On an application of the QMR approach to the Bi-CR method(Theory, Algorithms for Matrix/Eigenvalue Problems and Their Applications, Special Issue on "Joint Symposium of JSIAM Activity Groups 2007")

Abstract

The Bi-CG method, a well-known Krylov subspace method for solving non-symmetric linear systems, often shows an irregular convergence behavior in the residual norm. To avoid such a problem, Freund and Nachtigal proposed the QMR method. On the other hand, recently Sogabe et al. proposed the Bi-CR method, and showed experimentally that the Bi-CR method has good convergence. The purpose of this paper is to apply the QMR approach to the Bi-CR method to derive a new method, and to report the results of numerical experiments.