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Adaptively preconditioned GMRES algorithms

delete1998-01-01
delete100
PRE
AI
J
James Baglama
D
Daniela Calvetti
G
Gene H. Golub
L
Lothar Reichel
DOI：10.1137/S1064827596305258delete
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Abstract

Abstract

En 中文
The restarted GMRES algorithm proposed by Saad and Schultz [SIAM J. Sci. Statist. Comput., 7 (1986), pp. 856-869] is one of the most popular iterative methods for the solution of large linear systems of equations Ax = b with a nonsymmetric and sparse matrix. This algorithm is particularly attractive when a good preconditioner is available. The present paper describes two new methods for determining preconditioners from spectral information gathered by the Arnoldi process during iterations by the restarted GMRES algorithm. These methods seek to determine an invariant subspace of the matrix A associated with eigenvalues close to the origin and to move these eigenvalues so that a higher rate of convergence of the iterative methods is achieved.
Keywords:
iterative method
preconditioner
nonsymmetric linear system
Arnoldi process

Journal

SIAM Journal on Scientific Computing cover
SIAM Journal on Scientific Computing
IF:
2.6
Papers:
5.1K
Citations:
1.8W

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