Algorithm 865

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


References in zbMATH (referenced in 2 articles )

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  1. Gustavson, Fred G.; Waśniewski, Jerzy; Dongarra, Jack J.; Langou, Julien: Rectangular full packed format for Cholesky’s algorithm: factorization, solution, and inversion (2010)
  2. Gustavson, Fred G.; Reid, John K.; Wasniewski, Jerzy: Algorithm 865: Fortran 95 subroutines for Cholesky factorization in block hybrid format. (2007) ioport