A simple strategy for varying the restart parameter in GMRES(m)

A. H. Baker; E. R. Jessup; Tz V. Kolev

doi:10.1016/j.cam.2009.01.009

A simple strategy for varying the restart parameter in GMRES(m)

A. H. Baker, E. R. Jessup, Tz V. Kolev

Computational & Information Systems Lab

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48 Scopus citations

Abstract

When solving a system of linear equations with the restarted GMRES method, a fixed restart parameter is typically chosen. We present numerical experiments that demonstrate the beneficial effects of changing the value of the restart parameter in each restart cycle on the total time to solution. We propose a simple strategy for varying the restart parameter and provide some heuristic explanations for its effectiveness based on analysis of the symmetric case.

Original language	English
Pages (from-to)	751-761
Number of pages	11
Journal	Journal of Computational and Applied Mathematics
Volume	230
Issue number	2
DOIs	https://doi.org/10.1016/j.cam.2009.01.009
State	Published - Aug 15 2009

Keywords

GMRES
Iterative methods
Krylov subspace
Restart parameter

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10.1016/j.cam.2009.01.009

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abstract = "When solving a system of linear equations with the restarted GMRES method, a fixed restart parameter is typically chosen. We present numerical experiments that demonstrate the beneficial effects of changing the value of the restart parameter in each restart cycle on the total time to solution. We propose a simple strategy for varying the restart parameter and provide some heuristic explanations for its effectiveness based on analysis of the symmetric case.",

keywords = "GMRES, Iterative methods, Krylov subspace, Restart parameter",

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AU - Baker, A. H.

AU - Jessup, E. R.

AU - Kolev, Tz V.

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Y1 - 2009/8/15

N2 - When solving a system of linear equations with the restarted GMRES method, a fixed restart parameter is typically chosen. We present numerical experiments that demonstrate the beneficial effects of changing the value of the restart parameter in each restart cycle on the total time to solution. We propose a simple strategy for varying the restart parameter and provide some heuristic explanations for its effectiveness based on analysis of the symmetric case.

AB - When solving a system of linear equations with the restarted GMRES method, a fixed restart parameter is typically chosen. We present numerical experiments that demonstrate the beneficial effects of changing the value of the restart parameter in each restart cycle on the total time to solution. We propose a simple strategy for varying the restart parameter and provide some heuristic explanations for its effectiveness based on analysis of the symmetric case.

KW - GMRES

KW - Iterative methods

KW - Krylov subspace

KW - Restart parameter

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U2 - 10.1016/j.cam.2009.01.009

DO - 10.1016/j.cam.2009.01.009

M3 - Article

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EP - 761

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 2

ER -

A simple strategy for varying the restart parameter in GMRES(m)

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Keywords

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