An iterative block Arnoldi algorithm with modified approximate eigenvectors for large unsymmetric eigenvalue problems

A modified m-step Arnoldi algorithm proposed by Jia and Elsner for computing a few selected eigenpairs of large unsymmetric matrices is generalized to its block version. In the new method, we use new modified approximate eigenvectors obtained from a linear combination of Ritz vectors and the wasted...

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Bibliographic Details
Published in:Applied mathematics and computation Vol. 153; no. 3; pp. 611 - 643
Main Author: Wu, Gang
Format: Journal Article
Language:English
Published: New York, NY Elsevier Inc 14.06.2004
Elsevier
Subjects:
Block Arnoldi process
Exact sciences and technology
Krylov subspace
Mathematics
Modified approximate eigenvectors
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Orthogonal projection
Ritz values
Ritz vectors
Sciences and techniques of general use
Orthogonal projection
Block Arnoldi process
Ritz values
Modified approximate eigenvectors
Krylov subspace
Ritz vectors
Arnoldi algorithm
Numerical analysis
Approximate method
Matrix algebra
Applied mathematics
Eigenvector
Iterative method
Eigenvalue problem
Block matrix
ISSN:0096-3003, 1873-5649
Online Access:Get full text
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Summary:A modified m-step Arnoldi algorithm proposed by Jia and Elsner for computing a few selected eigenpairs of large unsymmetric matrices is generalized to its block version. In the new method, we use new modified approximate eigenvectors obtained from a linear combination of Ritz vectors and the wasted ( m+1)th block basis vector, whose residual norms are satisfied with some ( p+1)-dimensional minimization problems. The resulting block Arnoldi algorithm is not only better than the standard m-step one both in theory and in practice but also cheaper than the standard ( m+1)-step one. The relationships among the residual norms of Ritz pairs and those of new approximate eigenpairs are analyzed. Theoretical results show that the new method can overcome the drawback of nonconvergence, which exists in the conventional one in some extent. We carry out some numerical experiments, which exhibit that the new algorithm is more efficient and works better than its counterparts.
ISSN:0096-3003
1873-5649
DOI:10.1016/S0096-3003(03)00655-6