Finite iterative algorithms for extended Sylvester-conjugate matrix equations

An iterative algorithm is presented for solving the extended Sylvester-conjugate matrix equation. By this iterative method, the solvability of the matrix equation can be determined automatically. When the matrix equation is consistent, a solution can be obtained within finite iteration steps for any initial values in the absence of round-off errors. The algorithm is also generalized to solve a more general complex matrix equation. Two numerical examples are given to illustrate the effectiveness of the proposed methods.