Thick-Restart Lanczos Method for Large Symmetric Eigenvalue Problems

Authors:
Kesheng Wu;Horst Simon
Affiliations:
-;-
Venue:
SIAM Journal on Matrix Analysis and Applications
Year:
2000

Citing 0
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Abstract

In this paper, we propose a restarted variant of the Lanczos method for symmetric eigenvalue problems named the thick-restart Lanczos method. This new variant is able to retain an arbitrary number of Ritz vectors from the previous iterations with a minimal restarting cost. Since it restarts with Ritz vectors, it is simpler than similar methods, such as the implicitly restarted Lanczos method. We carefully examine the effects of the floating-point round-off errors on stability of the new algorithm and present an implementation of the partial reorthogonalization scheme that guarantees accurate Ritz values with a minimal amount of reorthogonalization. We also show a number of heuristics on deciding which Ritz pairs to save during restart in order to maximize the overall performance of the thick-restart Lanczos method.