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An extension of the conjugate residual method to nonsymmetric linear systems

โœ Scribed by T. Sogabe; M. Sugihara; S.-L. Zhang

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
752 KB
Volume
226
Category
Article
ISSN
0377-0427

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โœฆ Synopsis

algorithm Coupled two-term recurrences a b s t r a c t

The Conjugate Gradient (CG) method and the Conjugate Residual (CR) method are Krylov subspace methods for solving symmetric (positive definite) linear systems. To solve nonsymmetric linear systems, the Bi-Conjugate Gradient (Bi-CG) method has been proposed as an extension of CG. Bi-CG has attractive short-term recurrences, and it is the basis for the successful variants such as Bi-CGSTAB. In this paper, we extend CR to nonsymmetric linear systems with the aim of finding an alternative basic solver. Numerical experiments show that the resulting algorithm with short-term recurrences often gives smoother convergence behavior than Bi-CG. Hence, it may take the place of Bi-CG for the successful variants.

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