An extended shift-invert residual Arnoldi method

Matrix eigenvalue problems are frequently encountered in engineering and science. In this paper, we propose an extended shift-invert residual Arnoldi method for solving some smaller eigenvalues and the corresponding eigenvectors of a large and symmetric matrix, based on the idea of perfect Krylov su...

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Bibliographic Details
Published inComputational & applied mathematics Vol. 40; no. 2
Main Authors Yue, Su-Feng, Zhang, Jian-Jun
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 2021
Springer Nature B.V
Subjects
Applications of Mathematics
Applied physics
Computational mathematics
Computational Mathematics and Numerical Analysis
Eigenvalues
Eigenvectors
Mathematical analysis
Mathematical Applications in Computer Science
Mathematical Applications in the Physical Sciences
Mathematics
Mathematics and Statistics
Matrix methods
Subspace methods
Subspaces
Perfect Krylov subspace
Symmetric matrices
65F10
Eigenvalue
65F25
65F15
Iterative methods
15A18
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Summary:Matrix eigenvalue problems are frequently encountered in engineering and science. In this paper, we propose an extended shift-invert residual Arnoldi method for solving some smaller eigenvalues and the corresponding eigenvectors of a large and symmetric matrix, based on the idea of perfect Krylov subspace method proposed by Bai and Miao. We prove that the projected subspace of the proposed method is the same as the perfect Krylov subspace in exact computation. Based on this result, we also prove the convergence of the proposed method. Numerical experiments show that this method is superior to the perfect Krylov subspace method and the shift-invert residual Arnoldi method.
ISSN:2238-3603
1807-0302
DOI:10.1007/s40314-021-01444-3