A thick-restarted block Arnoldi algorithm with modified Ritz vectors for large eigenproblems

The block Arnoldi method is one of the most commonly used techniques for large eigenproblems. In this paper, we exploit certain modified Ritz vectors to take the place of Ritz vectors in the thick-restarted block Arnoldi algorithm, and propose a modified thick-restarted block Arnoldi algorithm for l...

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) Vol. 60; no. 3; pp. 873 - 889
Main Authors: Jiang, Wei, Wu, Gang
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.08.2010
Subjects:
Algorithms
Block Arnoldi
Blocking
Computation
Computer simulation
Iterative methods
Krylov subspace
Mathematical analysis
Mathematical models
Modified Ritz vector
Ritz vector
Subspace iteration
Subspaces
Thick-restarting
Vectors (mathematics)
Krylov subspace
Thick-restarting
Block Arnoldi
Ritz vector
Modified Ritz vector
Subspace iteration
ISSN:0898-1221, 1873-7668
Online Access:Get full text
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Summary:The block Arnoldi method is one of the most commonly used techniques for large eigenproblems. In this paper, we exploit certain modified Ritz vectors to take the place of Ritz vectors in the thick-restarted block Arnoldi algorithm, and propose a modified thick-restarted block Arnoldi algorithm for large eigenproblems. We then consider how to periodically combine the refined subspace iterative method with the modified thick-restarting block Arnoldi algorithm for computing a few dominant eigenpairs of a large matrix. The resulting algorithm is called a Subspace-Block Arnoldi algorithm. Numerical experiments show the efficiency of our new algorithms.
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ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2010.05.034