An efficient algorithm for solving extended Sylvester-conjugate transpose matrix equations

This note studies the iterative solutions to the extended Sylvester-conjugate transpose matrix equations with a unique solution. By using the hierarchical identification principle, an iterative algorithm is presented for solving this class of extended matrix equations. It is proved that the iterative solution consistently converges to the exact solution for any initial values. Meanwhile, by means of a real representation of a complex matrix, sufficient conditions are derived to guarantee that the iterative solutions given by the proposed algorithm converge to the exact solution for any initial matrices. Finally, a numerical example is given to illustrate the efficiency of the proposed approach.