An Extension of the Conjugate Residual Method for Solving Nonsymmetric Linear Systems(Algorithms for Matrix・Eigenvalue Problems and their Applications, <Special Issue>Joint Symposium of JSIAM Activity Groups 2005)

Abstract

The Conjugate Gradient (CG) method and the Conjugate Residual (CR) method are well-known Krylov subspace methods for solving symmetric (positive definite) linear systems. For solving nonsymmetric ones, Fletcher extended the CG method to nonsymmetric linear systems. The resulting method is also well known as the Bi-CG method. The purpose of this paper is to extend the CR method to nonsymmetric linear systems. Numerical experiments show that the resulting method, named Bi-Conjugate Residual (Bi-CR), is often more efficient than the Bi-CG method.