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Zbl 0770.65022
Freund, Roland W.; Gutknecht, Martin H.; Nachtigal, Noël M.
An implementation of the look-ahead Lanczos algorithm for non-Hermitian matrices. (English)
[J] SIAM J. Sci. Comput. 14, No.1, 137-158 (1993). ISSN 1064-8275; ISSN 1095-7197/e

The authors present an implementation of a look-ahead version of the Lanczos algorithm. Except for the very special situation of an incurable breakdown, this algorithm overcomes the problems of possible breakdowns and possible instabilities by skipping over those steps in which a breakdown or near breakdown would occur in the standard process. The proposed algorithm can handle look-ahead steps of any length and requires the same number of matrix-vector products and inner products as the standard Lanczos process without look-ahead.
[P.Narain (Bombay)]

MSC 2000:: *65F15 Eigenvalues (numerical linear algebra)

Keywords: Lanczos method; orthogonal polynomials; look-ahead steps; eigenvalue problems; iterative methods; non-Hermitian matrices; sparse linear systems

Cited in: Zbl 0898.65014

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