Preconditioned symmetric block triangular splitting iteration method for a class of complex symmetric linear systems

In this paper, a preconditioned symmetric block triangular splitting (PSBTS) iteration method is proposed for solving a class of block two-by-two real linear systems which arise from complex symmetric linear systems. The eigenvalue distributions and the convergence properties of the PSBTS iteration method are established, and the optimal values of the relaxation parameter and the corresponding spectral radius of the PSBTS iteration matrix are obtained, respectively. It is remarkable that the spectral radius of the PSBTS iteration method is smaller than that of the SBTS iteration method under suitable conditions. Finally, two numerical examples are tested for illustrating effectiveness and robustness of the PSBTS iteration method.