Iterative solutions to the Kalman-Yakubovich-conjugate matrix equation

Two operations are introduced for complex matrices. In terms of these two operations an infinite series expression is obtained for the unique solution of the Kalman-Yakubovich-conjugate matrix equation. Based on the obtained explicit solution, some iterative algorithms are given for solving this class of matrix equations. Convergence properties of the proposed algorithms are also analyzed by using some properties of the proposed operations for complex matrices.