A Fully Portable High Performance Minimal Storage Hybrid Format Cholesky Algorithm

Bjarne Stig Andersen, John A. Gunnels, Fred G. Gustavson, Jerzy Wasniewski

    Research output: Contribution to journalJournal articleResearchpeer-review

    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{\$\backslash\$'{s}}niewski.
    Original languageEnglish
    JournalA C M Transactions on Mathematical Software
    Volume31
    Issue number2
    Pages (from-to)201-227
    ISSN0098-3500
    DOIs
    Publication statusPublished - Jun 2005

    Keywords

    • algorithms
    • performance
    • BLAS
    • real symmetric matrices
    • complex Hermitian matrices
    • positive-definite matrices
    • Cholesky factorization and solution
    • recursive algorithms
    • novel packed-matrix data structures
    • linear systems of equations

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