A composite step biconjugate gradient algorithm for nonsymmetric linear systems
 Randolph E. Bank,
 Tony F. Chan
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Abstract
The BiConjugate Gradient (BCG) algorithm is the simplest and most natural generalization of the classical conjugate gradient method for solving nonsymmetric linear systems. It is wellknown that the method suffers from two kinds of breakdowns. The first is due to the breakdown of the underlying Lanczos process and the second is due to the fact that some iterates are not welldefined by the Galerkin condition on the associated Krylov subspaces. In this paper, we derive a simple modification of the BCG algorithm, the Composite Step BCG (CSBCG) algorithm, which is able to compute all the welldefined BCG iterates stably, assuming that the underlying Lanczos process does not break down. The main idea is to skip over a step for which the BCG iterate is not defined.
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 Title
 A composite step biconjugate gradient algorithm for nonsymmetric linear systems
 Journal

Numerical Algorithms
Volume 7, Issue 1 , pp 116
 Cover Date
 19940301
 DOI
 10.1007/BF02141258
 Print ISSN
 10171398
 Online ISSN
 15729265
 Publisher
 Baltzer Science Publishers, Baarn/Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 Biconjugate gradients
 nonsymmetric linear systems
 65N20
 65F10
 Industry Sectors
 Authors

 Randolph E. Bank ^{(1)}
 Tony F. Chan ^{(2)}
 Author Affiliations

 1. Department of Mathematics, University of California at San Diego, 92092, La Jolla, CA, USA
 2. Department of Mathematics, University of California at Los Angeles, 90024, Los Angeles, CA, USA