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. Sometime, 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.
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