Optimizing and improving of the C-to-R method for solving complex symmetric linear systems

For complex symmetric linear systems, Axelsson et al. (2014) proposed the C-to-R method. In this paper, by further studying the C-to-R method with W and T being symmetric positive semidefinite, the optimal iteration parameter for the C-to-R method αopt=222 is obtained and the C-to-R method is optimized. Furthermore, based on the optimized C-to-R method, we further propose an optimized preconditioner. Eigenvalue properties of the optimized preconditioned matrix are analyzed, which show that all the eigenvalues of the preconditioned matrix are located in tighter interval. Numerical results are presented, not only confirm the validity of the theoretical analysis, but also demonstrate the feasibility and effectiveness of the proposed optimized C-to-R method.