Efficient parameterized rotated shift-splitting preconditioner for a class of complex symmetric linear systems

By utilizing the equivalent real block two-by-two linear systems and the shift-splitting techniques, we establish an efficient parameterized rotated shift-splitting (PRSS) preconditioner for solving a class of complex symmetric linear systems. The proposed preconditioner is extracted from a stationary iteration method which is unconditionally convergent. Moreover, some spectral properties of the corresponding preconditioned matrix are studied in detail. Finally, numerical results are presented to show the feasibility and effectiveness of the proposed preconditioner.