Iterative method for mirror-symmetric solution of matrix equation AXB + CY D = E

Mirror-symmetric matrices have important applications in studying odd/even-mode decomposition of symmetric multiconductor transmission lines (MTL). In this paper, we propose an iterative algorithm to solve the mirror-symmetric solution of matrix equation AXB + CY D = E. With it, the solvability of the equation over mirror-symmetric X, Y can be determined automatically. When the equation is consistent, its solution can be obtained within finite iteration steps, and its least-norm mirror-symmetric solution can be obtained by choosing a special kind of initial iteration matrices. Furthermore, the related optimal approximation problem is also solved. Numerical examples are given to show the efficiency of the presented method