An extension of the conjugate residual method to nonsymmetric linear systems

Authors:
T. Sogabe;M. Sugihara;S. -L. Zhang
Affiliations:
Department of Computational Science and Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464-8603, Japan;Department of Mathematical Informatics, The University of Tokyo, Hongo, 7-3-1, Bunkyo-ku, Tokyo, 113-8656, Japan;Department of Computational Science and Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464-8603, Japan
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

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.