Language:   Search:   Contact
Zentralblatt MATH has released its new interface!
For an improved author identification, see the new author database of ZBMATH.

# Advanced Search

Query:
Fill in the form and click »Search«...
Format:
Display: entries per page entries
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

Login Username: Password:

Highlights
Master Server

### Zentralblatt MATH Berlin [Germany]

© FIZ Karlsruhe GmbH

Zentralblatt MATH master server is maintained by the Editorial Office in Berlin, Section Mathematics and Computer Science of FIZ Karlsruhe and is updated daily.

Other Mirror Sites

Copyright © 2013 Zentralblatt MATH | European Mathematical Society | FIZ Karlsruhe | Heidelberg Academy of Sciences
Published by Springer-Verlag | Webmaster