Finite iterative algorithms for the generalized Sylvester-conjugate matrix equation AX + BY = EXF + S

This paper investigates the generalized Sylvester-conjugate matrix equation, which includes the normal Sylvester-conjugate, Kalman-Yakubovich-con- jugate and generalized Sylvester matrix equations as its special cases. An iterative algorithm is presented for solving such a kind of matrix equations. This iterative method can give an exact solution within finite iteration steps for any initial values in the absence of round-off errors. Another feature of the proposed algorithm is that it is implemented by original coefficient matrices. By specifying the proposed algo- rithm, iterative algorithms for some special matrix equations are also developed. Two numerical examples are given to illustrate the effectiveness of the proposed methods.