  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.
