Bibliographic record for `Koikari:2008:ABS'

@Article{Koikari:2008:ABS,
  author =       "S. Koikari",
  title =        "Algorithm XXX: On a Block {Schur--Parlett} Algorithm for $\varphi$-functions Based on the sep-inverse 
                 Estimate",
  journal =      "{ACM} Transactions on Mathematical Software",
  accepted =     "3 September 2008",
  upcoming =     "true",
  abstract =     "FORTRAN 95 software is provided for computing the matrix values of $\varphi$-functions required in exponential 
                 integrators. The subroutines in the library accept as their argument a full, diagonal, or upper quasi-triangular 
                 matrix with real or complex entries in one of four precisions. Two different algorithms are implemented, one is 
                 the scaling and squaring method, and the other is a modified block Schur--Parlett algorithm. In the latter 
                 algorithm, a recursive three-by-three blocking is applied to the argument based on an estimate of the 
                 sep-inverse function. The estimation of the sep-inverse function is carried out by Hager--Higham estimator 
                 implemented as the subroutine {\tt xLACON} in LAPACK. Our modifications to the block Schur--Parlett algorithm 
                 are described together with the results of numerical experiments.",
}