, which requires less computation and has similar stability properties. That alternative transformation was first published over a decade ago, but has gone unnoticed by the community.", } @Article{Quintana-Orti:2006:IPR, author = "Gregorio Quintana-Ort\'{i} and Robert van de Geijn", title = "Improving the Performance of Reduction to {Hessenberg} Form", journal = j-TOMS, volume = "32", number = "2", pages = "180--194", month = jun, year = "2006", URL = "http://doi.acm.org/10.1145/1141885.1141887", abstract = "In this paper, a modification of the blocked algorithm for reduction to Hessenberg form is presented that improves performance by shifting more computation from less efficient matrix-vector operations to highly efficient matrix-matrix operations. Significant performance improvements are reported relative to the performance achieved by the current LAPACK implementation.", } @Article{Forth:2006:EOI, author = "Shaun A. Forth", title = "An Efficient Overloaded Implementation of Forward Mode Automatic Differentiation in {MATLAB}", journal = j-TOMS, volume = "32", number = "2", pages = "195--222", month = jun, year = "2006", URL = "http://doi.acm.org/10.1145/1141885.1141888", abstract = "The {\sc Mad} package described here facilitates the evaluation of first derivatives of multi-dimensional functions that are defined by computer codes written in MATLAB. The underlying algorithm is the well-known forward mode of automatic differentiation implemented via operator overloading on variables of the class {\tt fmad}. The main distinguishing feature of this MATLAB implementation is the separation of the linear combination of derivative vectors into a separate derivative vector class {\tt derivvec}. This allows for the straightforward performance optimisation of the overall package. Additionally by internally using a matrix (two-dimensional) representation of arbitrary dimension directional derivatives we may utilise MATLAB's sparse matrix class to propagate sparse directional derivatives for MATLAB code which uses arbitrary dimension arrays. On several examples the package is shown to be more efficient than Verma's ADMAT package.", } @Article{Kirby:2006:OFL, author = "Robert C. Kirby", title = "Optimizing {FIAT} with {Level 3 BLAS}", journal = j-TOMS, volume = "32", number = "2", pages = "223--235", month = jun, year = "2006", URL = "http://doi.acm.org/10.1145/1141885.1141889", abstract = "The code FIAT (FInite element Automatic Tabulator) provides necessary abstractions to define and tabulate a wide range of different finite elements on a reference element. We show here how the performance of the critical operations in its algorithms may be greatly improved by representing polynomials and linear functionals internally as vectors and hence setting up dense matrix operations. The performance gains are up to three orders of magnitude in cases studied. We also discuss how dimensional independence can be obtained through a use of graded incidence relations and give some applications to Lagrange and Brezzi-Douglas-Marini elements.", } @Article{Brisebarre:2006:CMP, author = "Nicolas Brisebarre and Jean-Michel Muller and Arnaud Tisserand", title = "Computing Machine-efficient Polynomial Approximations", journal = j-TOMS, volume = "32", number = "2", pages = "236--256", month = jun, year = "2006", URL = "http://doi.acm.org/10.1145/1141885.1141890", abstract = "Polynomial approximations are almost always used when implementing functions on a computing system. In most cases, the polynomial that best approximates (for a given distance and in a given interval) a function has coefficients that are not exactly representable with a finite number of bits. And yet, the polynomial approximations that are actually implemented do have coefficients that are represented with a finite --- and sometimes small --- number of bits: this is due to the finiteness of the floating-point representations (for software implementations), and to the need to have small, hence fast and/or inexpensive, multipliers (for hardware implementations). We then have to consider polynomial approximations for which the degree-$i$ coefficient has at most $m_i$ fractional bits: in other words, it is a rational number with denominator $2^{m_i}$. We provide a general and efficient method for finding the best polynomial approximation under this constraint. Moreover, our method also applies if some other constraints (such as requiring some coefficients to be equal to some predefined constants, or minimizing relative error instead of absolute error) are required.", } @Article{Kolonko:2006:SRS, author = "M. Kolonko and D. W\"{a}sch", title = "Sequential Reservoir Sampling with a Non-Uniform Distribution", journal = j-TOMS, volume = "32", number = "2", pages = "257--273", month = jun, year = "2006", URL = "http://doi.acm.org/10.1145/1141885.1141891", abstract = "We present a simple algorithm that allows sampling from a stream of data items without knowing the number of items in advance and without having to store all items in main memory. The sampling distribution may be general, i.e. the probability of selecting a data item $i$ may depend on the individual item. The main advantage of the algorithms is that they have to pass through the data items only once to produce a sample of arbitrary size $n$. We give different variants of the algorithm for sampling with and without replacement and analyze their complexity. We generalize earlier results of Knuth on reservoir sampling with a uniform sampling distribution. The general distribution considered here allows to sample an item with a probability equal to the relative weight (or `fitness') of the data item within the whole set of items. Applications include heuristic optimization procedures such as genetic algorithms, where solutions are sampled from a population with probability proportional to their fitness.", } @Article{Cameron:2006:MPA, author = "Frank Cameron", title = "A {Matlab} Package for Automatically Generating {Runge-Kutta} Trees, Order Conditions and Truncation Error Coefficients", journal = j-TOMS, volume = "32", number = "2", pages = "274--298", month = jun, year = "2006", URL = "http://doi.acm.org/10.1145/1141885.1141892", abstract = "In designing parts of Runge-Kutta methods order conditions and truncation error coefficients (TECs) are needed. Order conditions and TECs are typically presented as a set of trees combined with rules for producing algebraic expressions from the trees. The tree sets are defined recursively and can be generated by hand only for low orders. This paper describes a package of Matlab routines for automatically generating Runge-Kutta trees, order conditions and TECs. The routines are capable of generating Maple code, Matlab code or LaTeX expressions for ODEs or DAEs of index 1 and 2. In producing the package two theoretical problems are tackled: (a) avoiding the repeated generation of the same tree and (b) the efficient storage of TECs.", } @Article{Lerch:2006:FFI, author = "Michael Lerch and German Tischler and J\"{u}rgen Wolfe von Gudenberg and Werner Hofschuster and Walter Kr\"{a}mer", title = "filib++, a Fast Interval Library Supporting Containment Computations", journal = j-TOMS, volume = "32", number = "2", pages = "299--324", month = jun, year = "2006", URL = "http://doi.acm.org/10.1145/1141885.1141893", abstract = "{\tt filib++} is an extension of the interval library {\tt filib} originally developed at the University of Karlsruhe. The most important aim of {\tt filib} is the fast computation of guaranteed bounds for interval versions of a comprehensive set of elementary functions. {\tt filib++} extends this library in two aspects. First, it adds a second mode, the ``extended'' mode, that extends the exception-free computation mode (using special values to represent infinities and NaNs known from the IEEE floating-point standard 754) to intervals. In this mode, the so-called containment sets are computed to enclose the topological closure of a range of a function over an interval. Second, our new design uses templates and traits classes to obtain an efficient, easily extendable, and portable C++ library.", } @Article{Demmel:2006:EBE, author = "James Demmel and Yozo Hida and W. Kahan and Xiaoye S. Li and Soni Mukherjeek and E. Jason Riedy", title = "Error Bounds from Extra Precise Iterative Refinement", journal = j-TOMS, volume = "32", number = "2", pages = "325--351", month = jun, year = "2006", URL = "http://doi.acm.org/10.1145/1141885.1141894", abstract = "We present the design and testing of an algorithm for iterative refinement of the solution of linear equations, where the residual is computed with extra precision. This algorithm was originally proposed in 1948 and analyzed in the 1960s as a means to compute very accurate solutions to all but the most ill-conditioned linear systems. However two obstacles have until now prevented its adoption in standard subroutine libraries like LAPACK: (1) There was no standard way to access the higher precision arithmetic needed to compute residuals, and (2) it was unclear how to compute a reliable error bound for the computed solution. The completion of the new BLAS Technical Forum Standard has essentially removed the first obstacle. To overcome the second obstacle, we show how the application of iterative refinement can be used to compute an error bound in any norm at small cost, and use this to compute both an error bound in the usual infinity norm, and a componentwise relative error bound. We report extensive test results on over 6.2 million matrices of dimensions 5, 10, 100, and 1000. As long as a normwise (resp. componentwise) condition number computed by the algorithm is less than $1/\max{10,\sqrt{n}}\epsilon_w$, the computed normwise (resp. componentwise) error bound is at most $2\max{10,\sqrt{n}}\epsilon_w$, and indeed bounds the true error. Here, $n$ is the matrix dimension and $\epsilon_w = 2^{-24}$ is the working precision. Residuals were computed in double precision (53 bits of precision). In other words, the algorithm always computed a tiny error at negligible extra cost for most linear systems. For worse conditioned problems (which we can detect using condition estimation), we obtained small correct error bounds in over $90\%$ of cases.", } @Article{Benner:2006:AFS, author = "Peter Benner and Danier Kressner", title = "Algorithm 854: {Fortran} 77 Subroutines for Computing the Eigenvalues of {Hamiltonian} Matrices {II}", journal = j-TOMS, volume = "32", number = "2", pages = "352--373", month = jun, year = "2006", URL = "http://doi.acm.org/10.1145/1141885.1141895", abstract = "This article describes Fortran 77 subroutines for computing eigenvalues and invariant subspaces of Hamiltonian and skew-Hamiltonian matrices. The implemented algorithms are based on orthogonal symplectic decompositions, implying numerical backward stability as well as symmetry preservation for the computed eigenvalues. These algorithms are supplemented with balancing and block algorithms, which can lead to considerable accuracy and performance improvements. As a by-product, an efficient implementation for computing symplectic QR decompositions is provided. We demonstrate the usefulness of the subroutines for several, practically relevant examples.", } @Article{Sharp:2006:NSP, author = "P. W. Sharp", title = "N-body Simulations: The Performance of Eleven Integrators", journal = j-TOMS, volume = "32", number = "3", pages = "375--395", month = sep, year = "2006", URL = "http://doi.acm.org/10.1145/1163641.1163642", abstract = "We describe four challenging N-body test problems involving the Sun and planets and use them to compare the performance of nine non-symplectic and two symplectic integrators. Each problem has a long interval of integration and two have non-Newtonian gravitational interactions. The emphasis in our comparisons is on the accuracy of the solution, including the phase information, produced by the non-sympletic methods; the symplectic methods have been included to provide a contrast. The long intervals of integration necessitate small local error tolerances for the non-symplectic integrators. Among the variable-stepsize integrators, RKNINT requires the least CPU time on the two problems with Newtonian interactions and DIVA the least CPU time on the other two problems for the intervals of integration we used. We find error growth on some integrations is noticeably slower than predicted using asymptotic analysis of the truncation and round-off error. Our comparisons suggest the numerical solutions near the end of a billion year simulation in double precision with variable-stepsize non-symplectic methods would have poor accuracy, and fast, higher precision arithmetic could be used to advantage.", } @Article{Sala:2006:OOF, author = "Marzio Sala", title = "An Object-Oriented Framework for the Development of Scalable Parallel Multilevel Preconditioners", journal = j-TOMS, volume = "32", number = "3", pages = "396--416", month = sep, year = "2006", URL = "http://doi.acm.org/10.1145/1163641.1163643", abstract = "We present the design of a high-performance, object oriented framework that enables the rapid development and usage of efficient, scalable and portable implementations of multilevel preconditioners for distributed sparse real matrices, in both serial and (massively) parallel environments. The main feature of the proposed framework is the use of several programming paradigms for the diffierent implementation layers, with a strong emphasis on object oriented classes and operator overloading for the top layer, and optimized FORTRAN and C code for the layers underneath. We describe an implementation of the proposed framework, based on the ML library, the algebraic multilevel preconditioning package of Trilinos, which supports state-of-the-art parallel smoothed aggregation methods, and can be used to define general algebraic and geometric multilevel and multigrid preconditioners and solvers. The paper demonstrates that one can take advantage of object-oriented programming and operator overloading to obtain intuitive, easy-to-read and easy-to-develop codes, that are at the same time efficient and scalable. Several numerical experiments, obtained on serial and parallel computers, show that the overhead required by the object-oriented layer is very modest, therefore allowing developers to focus on the new algorithms they are developing and testing, rather than on the implementation details.", } @Article{Kirby:2006:CVF, author = "Robert C. Kirby and Anders Logg", title = "A Compiler for Variational Forms", journal = j-TOMS, volume = "32", number = "3", pages = "417--444", month = sep, year = "2006", URL = "http://doi.acm.org/10.1145/1163641.1163644", abstract = "As a key step towards a complete automation of the finite element method, we present a new algorithm for automatic and efficient evaluation of multilinear variational forms. The algorithm has been implemented in the form of a compiler, the FEniCS Form Compiler FFC. We present benchmark results for a series of standard variational forms, including the incompressible Navier-Stokes equations and linear elasticity. The speedup compared to the standard quadrature-based approach is impressive; in some cases the speedup is as large as a factor 1000.", } @Article{Meshar:2006:OSS, author = "Omer Meshar and Dror Irony and Sivan Toledo", title = "An Out-of-Core Sparse Symmetric Indefinite Factorization Method", journal = j-TOMS, volume = "32", number = "3", pages = "445--471", month = sep, year = "2006", URL = "http://doi.acm.org/10.1145/1163641.1163645", abstract = "We present a new out-of-core sparse symmetric-indefinite factorization algorithm. The most significant innovation of the new algorithm is a dynamic partitioning method for the sparse factor. This partitioning method results in very low input/output traffic and allows the algorithm to run at high computational rates even though the factor is stored on a slow disk. Our implementation of the new code compares well with both high-performance in-core sparse symmetric-indefinite codes and with a high-performance out-of-core sparse Cholesky code.", } @Article{Alhargan:2006:ASC, author = "Fayez A. Alhargan", title = "Algorithm 855: Subroutines for the Computation of {Mathieu} Characteristic Numbers and their General Orders", journal = j-TOMS, volume = "32", number = "3", pages = "472--484", month = sep, year = "2006", URL = "http://doi.acm.org/10.1145/1163641.1163646", abstract = "A continued fraction function algorithm is developed to evaluate general order Mathieu characteristic numbers, and a new technique is presented for evaluating Mathieu determinant which can be used to compute the order $\nu$ directly. Approximate expressions are developed to estimate the orders and Mathieu characteristic numbers for the root finding algorithms. The algorithms with minor modifications were used for computating of Mathieu coefficients of general order. The algorithms can deal with a large range of Mathieu characteristic number $c$, real and complex order $\nu$ and parameter $h$.", } @Article{Gray:2006:AAA, author = "Genetha A. Gray and Tamara G. Kolda", title = "Algorithm 856: {APPSPACK} 4.0: Asynchronous Parallel Pattern Search for Derivative-Free Optimization", journal = j-TOMS, volume = "32", number = "3", pages = "485--507", month = sep, year = "2006", URL = "http://doi.acm.org/10.1145/1163641.1163647", abstract = "APPSPACK is software for solving unconstrained and bound constrained optimization problems. It implements an asynchronous parallel pattern search method that has been specifically designed for problems characterized by expensive function evaluations. Using APPSPACK to solve optimization problems has several advantages: No derivative information is needed; the procedure for evaluating the objective function can be executed via a separate program or script; the code can be run in serial or parallel, regardless of whether or not the function evaluation itself is parallel; and the software is freely available. We describe the underlying algorithm, data structures, and features of APPSPACK version 4.0 as well as how to use and customize the software.", } @Article{Lecuyer:2006:ISB, author = "Pierre L'Ecuyer and Richard Simard", title = "Inverting the Symmetrical {Beta} Distribution", journal = j-TOMS, volume = "32", number = "4", pages = "509--520", month = dec, year = "2006", URL = "http://doi.acm.org/10.1145/1186785.1186786", abstract = "We propose a fast algorithm for computing the inverse symmetrical beta distribution. Four series (two around x = 0 and two around x = 1/2) are used to approximate the distribution function and its inverse is found via Newton's method. This algorithm can be used to generate beta random variates by inversion and is much faster than currently available general inversion methods for the beta distribution. It turns out to be very useful for generating gamma processes efficiently via bridge sampling.", } @Article{Kressner:2006:BAR, author = "Daniel Kressner", title = "Block Algorithms for Reordering Standard and Generalized {Schur} Forms", journal = j-TOMS, volume = "32", number = "4", pages = "521--532", month = dec, year = "2006", URL = "http://doi.acm.org/10.1145/1186785.1186787", abstract = "Block algorithms for reordering a selected set of eigenvalues in a standard or generalized Schur form are proposed. Efficiency is achieved by delaying orthogonal transformations and (optionally) making use of level 3 BLAS operations. Numerical experiments demonstrate that existing algorithms, as currently implemented in LAPACK, are outperformed by up to a factor of four.", } @Article{Dhillon:2006:DIM, author = "Inderjit S. Dhillon and Beresford N. Parlett and Christof V\"{o}mel", title = "The Design and Implementation of the {MRRR} Algorithm", journal = j-TOMS, volume = "32", number = "4", pages = "533--560", month = dec, year = "2006", URL = "http://doi.acm.org/10.1145/1186785.1186788", abstract = "In the 90s, Dhillon and Parlett devised a new algorithm (Multiple Relatively Robust Representations, MRRR) for computing numerically orthogonal eigenvectors of a symmetric tridiagonal matrix $T$ with $O(n^2)$ cost. While previous publications related to MRRR have as focus the theoretical aspects, a documentation of software issues has been missing. In this paper, we discuss the design and implementation of the new MRRR version {\sc stegr} that is going to be included in a future release of LAPACK. By giving an algorithmic description of MRRR and identifying governing parameters, we hope to make {\sc stegr} more easily accessible and suitable for future performance tuning. Furthermore, this should help users understand design choices and tradeoffs when using the code.", } @Article{Su:2006:APG, author = "Hai-Jun Su and J. Michael McCarthy and Masha Sosonkina and Layne T. Watson", title = "Algorithm 857: {POLSYS GLP}: A Parallel General Linear Product Homotopy Code for Solving Polynomial Systems of Equations", journal = j-TOMS, volume = "32", number = "4", pages = "561--579", month = dec, year = "2006", URL = "http://doi.acm.org/10.1145/1186785.1186789", abstract = "Globally convergent, probability-one homotopy methods have proven to be very effective for finding all the isolated solutions to polynomial systems of equations. After many years of development, homotopy path trackers based on probability-one homotopy methods are reliable and fast. Now, theoretical advances reducing the number of homotopy paths that must be tracked, and in the handling of singular solutions, have made probability-one homotopy methods even more practical. POLSYS GLP consists of Fortran 95 modules for finding all isolated solutions of a complex coefficient polynomial system of equations. The package is intended to be used on a distributed memory multiprocessor in conjunction with HOMPACK90 (Algorithm 777), and makes extensive use of Fortran 95 derived data types and MPI to support a general linear product (GLP) polynomial system structure. GLP structure is intermediate between the partitioned linear product structure used by POLSYS PLP (Algorithm 801) and the BKK-based structure used by PHCPACK. The code requires a GLP structure as input, and although finding the optimal GLP structure is a difficult combinatorial problem, generally physical or engineering intuition about a problem yields a very good GLP structure. POLSYS GLP employs a sophisticated power series end game for handling singular solutions, and provides support for problem definition both at a high level and via hand-crafted code. Di®erent GLP structures and their corresponding Bezout numbers can be systematically explored before committing to root finding.", } @Article{VanDeun:2006:ACI, author = "Joris Van Deun and Ronald Cools", title = "Algorithm 858: Computing Infinite Range Integrals of an Arbitrary Product of {Bessel} Functions", journal = j-TOMS, volume = "32", number = "4", pages = "580--596", month = dec, year = "2006", URL = "http://doi.acm.org/10.1145/1186785.1186790", abstract = "We present an algorithm to compute integrals of the form \begin{equation} \int_0^\inf x^m \prod_{i=1}^k J_{\nu_i}(a_i x) dx \end{equation) with $J_{\nu_i}(x)$ the Bessel function of the first kind and (real) order $\nu_i$. The parameter m is a real number such that $\sum_i \nu_i + m > -1$ and the coefficients $a_i$ are strictly positive real numbers. The main ingredients in this algorithm are the well-known asymptotic expansion for $J_{\nu_i}(x)$ and the observation that the infinite part of the integral can be approximated using the incomplete Gamma function $\Gamma(a,z)$. Accurate error estimates are included in the algorithm, which is implemented as a Matlab program.", } @Article{Amodio:2006:ABF, author = "Pierluigi Amodio and Giuseppe Romanazzi", title = "Algorithm 859: {BABDCR}: a {Fortran} 90 package for the Solution of Bordered {ABD} Linear Systems", journal = j-TOMS, volume = "32", number = "4", pages = "597--608", month = dec, year = "2006", URL = "http://doi.acm.org/10.1145/1186785.1186791", abstract = "BABDCR is a package of Fortran 90 subroutines for the solution of linear systems with Bordered Almost Block Diagonal coefficient matrices. It is designed to handle matrices with blocks of the same size, that is having a block upper bidiagonal structure with an additional block in the right upper corner. The algorithm implemented in the package performs cyclic reduction of the coefficient matrix in order to reduce the fill-in due to the corner block.", } @Article{Goncalves:2006:ASE, author = "Eduardo N. Gon\c{c}alves and Reinaldo M. Palhares and Ricardo H. C. Takahashi and Renato C. Mesquita", title = "Algorithm 860: {SimpleS}: An Extension of {Freudenthal's} Simplex Subdivision", journal = j-TOMS, volume = "32", number = "4", pages = "609--621", month = dec, year = "2006", URL = "http://doi.acm.org/10.1145/1186785.1186792", abstract = "This paper presents a simple efficient algorithm for the subdivision of a $d$-dimensional simplex in $k^d$ simplices, where $k$ is any positive integer number. The algorithm is an extension of Freudenthal's subdivision method. The proposed algorithm deals with the more general case of $k^d$ subdivision, and is considerably simpler than the {\it RedRefinementND} algorithm for implementation of Freudenthal's strategy. The proposed simplex subdivision algorithm is motivated by a problem in the field of robust control theory: the computation of a tight upper bound of a dynamical system performance index, for usage in a branch-and-bound algorithm.", } @Article{Erricolo:2006:AFS, author = "Danilo Erricolo", title = "Algorithm 861: {Fortran} 90 Subroutines for Computing the Expansion Coefficients of {Mathieu} Functions using {Blanch's} Algorithm", journal = j-TOMS, volume = "32", number = "4", pages = "622--634", month = dec, year = "2006", URL = "http://doi.acm.org/10.1145/1186785.1186793", abstract = "A translation to Fortran 90 of Gertrude Blanch's algorithm to compute the expansion coefficients of the series that represent Mathieu functions is presented. Its advantages are portability, higher precision, practicality of use and extended documentation. In addition, numerical validations and comparisons with other existing methods are presented.", } @Article{Bader:2006:AMT, author = "Brett W. Bader and Tamara G. Kolda", title = "Algorithm 862: {MATLAB} Tensor Classes for Fast Algorithm Prototyping", journal = j-TOMS, volume = "32", number = "4", pages = "635--653", month = dec, year = "2006", URL = "http://doi.acm.org/10.1145/1186785.1186794", abstract = "Tensors (also known as multidimensional arrays or N-way arrays) are used in a variety of applications ranging from chemometrics to psychometrics. We describe four MATLAB classes for tensor manipulations that can be used for fast algorithm prototyping. The tensor class extends the functionality of MATLAB's multidimensional arrays by supporting additional operations such as tensor multiplication. The {\tt tensor_as_matrix} class supports the ``matricization'' of a tensor, i.e., the conversion of a tensor to a matrix (and vice versa), a commonly used operation in many algorithms. Two additional classes represent tensors stored in decomposed formats: {\tt cp_tensor} and {\tt tucker_tensor}. We describe all of these classes and then demonstrate their use by showing how to implement several tensor algorithms that have appeared in the literature.", } @Article{Enright:2007:RRD, author = "W. H. Enright and Wayne B. Hayes", title = "Robust and Reliable Defect Control for {Runge Kutta} Methods", journal = j-TOMS, volume = "33", number = "1", month = mar, year = "2007", pages = "1", note = "Article 1, 19 pages", URL = "http://doi.acm.org/10.1145/1206040.1206041", abstract = "The quest for reliable integration of initial value problems (IVPs) for ordinary differential equations (ODEs) is a long-standing problem in numerical analysis. At one end of the reliability spectrum are fixed stepsize methods implemented using standard floating point, where the onus lies entirely with the user to ensure the stepsize chosen is adequate for the desired accuracy. At the other end of the reliability spectrum are rigorous interval-based methods, that can provide provably correct bounds on the error of a numerical solution. This rigour comes at a price, however: interval methods are generally 2-3 orders of magnitude more expensive than fixed stepsize floating-point methods. Along the spectrum between these two extremes lie various methods of different expense that estimate and control some measure of the local errors and adjust the stepsize accordingly. \par In this paper, we continue previous investigations into a class of interpolants for use in Runge-Kutta methods that have a defect function whose qualitative behaviour is asymptotically independent of the problem being integrated. In particular the point, in a step, where the maximum defect occurs as $h \rightarrow 0$ is known {\em a priori}. This property allows the defect to be monitored and controlled in an efficient and robust manner even for modestly large stepsizes. Our interpolants also have a defect with the highest possible order given the constraints imposed by the order of the underlying discrete formula. We demonstrate the approach on three Runge-Kutta methods of order 5, 6, and 8, and provide Fortran and preliminary Matlab interfaces to these three new integrators. We also consider how sensitive such methods are to roundoff errors. Numerical results for four problems on a range of accuracy requests are presented.", } @Article{Neher:2007:CSF, author = "Markus Neher", title = "Complex Standard Functions and Their Implementation in the {CoStLy} Library", journal = j-TOMS, volume = "33", number = "1", month = mar, year = "2007", pages = "2", note = "Article 2, 27 pages", URL = "http://doi.acm.org/10.1145/1206040.1206042", abstract = "The practical calculation of range bounds for some complex standard functions is addressed in this paper. The functions under consideration are root and power functions, the exponential, trigonometric and hyperbolic functions, and their inverse functions. For such a function $f$ and a given rectangular complex interval $z$, some interval $w$ is computed that contains all function values of $f$ in $z$. This is done by expressing the real and the imaginary part of $f$ as compositions of real standard functions and then estimating the ranges of these compositions. In many cases, the inclusions are optimal, such that $w$ is the smallest rectangular interval containing the range of $f$. The algorithms presented in this paper have been implemented in a C++ class library called CoStLy (Complex Standard Functions Library), which is distributed under the conditions of the GNU General Public License.", } @Article{Gould:2007:FFF, author = "Nicholas I. M. Gould and Philippe L. Toint", title = "{FILTRANE}, a {Fortran 95} Filter-Trust-Region Package for Solving Nonlinear Least-Squares and Nonlinear Feasibility Problems", journal = j-TOMS, volume = "33", number = "1", month = mar, year = "2007", pages = "3", note = "Article 3, 23 pages", URL = "http://doi.acm.org/10.1145/1206040.1206043", abstract = "FILTRANE, a new Fortran 95 package for finding vectors satisfying general sets of nonlinear equations and/or inequalities, is presented. Several algorithmic variants are discussed and extensively compared on a set of CUTEr test problems, indicating that the default variant is both reliable and efficient. This discussion provides a first experimental study of the parameters inherent in filter algorithms.", } @Article{Berland:2007:EMP, author = "H{\aa}vard Berland and B{\aa}rd Skaflestad and Will M. Wright", title = "{EXPINT} --- A {MATLAB} Package for Exponential Integrators", journal = j-TOMS, volume = "33", number = "1", month = mar, year = "2007", pages = "4", note = "Article 4, 17 pages", URL = "http://doi.acm.org/10.1145/1206040.1206044", abstract = "Recently, a great deal of attention has been focused on the construction of exponential integrators for semi-linear problems. In this paper we describe a MATLAB package which aims to facilitate the quick deployment and testing of exponential integrators, of Runge Kutta, multistep and general linear type. A large number of integrators are included in this package along with several well known examples. The so-called $\phi$ functions and their evaluation is crucial for accuracy, stability and efficiency of exponential integrators, and the approach taken here is through a modification of the scaling and squaring technique; the most common approach used for computing the matrix exponential.", } @Article{Morandini:2007:UDS, author = "Marco Morandini and Paolo Mantegazza", title = "Using Dense Storage to Solve Small Sparse Linear Systems", journal = j-TOMS, volume = "33", number = "1", month = mar, year = "2007", pages = "5", note = "Article 5, 12 pages", URL = "http://doi.acm.org/10.1145/1206040.1206045", abstract = "A data structure is used to build a linear solver specialized for relatively small sparse systems. The proposed solver, optimized for run-time performance at the expense of memory footprint, outperforms widely used direct and sparse solvers for systems with between 100 and 3000 equations. A multi-threaded version of the solver is shown to give some speedups for problems with medium fill-in, while it does not give any benefit for very sparse problems.", } @Article{Demetriou:2007:ALF, author = "Ioannis C. Demetriou", title = "Algorithm 863: {L2WPMA}, a {Fortran} 77 Package for Weighted Least Squares Piecewise Monotonic Data Approximation", journal = j-TOMS, volume = "33", number = "1", month = mar, year = "2007", pages = "6", note = "Article 6, 19 pages", URL = "http://doi.acm.org/10.1145/1206040.1206046", abstract = "Fortran software is developed that calculates a best piecewise monotonic approximation to $n$ univariate data contaminated by random errors. The underlying method minimizes the weighted sum of the squares of the errors by requiring $k-1$ sign changes in the first divided differences of the approximation, where $k$ is a given positive integer. Hence, the piecewise linear interpolant to the fit consists of $k$ monotonic sections, alternately increasing and decreasing. This calculation can have about $O(n^{k})$ local minima, because the positions of the turning points of the fit are integer variables of the problem. The method, however, by employing a dynamic programming technique divides the data into at most $k$ disjoint sets of adjacent data and solves a $k=1$ problem (monotonic fit or isotonic regression) for each set. So, it calculates efficiently a global solution in only $O(n\sigma+k\sigma^{2})$ computer operations when $k$ \(\geq\) 3, where $\sigma$ is the number of local minima of the data, always bounded by $n/2$. This complexity reduces to only $O(n)$ when $k=1$ or $k=2$ (unimodal case). At the end of the calculation a spline representation of the solution and the corresponding Lagrange multipliers are provided. The software package has been tested on a variety of data sets showing a performance that does provide in practice shorter computation times than the complexity indicates in theory. An application of the method on identifying turning points and monotonic trends of data from 1947-96 on the UK pound over the US dollar exchange rate is presented. Generally, the method may have useful applications as, for example, in estimating the turning points of a function from some noisy measurements of its values, or in image and signal processing, or in providing a preliminary or complementary smoothing phase to further analyses of the data.", } @Article{Martello:2007:AAG, author = "Silvano Martello and David Pisingery and Daniele Vigo and Edgar den Boef and Jan Korst", title = "Algorithm 864: Algorithms for General and Robot-Packable Variants of the Three-Dimensional Bin Packing Problem", journal = j-TOMS, volume = "33", number = "1", month = mar, year = "2007", pages = "7", note = "Article 7, 12 pages", URL = "http://doi.acm.org/10.1145/1206040.1206047", abstract = "We consider the problem of orthogonally packing a given set of rectangular-shaped boxes into the minimum number of three-dimensional rectangular bins. The problem is NP-hard in the strong sense and extremely difficult to solve in practice. We characterize relevant subclasses of packing and present an algorithm which is able to solve moderately large instances to optimality. We also present the corresponding C language procedure, stating the calling conventions for its use. Extensive computational experiments compare the algorithm for the three-dimensional bin packing when solving general orthogonal packings and when restricted to robot packings.", } @Article{Gustavson:2007:AFS, author = "Fred G. Gustavson and John K. Reid and Jerzy Wa{\'s}niewski", title = "Algorithm 865: {Fortran} 95 Subroutines for {Cholesky} Factorization in Blocked Hybrid Format", journal = j-TOMS, volume = "33", number = "1", month = mar, year = "2007", pages = "8", note = "Article 8, 5 pages", URL = "http://doi.acm.org/10.1145/1206040.1206048", abstract = "We present subroutines for the Cholesky factorization of a positive-definite symmetric matrix and for solving corresponding sets of linear equations. They exploit cache memory by using the block hybrid format proposed by the authors in a companion paper. The matrix is packed into $n(n+1)/2$ real variables, and the speed is usually better than that of the LAPACK algorithm that uses full storage ($n^2$ variables). Included are subroutines for rearranging a matrix whose upper or lower triangular part is packed by columns to this format and for the inverse rearrangement. Also included is a kernel subroutine that is used for the Cholesky factorization of the diagonal blocks since it is suitable for any positive-definite symmetric matrix that is small enough to be held in cache. We provide a comprehensive test program and simple example programs.", } @Article{Zhang:2007:SSI, author = "Hong Zhang and Barry Smith and Michael Sternberg and Peter Zapol", title = "{SIPs}: Shift-and-Invert Parallel Spectral Transformations", journal = j-TOMS, volume = "33", number = "2", month = jun, year = "2007", pages = "9", note = "Article 9, 19 pages", URL = "http://doi.acm.org/10.1145/1236463.1236464", abstract = "SIPs is a new efficient and robust software package implementing multiple shift-and-invert spectral transformations on parallel computers. Built on top of SLEPc and PETSc, it can compute very large numbers of eigenpairs for sparse symmetric generalized eigenvalue problems. The development of SIPs is motivated by applications in nanoscale materials modeling, in which the growing size of the matrices and the pathological eigenvalue distribution challenge the efficiency and robustness of the solver. In this paper, we present a parallel eigenvalue algorithm based on distributed spectrum slicing. We describe the object-oriented design and implementation techniques in SIPs, and demonstrate its numerical performance on an advanced distributed computer", } @Article{Gould:2007:NES, author = "Nicholas I. M. Gould and Jennifer A. Scott and Yifan Hu", title = "A Numerical Evaluation of Sparse Solvers for Symmetric Systems", journal = j-TOMS, volume = "33", number = "2", month = jun, year = "2007", pages = "10", note = "Article 10, 32 pages", URL = "http://doi.acm.org/10.1145/1236463.1236465", abstract = "In recent years a number of solvers for the direct solution of large sparse symmetric linear systems of equations have been developed. These include solvers that are designed for the solution of positive definite systems as well as those that are principally intended for solving indefinite problems. In this study, we use performance profiles as a tool for evaluating and comparing the performance of serial sparse direct solvers on an extensive set of symmetric test problems taken from a range of practical applications.", } @Article{Benson:2007:UGT, author = "S. Benson and M. Krishnan and L. McInnes and J. Nieplocha and J. Sarich", title = "Using the {GA} and {TAO} Toolkits for Solving Large-Scale Optimization Problems on Parallel Computers", journal = j-TOMS, volume = "33", number = "2", month = jun, year = "2007", pages = "11", note = "Article 11, 21 pages", URL = "http://doi.acm.org/10.1145/1236463.1236466", abstract = "Challenges in the scalable solution of large-scale optimization problems include the development of innovative algorithms and efficient tools for parallel data manipulation. This paper discusses two complementary toolkits from the collection of Advanced CompuTational Software (ACTS), namely, Global Arrays (GA) for parallel data management and the Toolkit for Advanced Optimization (TAO), which have been integrated to support large-scale scientific applications of unconstrained and bound constrained minimization problems. Most likely to benefit are minimization problems arising in classical molecular dynamics, free energy simulations, and other applications where the coupling among variables requires dense data structures. TAO uses abstractions for vectors and matrices so that its optimization algorithms can easily interface to distributed data management and linear algebra capabilities implemented in the GA library. The GA/TAO interfaces are available both in the traditional library mode and as components compliant with the Common Component Architecture (CCA). We highlight the design of each toolkit, describe the interfaces between them, and demonstrate their use.", } @Article{Meza:2007:OOO, author = "J.C. Meza and R.A. Oliva and P.D. Hough and P.J. Williams", title = "{OPT++}: An Object Oriented Toolkit for Nonlinear Optimization", journal = j-TOMS, volume = "33", number = "2", month = jun, year = "2007", pages = "12", note = "Article 12, 27 pages", URL = "http://doi.acm.org/10.1145/1236463.1236467", abstract = "Object-oriented programming is a relatively new tool in the development of optimization software. The code extensibility and the rapid algorithm prototyping capability enabled by this programming paradigm promise to enhance the reliability, utility, and ease of use of optimization software. While the use of object-oriented programming is growing, there are still few examples of general purpose codes written in this manner, and a common approach is far from obvious. This paper describes OPT++, a {C++} class library for nonlinear optimization. The design is predicated on the concept of distinguishing between an algorithm-independent class hierarchy for nonlinear optimization problems and a class hierarchy for nonlinear optimization methods that is based on common algorithmic traits. The interface is designed for ease of use while being general enough so that new optimization algorithms can be added easily to the existing framework. A number of nonlinear optimization algorithms have been implemented in OPT++ and are accessible through this interface. Furthermore, example applications demonstrate the simplicity of the interface as well as the advantages of a common interface in comparing multiple algorithms.", } @Article{Fousse:2007:MMP, author = "Laurent Fousse and Guillaume Hanrot and Vincent Lef\`evre and Patrick P\'elissier and Paul Zimmermann", title = "{MPFR}: A Multiple-Precision Binary Floating-Point Library with Correct Rounding", journal = j-TOMS, volume = "33", number = "2", month = jun, year = "2007", pages = "13", note = "Article 13, 15 pages", URL = "http://doi.acm.org/10.1145/1236463.1236468", abstract = "This paper presents a multiple-precision binary floating-point library, written in the ISO C language, and based on the GNU MP library. Its particularity is to extend to arbitrary-precision ideas from the IEEE 754 standard, by providing \emph{correct rounding} and \emph{exceptions}. We demonstrate how these strong semantics are achieved --- with no significant slowdown with respect to other arbitrary-precision tools --- and discuss a few applications where such a library can be useful.", } @Article{Elman:2007:AIM, author = "Howard C. Elman and Alison Ramage and David J. Silvester", title = "Algorithm 866: {IFISS}, a {Matlab} Toolbox for Modelling Incompressible Flow", journal = j-TOMS, volume = "33", number = "2", month = jun, year = "2007", pages = "14", note = "Article 14, 18 pages", URL = "http://doi.acm.org/10.1145/1236463.1236469", abstract = "IFISS is a graphical Matlab package for the interactive numerical study of incompressible flow problems. It includes algorithms for discretisation by mixed finite element methods and a posteriori error estimation of the computed solutions. The package can also be used as a computational laboratory for experimenting with state-of-the-art preconditioned iterative solvers for the discrete linear equation systems that arise in incompressible flow modelling. A unique feature of the package is its comprehensive nature; for each problem addressed, it enables the study of both discretisation and iterative solution algorithms as well as the interaction between the two and the resulting effect on overall efficiency.", } @Article{Crouse:2007:RAG, author = "David F. Crouse", title = "Remark on Algorithm 515: Generation of a Vector from the Lexicographic Index Combinations", journal = j-TOMS, volume = "33", number = "2", month = jun, year = "2007", pages = "15", note = "Article 15, 2 pages", URL = "http://doi.acm.org/10.1145/1236463.1236470", abstract = "We present a correction to Algorithm 515 [Buckles and Lybanon 1977].", } @Article{Rioux:2007:ANF, author = "J. Rioux and M. Halse and E. Aubanel and B.J. Balcom and J. Kaffanke and S. Romanzetti and T. Dierkes and N.j. Shah", title = "An Accurate Non-uniform {Fourier} Transform For {SPRITE} Magnetic Resonance Imaging Data", journal = j-TOMS, volume = "33", number = "3", month = aug, year = "2007", pages = "16", note = "Article 16, 21 pages", URL = "http://doi.acm.org/10.1145/1268769.1268770", abstract = "A new algorithm is proposed for computing the discrete Fourier Transform (DFT) of purely phase encoded data acquired during Magnetic Resonance Imaging (MRI) experiments. These experiments use the SPRITE (Single Point Ramped Imaging with $T_1$ Enhancement) method and multiple-point acquisition, sampling data in a non-uniform manner that prohibits reconstruction by Fast Fourier Transform. The Chirp Z-Transform algorithm of Rabiner, Schafer and Rader can be combined with phase corrections to compute the DFT of this data to extremely high accuracy. This algorithm outperforms the interpolation methods that are traditionally used to process non-uniform data, both in terms of execution time and in terms of accuracy as compared to the DFT.", } @Article{Kirby:2007:ECC, author = "Robert C. Kirby and Anders Logg", title = "Efficient Compilation of a Class of Variational Forms", journal = j-TOMS, volume = "33", number = "3", month = aug, year = "2007", pages = "17", note = "Article 17, 20 pages", URL = "http://doi.acm.org/10.1145/1268769.1268771", abstract = "We investigate the compilation of general multilinear variational forms over affines simplices and prove a representation theorem for the representation of the element tensor (element stiffness matrix) as the contraction of a constant reference tensor and a geometry tensor that accounts for geometry and variable coefficients. Based on this representation theorem, we design an algorithm for efficient pretabulation of the reference tensor. The new algorithm has been implemented in the FEniCS Form Compiler~(FFC) and improves on a previous loop-based implementation by several orders of magnitude, thus shortening compile-times and development cycles for users of FFC.", } @Article{Scott:2007:ESD, author = "Jennifer A. Scott and Yifan Hu", title = "Experiences of Sparse Direct Symmetric Solvers", journal = j-TOMS, volume = "33", number = "3", month = aug, year = "2007", pages = "18", note = "Article 18, 28 pages", URL = "http://doi.acm.org/10.1145/1268769.1268772", abstract = "We recently carried out an extensive comparison of the performance of state-of-the-art sparse direct solvers for the numerical solution of symmetric linear systems of equations. Some of these solvers were written primarily as research codes while others have been developed for commercial use. Our experiences of using the different packages to solve a wide range of problems arising from real applications were mixed. In this paper, we highlight some of these experiences with the aim of providing advice to both software developers and users of sparse direct solvers. We discuss key features that a direct solver should offer and conclude that while performance is an essential factor to consider when choosing a code, there are other features that a user should also consider looking for that vary significantly between packages.", } @Article{Ball:2007:EGR, author = "James S. Ball and Nelson H. F. Beebe", title = "Efficient {Gauss}-Related Quadrature for Two Classes of Logarithmic Weight Functions", journal = j-TOMS, volume = "33", number = "3", month = aug, year = "2007", pages = "19", note = "Article 19, 21 pages", URL = "http://doi.acm.org/10.1145/1268769.1268773", abstract = "Integrals with logarithmic singularities are often difficult to evaluate by numerical methods. In this work, a quadrature method is developed that allows the exact evaluation (up to machine accuracy) of integrals of polynomials with two general types of logarithmic weights. The total work for the determination of $N$ nodes and points of the quadrature method is $\Order{N^2}$. Subsequently, integrals can be evaluated with $\Order{N}$ operations and function evaluations, so the quadrature is efficient. This quadrature method can then be used to generate the nonclassical orthogonal polynomials for weight functions containing logarithms and obtain Gauss and Gauss-related quadratures for these weights. Two algorithms for each of the two types of logarithmic weights that incorporate these methods are given in this paper.", } @Article{Beebe:2007:AQP, author = "Nelson H. F. Beebe and James S. Ball", title = "Algorithm 867: {QUADLOG} --- A Package of Routines for Generating {Gauss}-Related Quadrature for Two Classes of Logarithmic Weight Functions", journal = j-TOMS, volume = "33", number = "3", month = aug, year = "2007", pages = "20", note = "Article 20, 30 pages", URL = "http://doi.acm.org/10.1145/1268769.1268774", abstract = "A collection of subroutines and examples of their uses are described for the quadrature method developed in the companion article. These allow the exact evaluation (up to computer truncation and rounding errors) of integrals of polynomials with two general types of logarithmic weights, and also with the corresponding nonlogarithmic weights. The recurrence coefficients for the related nonclassical orthogonal polynomials with logarithmic weight functions can also be obtained. Tests of accuracy on various platforms are presented. The routines are usable from Fortran, C, and C++ programs conforming to any of at least six international programming-language standards.", } @Article{Espelid:2007:AGD, author = "Terje O. Espelid", title = "Algorithm 868: Globally Doubly Adaptive Quadrature - Reliable {Matlab} Codes", journal = j-TOMS, volume = "33", number = "3", month = aug, year = "2007", pages = "21", note = "Article 21, 21 pages", URL = "http://doi.acm.org/10.1145/1268769.1268775", abstract = "We discuss how to modify a recently published Matlab code, {\tt coteglob}, such that the excellent performance this code demonstrates for low and intermediate accuracy requests is retained while the performance is improved for high accuracy requests. {\tt coteglob} is a globally adaptive code using a 5 and 9 point pair of Newton-Cotes rules. Combining an extended sequence of rules using 5, 9, 17 and 33 points with a doubly adaptive bisection strategy is the main focus of the paper. We also discuss local versus global adaptivity and conclude that globally adaptive codes are to be preferred. Based on this we develop several new globally adaptive codes that all compare favorably both with {\tt coteglob}, with Matlab's best currently available quadrature software {\tt quadl} and the general purpose QUADPACK codes {\tt dqk15} and {\tt dqk21}. We include the results from extensive testing using both a Lyness-Kaganove testing technique and a battery test.", } @Article{LEcuyer:2007:TCL, author = "Pierre L'Ecuyer and Richard Simard", title = "TestU01: A {C} Library for Empirical Testing of Random Number Generators", journal = j-TOMS, volume = "33", number = "4", month = aug, year = "2007", pages = "22", note = "Article 22, 40 pages", URL = "http://doi.acm.org/10.1145/1268776.1268777", abstract = "We introduce TestU01, a software library implemented in the ANSI C language, and offering a collection of utilities for the empirical statistical testing of uniform random number generators (RNGs). It provides general implementations of the classical statistical tests for RNGs, as well as several others tests proposed in the literature, and some original ones. Predefined tests suites for sequences of uniform random numbers over the interval (0, 1) and for bit sequences are available. Tools are also offered to perform systematic studies of the interaction between a specific test and the structure of the point sets produced by a given family of RNGs. That is, for a given kind of test and a given class of RNGs, to determine how large should be the sample size of the test, as a function of the generator's period length, before the generator starts to fail the test systematically. Finally, the library provides various types of generators implemented in generic form, as well as many specific generators proposed in the literature or found in widely-used software. The tests can be applied to instances of the generators predefined in the library, or to user-defined generators, or to streams of random numbers produced by any kind of device or stored in files. Besides introducing TestU01, the paper provides a survey and a classification of statistical tests for RNGs. It also applies batteries of tests to a long list of widely used RNGs.", } @Article{Pesch:2007:HSF, author = "Lars Pesch and Alexander Bell and Henk Sollie and Vijaya R. Ambati and Onno Bokhove and Jaap J. W. van der Vegt", title = "hpGEM --- A Software Framework for Discontinuous {Galerkin} Finite Element Methods", journal = j-TOMS, volume = "33", number = "4", month = aug, year = "2007", pages = "23", note = "Article 23, 25 pages", URL = "http://doi.acm.org/10.1145/1268776.1268778", abstract = "hpGEM, a novel framework for the implementation of discontinuous Galerkin finite element methods (FEMs), is described. We present data structures and methods that are common for many (discontinuous) FEMs and show how we have implemented the components as an object-oriented framework. This framework facilitates and accelerates the implementation of finite element programs, the assessment of algorithms, and their application to real-world problems. The article documents the status of the framework, exemplifies aspects of its philosophy and design, and demonstrates the feasibility of the approach with several application examples.", } @Article{Bangerth:2007:DGP, author = "W. Bangerth and R. Hartmann and G. Kanschat", title = "deal.II --- a General Purpose Object Oriented Finite Element Library", journal = j-TOMS, volume = "33", number = "4", month = aug, year = "2007", pages = "24", note = "Article 24, 27 pages", URL = "http://doi.acm.org/10.1145/1268776.1268779", abstract = "An overview of the software design and data abstraction decisions chosen for deal.II, a general purpose finite element library written in C++, is given. The library uses advanced object-oriented and data encapsulation techniques to break finite element implementations into smaller blocks that can be arranged to fit users requirements. Through this approach, deal.II supports a large number of different applications covering a wide range of scientific areas, programming methodologies, and application-specific algorithms, without imposing a rigid framework into which they have to fit. A judicious use of programming techniques allows us to avoid the computational costs frequently associated with abstract object-oriented class libraries. The paper presents a detailed description of the abstractions chosen for defining geometric information of meshes and the handling of degrees of freedom associated with finite element spaces, as well as of linear algebra, input/output capabilities and of interfaces to other software, such as visualization tools. Finally, some results obtained with applications built atop deal.II are shown to demonstrate the powerful capabilities of this toolbox.", } @Article{Bai:2007:PSB, author = "Yihua Bai and Robert C. Ward", title = "A Parallel Symmetric Block-Tridiagonal Divide-and-Conquer Algorithm", journal = j-TOMS, volume = "33", number = "4", month = aug, year = "2007", pages = "25", note = "Article 25, 23 pages", URL = "http://doi.acm.org/10.1145/1268776.1268780", abstract = "We present a parallel implementation of the block-tridiagonal divide-and-conquer algorithm that computes eigen-solutions of symmetric block-tridiagonal matrices to reduced accuracy. In our implementation, we use mixed data/task parallelism to achieve data distribution and workload balance. Numerical tests show that our implementation is efficient, scalable and computes eigenpairs to prescribed accuracy. We compare the performance of our parallel eigensolver with that of the ScaLAPACK divide-and-conquer eigensolver on block-tridiagonal matrices.", } @Article{Shampine:2007:AND, author = "L. F. Shampine", title = "Accurate Numerical Derivatives in {Matlab}", journal = j-TOMS, volume = "33", number = "4", month = aug, year = "2007", pages = "26", note = "Article 26, 17 pages", URL = "http://doi.acm.org/10.1145/1268776.1268781", abstract = "Complex step differentiation (CSD) is a technique for computing very accurate numerical derivatives in languages that support complex arithmetic. We describe here the development of a CSD package in Matlab called PMAD. We have extended work done in other languages for scalars to the arrays that are fundamental to Matlab. This extension raises questions that we have been able to resolve in a satisfactory way. Our goal has been to make it as easy as possible to compute approximate Jacobians in Matlab that are all but exact. Although PMAD has a fast option for the expert that implements CSD as in previous work, the default is an object-oriented implementation that asks very little of the user.", } @Article{Zwolak:2007:AOW, author = "Jason W. Zwolak and Paul T. Boggs and Layne T. Watson", title = "Algorithm 869: {ODRPACK95}: A Weighted Orthogonal Distance Regression Code with Bound Constraints", journal = j-TOMS, volume = "33", number = "4", month = aug, year = "2007", pages = "27", note = "Article 27, 12 pages", URL = "http://doi.acm.org/10.1145/1268776.1268782", abstract = "ODRPACK (TOMS Algorithm 676) has provided a complete package for weighted orthogonal distance regression for many years. The code is complete with user selectable reporting facilities, numerical and analytic derivatives, derivative checking, and many more features. The foundation for the algorithm is a stable and efficient trust region Levenberg-Marquardt minimizer that exploits the structure of the orthogonal distance regression problem. ODRPACK95 was created to extend the functionality and usability of ODRPACK. ODRPACK95 adds bound constraints, uses the newer Fortran 95 language, and simplifies the interface to the user called subroutine.", } @Article{Kodama:2007:RAS, author = "Masao Kodama", title = "A Remark on Algorithm 644", journal = j-TOMS, volume = "33", number = "4", month = aug, year = "2007", pages = "28", note = "Article 28, 3 pages", URL = "http://doi.acm.org/10.1145/1268776.1268783", abstract = "This remark details correction for errors in the functions which compute the modified Bessel function of the second kind and the log of the gamma function. In both cases these errors cause a loss of precision for a small range of values of the \nu argument. These routines are used in the calculation of a number of other functions within the package whose accuracy is thus similarly affected", } @Article{Kressner:2008:BVH, author = "Daniel Kressner", title = "Block variants of {Hammarling’s} method for solving {Lyapunov} equations", journal = j-TOMS, volume = "34", number = "1", month = jan, year = "2008", pages = "1", note = "Article 1, 15 pages", URL = "http://doi.acm.org/10.1145/1322436.1322437", abstract = "This paper is concerned with the efficient numerical solution of the Lyapunov equation $A^TX+XA = -C$ with a stable matrix $A$ and a symmetric positive semidefinite matrix $C$ of possibly small rank. We discuss the efficient implementation of Hammarling's method and propose among other algorithmic improvements a block variant, which is demonstrated to perform significantly better than existing implementations. An extension to the discrete-time Lyapunov equation $A^TXA - X = -C$ is also described.", } @Article{Rouson:2008:GFA, author = "Damian W. I. Rouson and Robert Rosenberg and Xiaofeng Xu and Irene Moulitsas and Stavros C. Kassinos", title = "A Grid-Free Abstraction of the {Navier-Stokes} Equations in {Fortran} 95/2003", journal = j-TOMS, volume = "34", number = "1", month = jan, year = "2008", pages = "2", note = "Article 2, 33 pages", URL = "http://doi.acm.org/10.1145/1322436.1322438", abstract = "Computational complexity theory inspires a grid-free abstraction of the Navier-Stokes equations in Fortran 95/2003. A novel complexity analysis estimates that structured programming time grows at least quadratically with the number of program lines. Further analysis demonstrates how an object-oriented strategy focused on mathematical objects renders the quadratic estimate scale-invariant, so the time required for the limiting factor in program development (debugging) no longer grows as the code grows. Compared to the coordinate-free C++ programming of Grant et al. [2000], grid-free Fortran programming eliminates a layer of procedure calls, eliminates a related need for the C++ template construct, and offers a shorter migration path for Fortran programmers. The grid-free strategy is demonstrated by constructing a physical-space driver for a Fourier-space Navier-Stokes solver. Separating the expression of the continuous mathematical model from the discrete numerics clarifies issues that are otherwise easily conflated. A run-time profile suggests that grid-free design substantially reduces the fraction of the procedures that significantly impacts run time, freeing more code to be structured in ways that reduce development time. Applying Amdahl’s law to the total solution time (development time plus run time) leads to a strategy that negligibly impacts development time but achieves 58 percent of the maximum possible speedup.", } @Article{Walther:2008:CSH, author = "Andrea Walther", title = "Computing Sparse {Hessians} with Automatic Differentiation", journal = j-TOMS, volume = "34", number = "1", month = jan, year = "2008", pages = "3", note = "Article 3, 15 pages", URL = "http://doi.acm.org/10.1145/1322436.1322439", abstract = "A new approach for computing a sparsity pattern for a Hessian is presented: nonlinearity information is propagated through the function evaluation yielding the nonzero structure. A complexity analysis of the proposed algorithm is given. Once the sparsity pattern is available, coloring algorithms can be applied to compute a seed matrix. To evaluate the product of the Hessian and the seed matrix, a vector version for evaluating second order adjoints is analysed. New drivers of ADOL-C are provided implementing the presented algorithms. Run-time analyses are given for some problems of the CUTE collection.", } @Article{Linardakis:2008:ASG, author = "Leonidas Linardakis and Nikos Chrisochoides", title = "Algorithm 870: A Static Geometric Medial Axis Domain Decomposition in {2D} {Euclidean} Space" journal = j-TOMS, volume = "34", number = "1", month = jan, year = "2008", pages = "4", note = "Article 4, 28 pages", URL = "http://doi.acm.org/10.1145/1322436.1322440", abstract = "We present a geometric domain decomposition method and its implementation, which produces good domain decompositions in terms of three basic criteria: (1) The boundary of the subdomains create good angles, i.e., angles no smaller than a given tolerance $\phi_0$, where the value of $\phi_0$ is determined by the application which will use the domain decomposition. (2) The size of the separator should be relatively small compared to the area of the subdomains. (3) The maximum area of the subdomains should be close to the average subdomain area. The domain decomposition method uses an approximation of a Medial Axis as an auxiliary structure for constructing the boundary of the subdomains (separators). The N-way decomposition is based on the 'divide and conquer' algorithmic paradigm and on a smoothing procedure that eliminates the creation of any new artifacts in the subdomains. This approach produces well shaped uniform and graded domain decompositions, which are suitable for parallel mesh generation.", } @Article{Schreppers:2008:ACP, author = "Walter Schreppers and Annie Cuyt", title = "Algorithm 871: A {C/C++} Precompiler for the Auto Generation of Multiprecision Programs" journal = j-TOMS, volume = "34", number = "1", month = jan, year = "2008", pages = "5", note = "Article 5, 20 pages", URL = "http://doi.acm.org/10.1145/1322436.1322441", abstract = "In the past decade a number of libraries for multiprecision floating-point arithmetic have been developed. We describe an easy to use, generic C/C++ transcription program or precompiler for the conversion of C or C++ source code into new code that uses a C++ multiprecision library of choice. The precompiler can convert any type in the input source code to another type in the output source code. The input source can be either C or C++, while the output code generated by the precompiler and using the new types, is C++. The type conversion is based on a simple XML configuration file which is provided by either the developer of the multiprecision library or by the user of the precompiler. The precompiler can also convert to data types with additional features, which are not supported in the types of the source code. Applicability of the precompiler is shown with the successful conversion of large subsets of the GNU Scientific Library and Numerical Recipes.", } @Article{Chernikov:2008:AP2, author = "Andrey N. Chernikov and Nikos P. Chrisochoides", title = "Algorithm 872: Parallel 2D Constrained {Delaunay} Mesh Generation", journal = j-TOMS, volume = "34", number = "1", month = jan, year = "2008", pages = "6", note = "Article 6, 20 pages", URL = "http://doi.acm.org/10.1145/1322436.1322442", abstract = "Delaunay refinement is a widely used method for the construction of guaranteed quality triangular and tetrahedral meshes. We present an algorithm and a software for the parallel constrained Delaunay mesh generation in two dimensions. Our approach is based on the decomposition of the original mesh generation problem into $N$ smaller subproblems which are meshed in parallel. The parallel algorithm is asynchronous with small messages which can be aggregated and exhibits low communication costs. On a heterogeneous cluster of more than 100 processors our implementation can generate over one billion triangles in less than 3 minutes, while the single-node performance is comparable to that of the fastest to our knowledge sequential guaranteed quality Delaunay meshing library (the Triangle).", } @Article{Sala:2008:PHP, author = "Marzio Sala and W. F. Spotz and M. A. Heroux", title = "{PyTrilinos}: High-Performance Distributed-Memory Solvers for {Python}", journal = j-TOMS, volume = "34", number = "2", month = mar, year = "2008", pages = "7", note = "Article 7, 33 pages", URL = "http://doi.acm.org/10.1145/1326548.1326549", abstract = "PyTrilinos is a collection of Python modules that are useful for serial and parallel scientific computing. This collection contains modules that cover serial and parallel dense linear algebra, serial and parallel sparse linear algebra, direct and iterative linear solution techniques, domain decomposition and multilevel preconditioners, nonlinear solvers and continuation algorithms. Also included are a variety of related utility functions and classes, including distributed I/O, coloring algorithms and matrix generation. PyTrilinos vector objects are integrated with the popular NumPy Python module, gathering together a variety of high-level distributed computing operations with serial vector operations. \par PyTrilinos is a set of interfaces to existing, compiled libraries. This hybrid framework uses Python as front-end, and efficient pre-compiled libraries for all computationally expensive tasks. Thus, we take advantage of both the flexibility and ease of use of Python, and the efficiency of the underlying C++, C and FORTRAN numerical kernels. The presented numerical results show that, for many important problem classes, the overhead required by the Python interpreter is negligible. \par To run in parallel, PyTrilinos simply requires a standard Python interpreter. The fundamental MPI calls are encapsulated under an abstract layer that manages all inter-processor communications. This makes serial and parallel scripts using PyTrilinos virtually identical.", } @Article{Avron:2008:PUP, author = "Haim Avron and Gil Shklarski and Sivan Toledo", title = "Parallel Unsymmetric-Pattern Multifrontal Sparse {LU} with Column Preordering", journal = j-TOMS, volume = "34", number = "2", month = mar, year = "2008", pages = "8", note = "Article 8, 31 pages", URL = "http://doi.acm.org/10.1145/1326548.1326550", abstract = "We present a new parallel sparse LU factorization algorithm and code. The algorithm uses a column-preordering partial-pivoting unsymmetric-pattern multifrontal approach. Our baseline sequential algorithm is based on UMFPACK 4 but is somewhat simpler and is often somewhat faster than UMFPACK version 4.0. Our parallel algorithm is designed for shared-memory machines with a small or moderate number of processors (we tested it on up to 32 processors). We experimentally compare our algorithm with SuperLU MT, an existing shared-memory sparse LU factorization with partial pivoting. SuperLU MT scales better than our new algorithm, but our algorithm is more reliable and is usually faster. More specifically, on matrices that are costly to factor, our algorithm is usually faster on up to 4 processors, and is usually faster on 8 and 16. We were not able to run SuperLU MT on 32. The main contribution of this paper is showing that the column- preordering partial-pivoting unsymmetric-pattern multifrontal approach, developed as a sequential algorithm by Davis in several recent versions of UMFPACK, can be effectively parallelized.", } @Article{Sala:2008:ODI, author = "Marzio Sala and Kendall S. Stanley and Michael A. Heroux", title = "On the Design of Interfaces to Sparse Direct Solvers", journal = j-TOMS, volume = "34", number = "2", month = mar, year = "2008", pages = "9", note = "Article 9, 22 pages", URL = "http://doi.acm.org/10.1145/1326548.1326551", abstract = "We discuss the design of general, flexible, consistent, reusable and efficient interfaces to software libraries for the direct solution of systems of linear equations on both serial and distributed memory architectures. We introduce a set of abstract classes to access the linear system matrix elements and their distribution, access vector elements, and control the solution of the linear system. \par We describe a concrete implementation of the proposed interfaces, and report examples of applications and numerical results showing that the overhead induced by the object-oriented design is negligible under typical conditions of usage. We include examples of applications, and we comment on the advantages and limitations of the design.", } @Article{VanZee:2008:SPF, author = "Field G. Van Zee and Paolo Bientinesi and Tze Meng Low and Robert A. van de Geijn", title = "Scalable Parallelization of FLAME Code via the Workqueuing Model", journal = j-TOMS, volume = "34", number = "2", month = mar, year = "2008", pages = "10", note = "Article 10, 29 pages", URL = "http://doi.acm.org/10.1145/1326548.1326552", abstract = "We discuss the OpenMP parallelization of linear algebra algorithms that are coded using the Formal Linear Algebra Methods Environment (FLAME) API. This API expresses algorithms at a higher level of abstraction, avoids the use loop and array indices, and represents these algorithms as they are formally derived and presented. We report on two implementations of the workqueuing model, neither of which requires the use of explicit indices to specify parallelism. The first implementation uses the experimental taskq pragma, which may influence the adoption of a similar construct into OpenMP 3.0. The second workqueuing implementation is domain-specific to FLAME but allows us to illustrate the benefits of sorting tasks according to their computational cost prior to parallel execution. In addition, we discuss how scalable parallelization of dense linear algebra algorithms via OpenMP will require a two-dimensional partitioning of operands much like a 2D data distribution is needed on distributed memory architectures. We illustrate the issues and solutions by discussing the parallelization of the symmetric rank-k update and report impressive performance on an SGI system with 14 Itanium2 processors.", } @Article{Rojas:2008:ALM, author = "Marielba Rojas and Sandra A. Santos and Danny C. Sorensen", title = "Algorithm 873: {LSTRS}: {MATLAB} Software for Large-Scale Trust-Region Subproblems and Regularization", journal = j-TOMS, volume = "34", number = "2", month = mar, year = "2008, pages = "11", note = "Article 11, 28 pages", URL = "http://doi.acm.org/10.1145/1326548.1326553", abstract = "A MATLAB 6.0 implementation of the LSTRS method is presented. LSTRS was described in Rojas, M., Santos, S.A., and Sorensen, D.C., A new matrix-free method for the large-scale trust-region subproblem, {\it SIAM J. Optim.}, {\bf 11}(3):611-646, 2000. LSTRS is designed for large-scale quadratic problems with one norm constraint. The method is based on a reformulation of the trust-region subproblem as a parameterized eigenvalue problem, and consists of an iterative procedure that finds the optimal value for the parameter. The adjustment of the parameter requires the solution of a large-scale eigenvalue problem at each step. LSTRS relies on matrix-vector products only and has low and fixed storage requirements, features that make it suitable for large-scale computations. In the MATLAB implementation, the Hessian matrix of the quadratic objective function can be specified either explicitly, or in the form of a matrix-vector multiplication routine. Therefore, the implementation preserves the matrix-free nature of the method. A description of the LSTRS method and of the MATLAB software, version 1.2, is presented. Comparisons with other techniques and applications of the method are also included. A guide for using the software and examples are provided.", } @Article{Goto:2008:AHP, author = "Kazushige Goto and Robert A. van de Geijn", title = "Anatomy of a High-Performance Matrix Multiplication", journal = j-TOMS, volume = "34", number = "3", month = may, year = "2008", pages = "12", note = "Article 12, 25 pages", URL = "http://doi.acm.org/10.1145/1356052.1356053", abstract = "We present the basic principles which underlie the high-performance implementation of the matrix-matrix multiplication that is part of the widely used GotoBLAS library. Design decisions are justified by successively refining a model of architectures with multilevel memories. A simple but effective algorithm for executing this operation results. Implementations on a broad selection of architectures are shown to achieve near-peak performance.", } @Article{Piiroinen:2008:EDM, author = "Petri T. Piiroinen and Yuri A. Kuznetsov", title = "An Event-Driven Method to Simulate {Filippov} Systems with Accurate Computing of Sliding Motions", journal = j-TOMS, volume = "34", number = "3", month = may, year = "2008", pages = "13", note = "Article 13, 24 pages", URL = "http://doi.acm.org/10.1145/1356052.1356054", abstract = "This paper describes how to use smooth solvers for simulation of a class of piecewise smooth dynamical systems, called Filippov systems, with discontinuous vector fields. In these systems constrained motion along a discontinuity surface (so-called sliding) is possible and requires special treatment numerically. The introduced algorithms are based on an extension to Filippov’s method to stabilise the sliding flow together with accurate detection of the entrance and exit of sliding regions. The methods are implemented in a general way in MATLAB and sufficient details are given to enable users to modify the code to run on arbitrary examples. Here, the method is used to compute the dynamics of three example systems, a dry-friction oscillator, a relay feedback system and a model of an oil well drill-string.", } @Article{Howell:2008:, author = "Gary W. Howell and James W. Demmel and Charles T. Fulton and Sven Hammarling and Karen Marmol", title = "Cache Efficient Bidiagonalization Using {BLAS} 2.5 Operators", journal = j-TOMS, volume = "34", number = "3", month = may, year = "2008", pages = "14", note = "Article 14, 33 pages", URL = "http://doi.acm.org/10.1145/1356052.1356055", abstract = "On cache based computer architectures using current standard algorithms, Householder bidiagonalization requires a significant portion of the execution time for computing matrix singular values and vectors. In this paper we reorganize the sequence of operations for Householder bidiagonalization of a general $m \times n$ matrix, so that two (\_GEMV) vector-matrix multiplications can be done with one pass of the unreduced trailing part of the matrix through cache. Two new BLAS operations approximately cut in half the transfer of data from main memory to cache, reducing execution times by up to 25 per cent. We give detailed algorithm descriptions and compare timings with the current LAPACK bidiagonalization algorithm.", } @Article{Wang:2008:ABS, author = "R. Wang and P. Keast and P. H. Muir", title = "Algorithm 874: {BACOLR}---Spatial and Temporal Error Control Software for {PDEs} based on High Order Adaptive Collocation", journal = j-TOMS, volume = "34", number = "3", month = may, year = "2008", pages = "15", note = "Article 15, 28 pages", URL = "http://doi.acm.org/10.1145/1356052.1356056", abstract = "In this paper we discuss a new software package, BACOLR, for the numerical solution of a general class of time-dependent 1-D PDEs. This package employs high order adaptive methods in time and space within a method-of-lines approach and provides tolerance control of the spatial and temporal errors. The DAEs resulting from the spatial discretization (based on B-spline collocation) are handled by a substantially modified version of the Runge-Kutta solver, RADAU5. For each time step, the RADAU5 code computes an estimate of the temporal error and requires it to satisfy the user tolerance. After each time step BACOLR then computes a high order estimate of the spatial error and requires this error estimate to satisfy the user tolerance. BACOLR was developed through a substantial modification of the adaptive method-of-lines package, BACOL. In this paper we introduce the BACOLR package and present numerical results to show that the performance of BACOLR is comparable to and in some cases significantly superior to that of BACOL, which was shown in previous work to be more efficient, reliable and robust than other existing codes, especially for problems with solutions exhibiting narrow spikes or boundary layers.", } @Article{Benson:2008:ADS, author = "Steven J. Benson and Yinyu Ye", title = "Algorithm 875: {DSDP5}---Software for Semidefinite Programming", journal = j-TOMS, volume = "34", number = "3", month = may, year = "2008", pages = "16", note = "Article 16, 20 pages", URL = "http://doi.acm.org/10.1145/1356052.1356057", abstract = "DSDP implements the dual-scaling algorithm for semidefinite programming. The source code for this interior-point algorithm, written entirely in ANSI C, is freely available under an open source license. The solver can be used as a subroutine library, as a function within the Matlab environment, or as an executable that reads and writes to data files. Initiated in 1997, DSDP has developed into an efficient and robust general-purpose solver for semidefinite programming. Its features include a convergence proof with polynomially bounded worst-case complexity, primal and dual feasible solutions when they exist, certificates of infeasibility when solutions do not exist, initial points that can be feasible or infeasible, relatively low memory requirements for an interior-point method, sparse and low-rank data structures, extensibility that allows applications to customize the solver and improve its performance, a subroutine library that enables it to be linked to larger applications, scalable performance for large problems on parallel architectures, and a well-documented interface and examples of its use. The package has been used in many applications and tested for efficiency, robustness, and ease of use.", } @Article{Buttari:2008:UMP, author = "Alfredo Buttari and Jack Dongarra and Jakub Kurzak and Piotr Luszczek and Stanimire Tomov", title = "Using Mixed Precision for Sparse Matrix Computations to Enhance the Performance while Achieving 64-bit Accuracy", journal = j-TOMS, volume = "34", number = "4", month = jul, year = "2008", pages = "17", note = "Article 17, 22 pages", URL = "http://doi.acm.org/10.1145/1377596.1377597", abstract = "By using a combination of 32-bit and 64-bit floating point arithmetic the performance of many sparse linear algebra algorithms can be significantly enhanced while maintaining the 64-bit accuracy of the resulting solution. These ideas can be applied to sparse multifrontal and supernodal direct techniques and sparse iterative techniques such as Krylov subspace methods. The approach presented here can apply not only to conventional processors but also to exotic technologies such as Field Programmable Gate Arrays (FPGA), Graphical Processing Units (GPU), and the Cell BE processor.", } @Article{Utke:2008:OMO, author = "Jean Utke and Uwe Naumann and Mike Fagan and Nathan Tallent and Michelle Strout and Patrick Heimbach and Chris Hill and Carl Wunsch", title = "OpenAD/F: A Modular, Open-Source Tool for Automatic Differentiation of {Fortran} Codes", journal = j-TOMS, volume = "34", number = "4", month = jul, year = "2008", pages = "18", note = "Article 18, 36 pages", URL = "http://doi.acm.org/10.1145/1377596.1377598", abstract = "The OpenAD/F tool allows the evaluation of derivatives of functions defined by a Fortran program. The derivative evaluation is performed by a Fortran code resulting from the analysis and transformation of the original program that defines the function of interest. OpenADF has been designed with a particular emphasis on modularity, flexibility, and the use of open source components. While the code transformation follows the basic principles of automatic differentiation, the tool implements new algorithmic approaches at various levels, for example, for basic block preaccumulation and call graph reversal. Unlike most other automatic differentiation tools, OpenAD/F uses components provided by the OpenAD framework, which supports a comparatively easy extension of the code transformations in a language-independent fashion. It uses code analysis results implemented in the OpenAnalysis component. The interface to the language-independent transformation engine is an XML-based format, specified through an XML schema. The implemented transformation algorithms allow efficient derivative computations using locally optimized cross-country sequences of vertex, edge, and face elimination steps. Specifically, for the generation of adjoint codes, OpenAD/F supports various code reversal schemes with hierarchical checkpointing at the subroutine level. As an example from geophysical fluid dynamics a nonlinear time-dependent scalable, yet simple, barotropic ocean model is considered. OpenAD/F's reverse mode is applied to compute sensitivities of some of the model's transport properties with respect to gridded fields such as bottom topography as independent (control) variables.", } @Article{Moghaddam:2008:ECU, author = "Hassan Goldani-Moghaddam and Wayne H. Enright", title = "Efficient Contouring on Unstructured Meshes for Partial Differential Equations", journal = j-TOMS, volume = "34", number = "4", month = jul, year = "2008", pages = "19", note = "Article 19, 25 pages", URL = "http://doi.acm.org/10.1145/1377596.1377599", abstract = "We introduce three fast contouring algorithms for visualizing the solution of Partial Differential Equations based on the PCI (Pure Cubic Interpolant). The PCI is a particular piecewise bicubic polynomial interpolant defined over an unstructured mesh. Unlike standard contouring approaches, our contouring algorithms do not need a fine structured approximation and work efficiently with the original scattered data. The basic idea is to first identify the intersection points between contour curves and the sides of each triangle and then draw smooth contour curves connecting these points. We compare these contouring algorithms with the built-in Matlab {\it contour} procedure and other contouring algorithms. We demonstrate that our algorithms are both more accurate and faster than the others.", } @Article{Gao:2008:IEA, author = "Weiguo Gao and Xiaoye S. Li and Chao Yang and Zhaojun Bai", title = "An Implementation and Evaluation of the {AMLS} Method for Sparse Eigenvalue Problems", journal = j-TOMS, volume = "34", number = "4", month = jul, year = "2008", pages = "20", note = "Article 20, 28 pages", URL = "http://doi.acm.org/10.1145/1377596.1377600", abstract = "We describe an efficient implementation and present a performance study of an Algebraic Multi-Level Sub-structuring (AMLS) method for sparse eigenvalue problems. We assess the time and memory requirements associated with the key steps of the algorithm, and compare it with the shift-and-invert Lanczos algorithm. Our eigenvalue problems come from two very different application areas: the accelerator cavity design and the normal mode vibrational analysis of the polyethylene particles. We show that the AMLS method, when implemented carefully, outperforms the traditional method in broad application areas, when large number of eigenvalues are sought, with relatively low accuracy.", } @Article{Atkinson:2008:ASF, author = "Kendall E. Atkinson and Larry F. Shampine", title = "Algorithm 876: Solving {Fredholm} Integral Equations of the Second Kind in {Matlab}", journal = j-TOMS, accepted = "2 July 2007", volume = "34", number = "4", month = jul, year = "2008", pages = "21", note = "Article 21, 20 pages", URL = "http://doi.acm.org/10.1145/1377596.1377601", abstract = "We present here the algorithms and user interface of a Matlab program, Fie, that solves numerically Fredholm integral equations of the second kind on an interval $[a,b]$ to a specified, modest accuracy. The kernel function $K(s,t)$ is to be moderately smooth on $[a,b] \times [a,b]$ except possibly across the diagonal $s=t$. If the interval is finite, Fie provides for kernel functions that behave in a variety of ways across the diagonal, viz. $K(s,t)$ may be smooth, have a discontinuity in a low-order derivative, have a logarithmic singularity, or have an algebraic singularity. Fie also solves a large class of integral equations with moderately smooth kernel function on $[0,\infty)$.", } @Article{Kodama:2008:ASP, author = "Masao Kodama", title = "Algorithm 877: A Subroutine Package for Cylindrical Functions of Complex Order and Nonnegative Argument", journal = j-TOMS, volume = "34", number = "4", month = jul, year = "2008", pages = "22", note = "Article 22, 21 pages", URL = "http://doi.acm.org/10.1145/1377596.1377602", abstract = "The present algorithm provides a package of subroutines for calculating the cylindrical functions $J_\nu(x)$, $N_\nu(x)$, $H^{(1)}_\nu\!(x)$, $H^{(2)}_\nu\!(x)$ where the order $\nu$ is complex and the real argument $x$ is nonnegative. The algorithm is written in Fortran 95 and calculates the functions using single, double or quadruple precision according to the value of a parameter defined in the algorithm. The methods of calculating the functions are based on a series expansion, Debye's asymptotic expansions, Olver's asymptotic expansions and recurrence methods (Miller's algorithms). The relative errors of the functional values computed by this algorithm using double precision are less than $2.4\times 10^{-13}$ in the region $0\le {\rm Re}\,\nu\le 64$, $0\le{\rm Im}\,\nu\le 63$, $0.024\le x\le 97$.", } @Article{Bartlett:2008:HDS, author = "Roscoe A. Bartlett and Bart G. van Bloemen Waanders and Martin Berggren", title = "Hybrid Differentiation Strategies for Simulation and Analysis of Applications in {C++}", journal = j-TOMS, volume = "35", number = "1", month = jul, year = "2008", pages = "1", note = "Article 1, 27 pages", URL = "http://doi.acm.org/10.1145/1377603.1377604", abstract = "Computationally efficient and accurate derivatives are important to the success of many different types of numerical methods. Automatic differentation (AD) approaches compute truncation-free derivatives and can be efficient in many cases. Although present AD tools can provide a convenient implementation mechanism, the computational efficiency rarely compares to analytically derived versions that have been carefully implemented. The focus of this work is to combine the strength of these methods into a hybrid strategy that attempts to achieve an optimal balance of implementation and computational efficiency by selecting the appropriate components of the target algorithms for AD and analytical derivation. Although several AD approaches can be considered, our focus is on the use of template overloading forward AD tools in C++ applications. We demonstrate this hybrid strategy for a system of partial differential equations in gas dynamics. These methods apply however to other systems of differentiable equations, including DAEs and ODEs.", } @Article{Naumann:2008:OVE, author = "Uwe Naumann and Yuxiao Hu", title = "Optimal Vertex Elimination in Single-Expression-Use Graphs", volume = "35", number = "1", journal = j-TOMS, month = jul, year = "2008", pages = "2", note = "Article 2, 20 pages", URL = "http://doi.acm.org/10.1145/1377603.1377605", abstract = "The source transformation tool for automatic differentiation of Fortran programs ADIFOR uses a preaccumulation technique to speed up tangent-linear codes significantly compared to the standard forward mode. Reverse mode automatic differentiation is applied to all scalar assignments to generate efficient code for the computation of local gradients. It has been well known for some time that reverse mode is not necessarily the optimal choice for the computation of these statement-level gradients as it does not minimize the number of operations required. This paper presents an efficient algorithm for the solution of this combinatorial optimization problem. The corresponding software is freely available for downloading on our website. Developers of software for automatic differentiation are invited to integrate the algorithm into their tools. \par Gradients of scalar multivariate functions can be computed by elimination methods on the linearized computational graph. The combinatorial optimization problem that aims to minimize the number of arithmetic operations performed by the elimination algorithm is known to be NP-complete. In this paper we present a polynomial algorithm for solving a relevant subclass of this problem’s instances. The proposed method relies on the ability to compute vertex covers in bipartite graphs in polynomial time. A simplified version of this graph algorithm is used in a research prototype of the differentiation-enabled NAGWare Fortran compiler for the preaccumulation of local gradients of scalar assignments in the context of automatic generation of efficient tangent-linear code for numerical programs.", } @Article{Bientinesi:2008:FAR, author = "Paolo Bientinesi and Brian Gunter and Robert A. Van de Geijn", title = "Families of Algorithms Related to the Inversion of a Symmetric Positive Definite Matrix", journal = j-TOMS, volume = "35", number = "1", month = jul, year = "2008", pages = "3", note = "Article 3, 22 pages", URL = "http://doi.acm.org/10.1145/1377603.1377606", abstract = "We study the high-performance implementation of the inversion of a Symmetric Positive Definite (SPD) matrix on architectures ranging from sequential processors to Symmetric MultiProcessors to distributed memory parallel computers. This inversion is traditionally accomplished in three ``sweeps'': a Cholesky factorization of the SPD matrix, the inversion of the resulting triangular matrix, and finally the multiplication of the inverted triangular matrix by its own transpose. We state different algorithms for each of these sweeps as well as algorithms that compute the result in a single sweep. One algorithm outperforms the current ScaLAPACK implementation by 20-30 percent due to improved load-balance on a distributed memory architecture.", } @Article{Goto:2008:HPI, author = "Kazushige Goto and Robert van de Geijn", title = "High Performance Implementation of the Level-3 {BLAS}", journal = j-TOMS, volume = "35", number = "1", month = jul, year = "2008", pages = "4", note = "Article 4, 14 pages", URL = "http://doi.acm.org/10.1145/1377603.1377607", abstract = "A simple but highly effective approach for transforming high-performance implementations on cache-based architectures of matrix-matrix multiplication into implementations of other commonly used matrix-matrix computations (the level-3 BLAS) is presented. Exceptional performance is demonstrated on various architectures.", } @Article{Jonasson:2008:EEV, author = "Kristjan Jonasson and Sebastian E. Ferrando", title = "Evaluating Exact {VARMA} Likelihood and its Gradient when Data are Incomplete", volume = "35", number = "1", journal = j-TOMS, month = jul, year = "2008", pages = "5", note = "Article 5, 16 pages", URL = "http://doi.acm.org/10.1145/1377603.1377608", abstract = "A detailed description of an algorithm for the evaluation and differentiation of the likelihood function for VARMA processes in the general case of missing values is presented. The method is based on combining the Cholesky decomposition method for complete data VARMA evaluation and the Sherman-Morrison-Woodbury formula. Potential saving for pure VAR processes is discussed and formulae for the estimation of missing values and shocks are provided. A theorem on the determinant of a low rank update is proved. Matlab implementation of the algorithm is in a companion paper.", } @Article{Jonasson:2008:AEV, author = "Kristjan Jonasson", title = "Algorithm 878: Exact {VARMA} Likelihood and its Gradient for Complete and Incomplete Data with {Matlab}", journal = j-TOMS, volume = "35", number = "1", month = jul, year = "2008", pages = "6", note = "Article 6, 11 pages", URL = "http://doi.acm.org/10.1145/1377603.1377609", abstract = "Matlab functions for the evaluation of the exact log-likelihood of VAR and VARMA time series models are presented (vector autoregressive moving average). The functions accept incomplete data, and calculate analytical gradients, which may be used in parameter estimation with numerical likelihood maximization. Allowance is made for possible savings when estimating seasonal, structured or distributed lag models. Also provided is a function for creating simulated VARMA time series that have an accurate distribution from term one (they are spin-up free). The functions are accompanied by a a simple example driver, a program demonstrating their use for real parameter fitting, as well as a test suite for verifying their correctness and aid further development. The paper concludes with description of numerical results obtained with the algorithm.", } @Article{Lee:2008:AET, author = "Che-Rung Lee and G. W. Stewart", title = "Algorithm 879: {EIGENTEST}: A Test Matrix Generator for Large-Scale Eigenproblems", journal = j-TOMS, volume = "35", number = "1", month = jul, year = "2008", pages = "7", note = "Article 7, 11 pages", URL = "http://doi.acm.org/10.1145/1377603.1377610", abstract = "EIGENTEST is a package that produces real test matrices with known eigensystems. A test matrix, called an eigenmat, is generated in a factored form, in which the user can specify the eigenvalues and has some control over the condition of the eigenvalues and eigenvectors. An eigenmat $A$ of order $n$ requires only $O(n)$ storage for its representation. Auxiliary programs permit the computation of $(A - sI)b$, $(A - s I)^{\rm -T} b$, $(A - s I)^{-1} b$, and $(A - s I)^{\rm -T}b$ in $O(n)$ operations. A special routine computes specified eigenvectors of an eigenmat and the condition of its eigenvalue. Thus eigenmats are suitable for testing algorithms based on Krylov sequences, as well as others based on matrix-vector products. This paper introduces the eigenmat and describes implementations in Fortran~77, Fortran~95, C, and Matlab.", } @Article{Marques:2008:ATI, author = "Osni A. Marques and Christof V\"omel and James W. Demmel and Beresford N. Parlett", title = "Algorithm 880: A Testing Infrastructure for Symmetric Tridiagonal Eigensolvers", journal = j-TOMS, volume = "35", number = "1", month = jul, year = "2008", pages = "8", note = "Article 8, 13 pages", URL = "http://doi.acm.org/10.1145/1377603.1377611", abstract = "LAPACK is often mentioned as a positive example of a software library that encapsulates complex, robust, and widely used numerical algorithms for a wide range of applications. At installation time, the user has the option of running a (limited) number of test cases to verify the integrity of the installation process. On the algorithm developer's side, however, more exhaustive tests are usually performed to study algorithm behavior on a variety of problem settings and also computer architectures. In this process, difficult test cases need to be found that reflect particular challenges of an application or push algorithms to extreme behavior. These tests are then assembled into a comprehensive collection, therefore making it possible for any new or competing algorithm to be stressed in a similar way. This paper describes an infrastructure for exhaustively testing the symmetric tridiagonal eigensolvers implemented in LAPACK. It consists of two parts: a selection of carefully chosen test matrices with particular idiosyncrasies and a portable testing framework that allows for easy testing and data processing. The tester facilitates experiments with algorithmic choices, parameter and threshold studies, and performance comparisons on different architectures.", } @Article{Huyer:2008:SSN, author = "Waltraud Huyer and Arnold Neumaier", title = "SNOBFIT – Stable Noisy Optimization by Branch and Fit", journal = j-TOMS, volume = "35", number = "2", month = jul, year = "2008", pages = "9", note = "Article 9, 25 pages", URL = "http://doi.acm.org/10.1145/1377612.1377613", abstract = "The software package SNOBFIT for bound constrained (and soft constrained) noisy optimization of an expensive objective function is described. It combines global and local search by branching and local fits. The program is made robust and flexible for practical use by allowing for hidden constraints, batch function evaluations, change of search regions, etc.", } @Article{Kirby:2008:BDC, author = "Robert C. Kirby and Anders Logg", title = "Benchmarking Domain-specific Compiler Optimizations for Variational Forms", journal = j-TOMS, volume = "35", number = "2", month = jul, year = "2008", pages = "10", note = "Article 10, 18 pages", URL = "http://doi.acm.org/10.1145/1377612.1377614", abstract = "We examine the effect of using complexity-reducing relations [?] to generate optimized code for the evaluation of finite element variational forms. The optimizations are implemented in a prototype code named FErari, which has been integrated as an optimizing backend to the FEniCS Form Compiler, FFC. In some cases, FErari provides very little speedup, while in other cases, we obtain reduced local operation counts of a factor of as much as 7.9 and speedups for the assembly of the global sparse matrix of as much as a factor of 2.8.", } @Article{Quintana-Orti:2008:, author = "Enrique Quintana-Ort\'{i} and Robert A. van de Geijn", title = "Updating an LU factorization with Pivoting", journal = j-TOMS, volume = "35", number = "2", month = jul, year = "2008", pages = "11", note = "Article 11, 16 pages", URL = "http://doi.acm.org/10.1145/1377612.1377615", abstract = "We show how to compute an LU factorization of a matrix when the factors of a leading principle submatrix are already known. The approach incorporates pivoting akin to partial pivoting, a strategy we call incremental pivoting. An implementation using the Formal Linear Algebra Methods Environment (FLAME) Application Programming Interface (API) is described. Experimental results demonstrate practical numerical stability and high performance on an Intel Itanium2 processor based server.", } @Article{Drmac:2008:, author = "Zlatko Drma\v{c} and Zvonimir Bujanovi\'{c}", title = "On the Failure of Rank Revealing QR Factorization Software --- A Case Study", journal = j-TOMS, volume = "35", number = "2", month = jul, year = "2008", pages = "12", note = "Article 12, 28 pages", URL = "http://doi.acm.org/10.1145/1377612.1377616", abstract = "This paper reports an unexpected and rather erratic behavior of the LAPACK software implementation of the QR factorization with Businger{Golub column pivoting. It is shown that, due to finite precision arithmetic, the software implementation of the factorization can catastrophically fail to produce properly structured triangular factor, thus leading to potentially severe underestimate of a matrix's numerical rank. The 30 year old problem, dating back to LINPACK, has (undetectedly) badly affected many computational routines and software packages, as well as the study of rank revealing QR factorizations. We combine computer experiments and numerical analysis to isolate, analyze and fix the problem. Our modification of the current LAPACK xGEQP3 routine is already included in the LAPACK 3.1.0 release. The modified routine is numerically more robust and with a negligible overhead. We also provide a new, equally efficient and provably numerically safe, partial column norm updating strategy.", } @Article{Fraysse:2008:ASF, author = "Val\'erie Frayss\'e and Luc Giraud and Serge Gratton", title = "Algorithm 881: A Set of Flexible {GMRES} Routines for Real and Complex Arithmetics on High Performance Computers", journal = j-TOMS, volume = "35", number = "2", month = jul, year = "2008", pages = "13", note = "Article 13, 12 pages", URL = "http://doi.acm.org/10.1145/1377612.1377617", abstract = "In this paper we describe our implementations of the FGMRES algorithm for both real and complex, single and double precision arithmetics suitable for serial, shared memory and distributed memory computers. For the sake of portability, simplicity, flexibility and efficiency the FGMRES solvers have been implemented in Fortran 77 using the reverse communication mechanism for the matrix-vector product, the preconditioning and the dot product computations. For distributed memory computation, several orthogonalization procedures have been implemented to reduce the cost of the dot product calculation, that is a well-known bottleneck of efficiency for the Krylov methods. Furthermore, either implicit or explicit calculation of the residual at restart is possible depending on the actual cost of the matrix-vector product. Finally the implemented stopping criterion is based on a normwise backward error.", } @Article{VanDeun:2007:ANB, author = "Joris Van Deun and Karl Deckers and Adhemar Bultheel and J. A. C. Weideman", title = "Algorithm 882: Near Best Fixed Pole Rational Interpolation with Applications in Spectral Methods", journal = j-TOMS, volume = "35", number = "2", month = jul, year = "2008", pages = "14", note = "Article 14, 21 pages", URL = "http://doi.acm.org/10.1145/1377612.1377618", abstract = "We present a numerical procedure to compute the nodes and weights in rational Gauss-Chebyshev quadrature formulas. Under certain conditions on the poles, these nodes are near best for rational interpolation with prescribed poles (in the same sense that Chebyshev points are near best for polynomial interpolation). As an illustration, we use these interpolation points to solve a differential equation with an interior boundary layer using a rational spectral method. \par The algorithm to compute the interpolation points (and, if required, the quadrature weights) is implemented as a \textsc{Matlab} program.", } @Article{Waki:2008:ASS, author = "Hayato Waki and Sunyoung Kim and Masakazu Kojima and Mazakazu Muramatsu", title = "Algorithm 883: {SparsePOP} : a Sparse Semidefinite Programming Relaxation of Polynomial Optimization Problems", journal = j-TOMS, volume = "35", number = "2", month = jul, year = "2008", pages = "15", note = "Article 15, 13 pages", URL = "http://doi.acm.org/10.1145/1377612.1377619", abstract = "SparesPOP is a MATLAB implementation of the sparse semidefinite programming (SDP) relaxation method for approximating a global optimal solution of a polynomial optimization problem (POP) proposed by Waki, Kim, Kojima and Muramatsu. The sparse SDP relaxation exploits a sparse structure of polynomials in POPs when applying ``a hierarchy of LMI relaxations of increasing dimensions'' by Lasserre. The efficiency of SparsePOP to approximate optimal solutions of POPs is thus increased, and larger scale POPs can be handled.", } @Article{Dominguez:2008:ASM, author = "V\'{i}ctor Dom\'{i}nguez and Francisco-Javier Sayas", title = "Algorithm 884: A Simple {Matlab} Implementation of the {Argyris} Element", journal = j-TOMS, volume = "35", number = "2", month = jul, year = "2008", pages = "16", note = "Article 16, 11 pages", URL = "http://doi.acm.org/10.1145/1377612.1377620", abstract = "In this work we propose a new algorithm to evaluate the basis functions of the Argyris finite element and their derivatives. The main novelty here is an efficient way to calculate the matrix which gives the change of coordinates between the bases of the Argyis element for the reference and for an arbitrary triangle. This matrix is factored as the product of two rectangular matrices with a strong block structure which makes their computation very easy. We show and comment an implementation of this algorithm in Matlab. Two numerical experiments, an interpolation of a smooth function on a triangle and the finite element solution of the Dirichlet problem for the bilaplacian, are presented in the last section to check the performance of our implementation", } %%% ==================================================================== %%% Bibliography entries from Transactions on Programming Languages and %%% Systems: @Article{Hanson:1981:APE, author = "David R. Hanson", title = "{Algorithm 568}: {PDS}\emdash {A} Portable Directory System", journal = j-TOPLAS, volume = "3", number = "2", pages = "162--167", month = apr, year = "1981", CODEN = "ATPSDT", ISSN = "0164-0925", bibdate = "Fri Sep 9 14:11:06 1994", URL = "http://doi.acm.org/10.1145/357133.357137", acknowledgement = ack-nhfb, } @Misc{ACM:2002:CSE, author = "ACM", title = "{CALGO} Special Edition {CD}", howpublished = "CD-ROM organized as a Web site.", year = "2002", ISBN = "1-58113-333-2", bibdate = "Thu Jan 31 05:49:15 2002", note = "ACM order number 201001.", price = "US\$99.95 (member), US\$159.95 (nonmember), US\$199.95 (library)", acknowledgement = ack-nhfb, }