A technique for accelerating the convergence of restarted gmres

A. H. Baker; E. R. Jessup; T. Manteuffel

doi:10.1137/S0895479803422014

A technique for accelerating the convergence of restarted gmres

A. H. Baker
, E. R. Jessup
, T. Manteuffel

Lawrence Livermore National Laboratory
University of Colorado Boulder

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

187 Scopus citations

Abstract

We have observed that the residual vectors at the end of each restart cycle of restarted GMRES often alternate direction in a cyclic fashion, thereby slowing convergence. We present a new technique for accelerating the convergence of restarted GMRES by disrupting this alternating pattern. The new algorithm resembles a full conjugate gradient method with polynomial preconditioning, and its implementation requires minimal changes to the standard restarted GMRES algorithm.

Original language	English
Pages (from-to)	962-984
Number of pages	23
Journal	SIAM Journal on Matrix Analysis and Applications
Volume	26
Issue number	4
DOIs	https://doi.org/10.1137/S0895479803422014
State	Published - 2005
Externally published	Yes

Keywords

GMRES
Iterative methods
Krylov subspace
Nonsymmetric linear systems
Restart

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10.1137/S0895479803422014

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abstract = "We have observed that the residual vectors at the end of each restart cycle of restarted GMRES often alternate direction in a cyclic fashion, thereby slowing convergence. We present a new technique for accelerating the convergence of restarted GMRES by disrupting this alternating pattern. The new algorithm resembles a full conjugate gradient method with polynomial preconditioning, and its implementation requires minimal changes to the standard restarted GMRES algorithm.",

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AU - Jessup, E. R.

AU - Manteuffel, T.

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AB - We have observed that the residual vectors at the end of each restart cycle of restarted GMRES often alternate direction in a cyclic fashion, thereby slowing convergence. We present a new technique for accelerating the convergence of restarted GMRES by disrupting this alternating pattern. The new algorithm resembles a full conjugate gradient method with polynomial preconditioning, and its implementation requires minimal changes to the standard restarted GMRES algorithm.

KW - GMRES

KW - Iterative methods

KW - Krylov subspace

KW - Nonsymmetric linear systems

KW - Restart

UR - https://www.scopus.com/pages/publications/27144443419

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DO - 10.1137/S0895479803422014

M3 - Article

AN - SCOPUS:27144443419

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EP - 984

JO - SIAM Journal on Matrix Analysis and Applications

JF - SIAM Journal on Matrix Analysis and Applications

IS - 4

ER -

A technique for accelerating the convergence of restarted gmres

Abstract

Keywords

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