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Zbl 0888.65030
Gutknecht, Martin H.
Lanczos-type solvers for nonsymmetric linear systems of equations. (English)
[A] Iserles, A. (ed.), Acta Numerica Vol. 6, 1997. Cambridge: Cambridge University Press. 271-397 (1997). ISBN 0-521-59106-6

The paper is a detailed and well written review of various Lanczos-type solvers for large linear systems with sparse nonsymmetric matrices. A list of about 150 references is given. Special attention is paid to possible breakdowns of the algorithms and ways to cure them.\par The important role of preconditioning is underlined and several examples of good preconditioners are given.\par Reviewer's remarks: One of the most effective approaches to grid systems $Ax= b$ should be mentioned. It deals with the symmetrization $B^{-1}A^* B^{-1}(Ax-b)= 0$, where $B= B^*>0$ is a good model operator for $A$ [see {\it E. G. D'yakonov}, Optimization in solving elliptic problems (1996; Zbl 0852.65087)]. It enables one to use modified Richardson iterations with proper parameters and their adaption, as well.
[E.D'yakonov (Moskva)]

MSC 2000:: *65F10 Iterative methods for linear systems
65F50 Sparse matrices
65F35 Matrix norms, etc. (numerical linear algebra)

Keywords: Lanczos-type methods; large linear systems; sparse nonsymmetric matrices; algorithms; preconditioning

Citations: Zbl 0852.65087

Cited in: Zbl 1225.65006

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