The Lanczos Method with Semi-Definite Inner Product |
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Authors: | Karl Meerbergen |
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Affiliation: | (1) Free Field Technologies, 16 place de l'Université, 1348 Louvain-la-Neuve, Belgium |
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Abstract: | The spectral transformation Lanczos method is very popular for solving large scale real symmetric generalized eigenvalue problems. The method uses a special inner product so that the symmetric Lanczos method can be used. Sometimes, a semi-definite inner product must be used. This may lead to instabilities and break-down. In this paper, we suggest cures for breakdown by use of implicit restarting and the pseudo-Lanczos method.This revised version was published online in October 2005 with corrections to the Cover Date. |
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Keywords: | Eigenvalue problem positive semi-definite matrice Lanczos method |
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