Stability of a pivoting strategy for parallel Gaussian elimination

J. L. Mead; Rosemary Renaut; Bruno Welfert

doi:10.1023/A:1021931632067

Stability of a pivoting strategy for parallel Gaussian elimination

Mathematical and Statistical Sciences, School of (SoMSS)

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

Gaussian elimination with partial pivoting achieved by adding the pivot row to the kth row at step k, was introduced by Onaga and Takechi in 1986 as a means for reducing communications in parallel implementations. In this paper it is shown that the growth factor of this partial pivoting algorithm is bounded above by μ_n < 3^n-1, as compared to 2^n-1 for the standard partial pivoting. This bound μ_n, close to 3^n-2, is attainable for a class of near-singular matrices. Moreover, for the same matrices the growth factor is small under partial pivoting.

Original language	English (US)
Pages (from-to)	633-639
Number of pages	7
Journal	BIT Numerical Mathematics
Volume	41
Issue number	3
DOIs	https://doi.org/10.1023/A:1021931632067
State	Published - Sep 2001

Keywords

Gaussian elimination
Growth factor
Parallel algorithm
Stability

ASJC Scopus subject areas

Software
Computer Networks and Communications
Computational Mathematics
Applied Mathematics

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AU - Renaut, Rosemary

AU - Welfert, Bruno

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AB - Gaussian elimination with partial pivoting achieved by adding the pivot row to the kth row at step k, was introduced by Onaga and Takechi in 1986 as a means for reducing communications in parallel implementations. In this paper it is shown that the growth factor of this partial pivoting algorithm is bounded above by μn < 3n-1, as compared to 2n-1 for the standard partial pivoting. This bound μn, close to 3n-2, is attainable for a class of near-singular matrices. Moreover, for the same matrices the growth factor is small under partial pivoting.

KW - Gaussian elimination

KW - Growth factor

KW - Parallel algorithm

KW - Stability

UR - https://www.scopus.com/pages/publications/0012087577

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JF - BIT Numerical Mathematics

IS - 3

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Stability of a pivoting strategy for parallel Gaussian elimination

Abstract

Keywords

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