Gradient Based Iterative Solutions for Sylvester-Conjugate Matrix Equations

This paper presents a gradient based iterative algorithm for Sylvester-conjugate matrix equations with a unique solution. By introducing a relaxation parameter and applying the hierarchical identification principle, an iterative algorithm is constructed to solve Sylvester matrix equations. By applying a real representation of a complex matrix as a tool and using some properties of the real representation, convergence analysis indicates that the iterative solutions converge to the exact solutions for any initial values under certain assumptions.Numerical examples are given to illustrate the efficiency of the proposed approach.