Shift-Invert Arnoldi's Method with Preconditioned Iterative Solves
Copyright policy )Shift-Invert Arnoldi's Method with Preconditioned Iterative Solves
The authors consider the computation of a few eigenvectors and the corresponding eigenvalues of a large sparse nonsymmetric matrix using the shift-invert Arnoldi method with and without implicit restarts. They extend the relaxation strategy of \textit{V. Simoncini} [SIAM J. Numer. Anal. 43, 1155--1174 (2005; Zbl 1093.65037)] to the implicitly restarted Arnoldi method. The strategy of tuning the preconditioner by a low rank change, which the authors [IMA J. Numer. Anal. 28, 522--551 (2008; Zbl 1151.65030)] used earlier for inexact inverse iteration, is extended to the shift-invert Arnoldi method with inexact inner solves. Numerical results show that this combination of tuned preconditioner and relaxation strategy can reduce the number of inner iterations by nearly a half.
- Department of Mathematical Sciences Russian Federation
Numerical computation of eigenvalues and eigenvectors of matrices, implicitly restarted Arnoldi's method, tuned preconditioner, eigenvectors, GMRES, numerical results, Computational methods for sparse matrices, inexact inverse iteration, large sparse nonsymmetric matrix, iterative methods, Preconditioners for iterative methods, eigenvalue computation, inexact methods
Numerical computation of eigenvalues and eigenvectors of matrices, implicitly restarted Arnoldi's method, tuned preconditioner, eigenvectors, GMRES, numerical results, Computational methods for sparse matrices, inexact inverse iteration, large sparse nonsymmetric matrix, iterative methods, Preconditioners for iterative methods, eigenvalue computation, inexact methods
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