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Lanczos-type solvers for nonsymmetric linear systems of equations

Published online by Cambridge University Press:  07 November 2008

Martin H. Gutknecht
Martin H. Gutknecht
Affiliation:
Swiss Center for Scientific Computing ETH-Zentrum, CH-8092 Zürich, Switzerland E-mail: mhg@scsc.ethz.ch
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Abstract

Among the iterative methods for solving large linear systems with a sparse (or, possibly, structured) nonsymmetric matrix, those that are based on the Lanczos process feature short recurrences for the generation of the Krylov space. This means low cost and low memory requirement. This review article introduces the reader not only to the basic forms of the Lanczos process and some of the related theory, but also describes in detail a number of solvers that are based on it, including those that are considered to be the most efficient ones. Possible breakdowns of the algorithms and ways to cure them by look-ahead are also discussed.

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Research Article
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Acta Numerica , Volume 6 , January 1997 , pp. 271 - 397
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Copyright © Cambridge University Press 1997

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