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

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