Extended Conjugate Residual Methods For Solving Nonsymmetric Linear Systems

摘要

The Bi-Conjugate Gradient (Bi-CG) method is one of the most popular Krylov subspace methods for solving nonsymmetric linear systems, and it is considered as a natural generalization of the Conjugate Gradient (CG) method based on the Lanczos algorithm. In this paper, we propose a Bi-Conjugate Residual (Bi-CR) method, which can be considered as a natural generalization of the Conjugate Residual (CR) method based on the Lanczos algorithm. Numerical experiments indicate that the Bi-CR method often converges faster and gives much smoother convergence behavior than the Bi-CG method.