A new iterative method for solving a class of two-by-two block complex linear systems

We present a stationary iteration method, namely Alternating Symmetric positive definite and Scaled symmetric semidefinite Splitting (ASSS), for solving the system of linear equations obtained by using finite element discretization distributed optimal control problem together with time-periodic parabolic equations. An upper bound spectral radius method is given which always less than 1. So convergence ASSS guaranteed. The induced preconditioner applied to accelerate speed GMRES system. Numerical results are presented demonstrate effectiveness both preconditioner.