Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/a-comparison-of-iterative-methods-for-solving-nonsymmetric-linear-vcwJIAkLgI
References (11)
-
Y. Saad, M. H. Schultz (1986)
GMRES: a generalized minimum residual algorithm for solving nonsymmetric linear systemsSIAM J. Sci. Stat. Comput., 7
-
C. Lanczos (1952)
Solution for systems of linear equations by minimized iterationJ. Res. Nat. Bur. Stand., 49
-
B. N. Parlett, D. R. Taylor, Z. A. Liu (1985)
A look-ahead Lanczos algorithm for unsymmetric matricesMath. Comp., 44
-
H. A. van der Vorst (1981)
Iterative solution methods for certain sparse linear systems with a nonsymmetric matrix arising from PDE problemsJ. Comput. Phys., 44
-
H. A. van der Vorst (1990)
Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems -
H. C. Elman (1982)
Iterative methods for large, sparse, nonsymmetric systems of linear equations -
P. Sonneveld (1989)
CGS, a fast Lanczos-type solver for nonsymmetric linear systemsSIAM J. Sci. Stat. Comput., 10
-
R. Barrett (1994)
Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods -
R. Fletcher (1976)
Lecture Notes in Math.506 -
Y. Saad (1982)
The Lanczos biorthogonalization algorithm and other oblique projection methods for solving large unsymmetric systemsSIAM J. Numer. Anal., 19
-
M. R. Hestenes, E. Stiefel (1952)
Methods of conjugate gradients for solving linear systemsJ. Res. Nat. Bur. Stand., 49
- Publisher
- Springer Journals
- Copyright
- Copyright © 1998 by Kluwer Academic Publishers
- Subject
- Mathematics; Mathematics, general; Computer Science, general; Theoretical, Mathematical and Computational Physics; Complex Systems; Classical Mechanics
- ISSN
- 0167-8019
- eISSN
- 1572-9036
- DOI
- 10.1023/A:1005919601192
- Publisher site
- See Article on Publisher Site
Abstract
Iterative methods, which were initially developed for the solution of symmetric linear systems, have more recently been extended to the nonsymmetric case. Nonsymmetric linear systems arise in many applications, including the solution of elliptic partial differential equations. In this work, we provide a brief description of and discuss the relationship between five commonly used iterative techniques: CGNR, GMRES, BiCG, CGS and BiCGSTAB. We highlight the relative merits and deficiencies of each technique through the implementation of each in the numerical solution of several differential equations test problems. Preconditioning is used in each case. We also discuss the mathematical equivalence between a nonsymmetric Lanczos orthogonalization, and BiCG.
Journal
Acta Applicandae Mathematicae – Springer Journals
Published: Oct 2, 2004