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

Fred G. Gustavson, John K. Reid, Jerzy Wasniewski

    Research output: Contribution to journalJournal articleResearchpeer-review

    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 article. 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 (n2 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. © 2007 ACM.
    Original languageEnglish
    JournalA C M Transactions on Mathematical Software
    Volume33
    Issue number1
    Pages (from-to)1-5
    ISSN0098-3500
    DOIs
    Publication statusPublished - 2007

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