A preconditioned version of the MBP iteration method for a class of complex symmetric linear systems

In this paper, we consider the iterative solution of a class of complex symmetric linear systems and construct a preconditioned variant of the modified block product (PMBP) iteration method. The proposed method is established by applying the preconditioning technique to the MBP method presented recently. The convergence conditions, optimal iteration parameters, and corresponding optimal convergence factor of the PMBP iteration method are determined. Meanwhile, a practical way to choose the iteration parameters for the PMBP iteration method is proposed. Furthermore, comparisons between the PMBP iteration method and some existing ones verify that the PMBP iteration method owns faster convergence rate than some known ones. Finally, some numerical experiments are provided to demonstrate the effectiveness and the superiority of the proposed PMBP method.