Generalized Conjugate A-Orthogonal Residual Squared Method for Complex Non-Hermitian Linear Systems

Abstract

Recently numerous numerical experiments on realistic calculation have shown that the conjugate A-orthogonal residual squared (CORS) method is often competitive with other popular methods. However, the CORS method, like the CGS method, shows irregular convergence, especially appears large intermediate residual norm, which may lead to worse approximate solutions and slower convergence rate. In this paper, we present a new product-type method for solving complex non-Hermitian linear systems based on the biconjugate A-orthogonal residual (BiCOR) method, where one of the polynomials is a BiCOR polynomial, and the other is a BiCOR polynomial with the same degree corresponding to different initial residual. Numerical examples are given to illustrate the effectiveness of the proposed method.