A transpose-free quasi-minimal residual variant of the CORS method for solving non-Hermitian linear systems

Recently, the conjugate A-orthogonal residual squared (CORS) method is often competitive and superior to other Krylov subspace methods for solving complex non-Hermitian linear systems from many realistic problems. However, like the conjugate gradient squared (CGS) method, the CORS method often exhibits irregular convergence behavior with wild oscillations in the residual norm. To try and remedy this problem, we develop a transpose-free quasi-minimal residual (TFQMR) variant of the CORS method, which leads to smooth convergence curves with a convergence rate similar to the CORS method. We also give convergence results for this new method. Finally, numerical examples are reported to illustrate the effectiveness of the proposed method.