An approximate matrix inversion procedure by parallelization of the sherman-morrison formula

Kentaro Moriya, Linjie Zhang, Takashi Nodera

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

The Sherman-Morrison formula is one scheme for computing the approximate inverse preconditioner of a large linear system of equations. However, parallelizing a preconditioning approach is not straightforward as it is necessary to include a sequential process in the matrix factorization. In this paper, we propose a formula that improves the performance of the Sherman-Morrison preconditioner by partially parallelizing the matrix factorization. This study shows that our parallel technique implemented on a PC cluster system of eight processing elements significantly reduces the computational time for the matrix factorization compared with the time taken by a single processor. Our study has also verified that the Sherman-Morrison preconditioner performs better than ILU or MR preconditioners.

Original languageEnglish
Pages (from-to)1-9
Number of pages9
JournalANZIAM Journal
Volume51
Issue number1
DOIs
Publication statusPublished - 2009 Jul

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Sherman-Morrison Formula
Matrix Inversion
Parallelization
Preconditioner
Matrix Factorization
Approximate Inverse
PC Cluster
Linear system of equations
Preconditioning
Necessary
Computing

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

Cite this

An approximate matrix inversion procedure by parallelization of the sherman-morrison formula. / Moriya, Kentaro; Zhang, Linjie; Nodera, Takashi.

In: ANZIAM Journal, Vol. 51, No. 1, 07.2009, p. 1-9.

Research output: Contribution to journalArticle

Moriya, Kentaro ; Zhang, Linjie ; Nodera, Takashi. / An approximate matrix inversion procedure by parallelization of the sherman-morrison formula. In: ANZIAM Journal. 2009 ; Vol. 51, No. 1. pp. 1-9.
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