Bibliographic record for `Davis:2008:DSS'
@Article{Davis:2008:DSS,
author = "Timothy A. Davis and William W. Hager",
title = "Dynamic Supernodes in Sparse {Cholesky} Update/downdate and Triangular Solves",
journal = "{ACM} Transactions on Mathematical Software",
volume = "35",
number = "4",
accepted = "2 May 2008",
upcoming = "true",
abstract = "The supernodal method for sparse Cholesky factorization represents the factor $L$ as a set of supernodes, each
consisting of a contiguous set of columns of $L$ with identical nonzero pattern. A conventional supernode is stored as
a dense submatrix. While this is suitable for sparse Cholesky factorization where the nonzero pattern of $L$ does not
change, it is not suitable for methods that modify a sparse Cholesky factorization after a low-rank change to $A$ (an
update/downdate, $\overline{A} = A \pm WW^T$). Supernodes merge and split apart during an update/downdate. Dynamic
supernodes are introduced, which allow a sparse Cholesky update/downdate to obtain performance competitive with
conventional supernodal methods. A dynamic supernodal solver is shown to exceed the performance of the conventional
(BLAS-based) supernodal method for solving triangular systems. These methods are incorporated into CHOLMOD, a sparse
Cholesky factorization and update/downdate package, which forms the basis of \verb'x=A\b' in MATLAB when \verb'A' is
sparse and symmetric positive definite.",
}
The bibliography is provided courtesy of the
BibNet Project.