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A variation on the block Arnoldi method for large unsymmetric matrix eigenproblems

A variation on the block Arnoldi method for large unsymmetric matrix eigenproblems The approximate eigenvectors or Ritz vectors obtained by the block Arnoldi method may converge very slowly and even fail to converge even if the approximate eigenvalues do. In order to improve the quality of the Ritz vectors, a modified strategy is proposed such that new approximate eigenvectors are certain combinations of the Ritz vectors and thewasted (m+1) th block basis vector and their corresponding residual norms are minimized in a certain sense. They can be cheaply computed by solving a few smallp-dimensional minimization problems. The resulting modifiedm-step block Arnoldi method is better than the standardm-step one in theory and cheaper than the standard (m+1)-step one. Based on this strategy, a modifiedm-step iterative block Arnoldi algorithm is presented. Numerical experiments are reported to show that the modifiedm-step algorithm is often considerably more efficient than the standard (m+1)-step iterative one. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

A variation on the block Arnoldi method for large unsymmetric matrix eigenproblems

Acta Mathematicae Applicatae Sinica , Volume 14 (4) – Jul 4, 2007

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Publisher
Springer Journals
Copyright
Copyright © 1998 by Science Press
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF02683827
Publisher site
See Article on Publisher Site

Abstract

The approximate eigenvectors or Ritz vectors obtained by the block Arnoldi method may converge very slowly and even fail to converge even if the approximate eigenvalues do. In order to improve the quality of the Ritz vectors, a modified strategy is proposed such that new approximate eigenvectors are certain combinations of the Ritz vectors and thewasted (m+1) th block basis vector and their corresponding residual norms are minimized in a certain sense. They can be cheaply computed by solving a few smallp-dimensional minimization problems. The resulting modifiedm-step block Arnoldi method is better than the standardm-step one in theory and cheaper than the standard (m+1)-step one. Based on this strategy, a modifiedm-step iterative block Arnoldi algorithm is presented. Numerical experiments are reported to show that the modifiedm-step algorithm is often considerably more efficient than the standard (m+1)-step iterative one.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jul 4, 2007

References