The Lanczos method with semi-definite inner product

Meerbergen, K.
(2001) International Conference on Numerical Mathematics — Location: UNIV LUND, LUND (Sweden) (9.August.2000)

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  • Meerbergen, K.
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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. 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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Meerbergen, K. (2001). The Lanczos method with semi-definite inner product. Bit (Lisse) : numerical mathematics, 41(5), 1069-1078. https://doi.org/10.1023/A:1021953631584 (Original work published 2001)