LAWN 294: Aasen's Symmetric Inde nite Linear Solvers in LAPACK

TitleLAWN 294: Aasen's Symmetric Inde nite Linear Solvers in LAPACK
Publication TypeTech Report
Year of Publication2017
AuthorsYamazaki, I., and J. Dongarra
Technical Report Series TitleLAPACK Working Note
NumberLAWN 294, ICL-UT-17-13
Date Published12-2017
InstitutionUniversity of Tennessee
Abstract

Recently, we released two LAPACK subroutines that implement Aasen's algorithms for solving a symmetric indefinite linear system of equations. The first implementation is based on a partitioned right-looking variant of Aasen's algorithm (the column-wise left-looking panel factorization, followed by the right-looking trailing submatrix update using the panel). The second implements the two-stage left-looking variant of the algorithm (the block-wise left- looking algorithm that reduces the matrix to the symmetric band form, followed by the band LU factorization). In this report, we discuss our implementations and present our experimental results to compare the stability and performance of these two new solvers with those of the other two symmetric indefinite solvers in LAPACK (i.e., the Bunch-Kaufman and rook pivoting algorithms).

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