A modified block alternating splitting iteration method for solving a class of two-by-two block complex linear systems

A modified version of the block alternating splitting (MBAS) iteration method is presented for solving the system arising from finite element discretization of the distributed optimal control problem with time-periodic parabolic equations. We prove that the MBAS iteration method is unconditionally convergent. We also present an estimation formula for the iteration parameter of the MBAS preconditioner. Numerical results are presented to verify the efficiency of both the MBAS iteration method and the MBAS preconditioner.