Algorithm 865: Fortran 95 subroutines for Cholesky factorization in block hybrid format

Algorithm 865: Fortran 95 subroutines for Cholesky factorization in block hybrid format
Fred G. Gustavson, John K. Reid, Jerzy Wasniewski
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 as 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.
Keywords	Cholesky algorithm, Fortran95 subroutines, Solution of linear system of equetions
Type	Journal paper [With referee]
Journal	ACM Transactions on Mathematical Software
Year	2007 Month March Vol. 33 No. 1 pp. 1-5
Publisher	{ACM} Transactions on Mathematical Software
Publication link	http://math.nist.gov/toms/cgi-bin/TOMSbibget?Gustavson:2007:AFS
BibTeX data	[bibtex]
IMM Group(s)	Scientific Computing