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On Restarting the Arnoldi Method for Large Nonsymmetric Eigenvalue Problems

Author: Ronald B. Morgan
Journal: Math. Comp. 65 (1996), 1213-1230
MSC (1991): Primary 65F15, 15A18
MathSciNet review: 1348046
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Abstract: The Arnoldi method computes eigenvalues of large nonsymmetric matrices. Restarting is generally needed to reduce storage requirements and orthogonalization costs. However, restarting slows down the convergence and makes the choice of the new starting vector difficult if several eigenvalues are desired. We analyze several approaches to restarting and show why Sorensen's implicit QR approach is generally far superior to the others. Ritz vectors are combined in precisely the right way for an effective new starting vector. Also, a new method for restarting Arnoldi is presented. It is mathematically equivalent to the Sorensen approach but has additional uses.

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Additional Information

Ronald B. Morgan
Affiliation: Department of Mathematics, Baylor University, Waco, Texas 76798-7328

Keywords: Arnoldi, Krylov subspaces, eigenvalues, sparse matrices, nonsymmetric matrices
Received by editor(s): July 3, 1991
Received by editor(s) in revised form: March 19, 1993, November 22, 1994, and February 13, 1995
Additional Notes: This research was partially supported by the National Science Foundation under contract CCR-8910665.
Article copyright: © Copyright 1996 American Mathematical Society