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a b s t r a c tOptimization problems with partial differential equations as constraints arise widely in many areas of science and engineering. In this paper, we focus on solving a class of block two-by-two complex linear systems arising from the distributed optimal control with timeperiodic parabolic equations. A new block alternating splitting (BAS) iteration method is presented for solving the class of complex linear systems. The convergence theory and the spectral properties of the BAS iteration method are discussed. Numerical experiments are presented to illustrate the efficiency of the BAS iteration as a solver as well as a preconditioner for Krylov subspace methods.

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