A new algorithm for the symmetric solution of the matrix equations AXB=E and CXD=F

Abstract

We propose a new iterative algorithm to compute the symmetric solution of the matrix equations $AXB=E$ and $CXD=F$. The greatest advantage of this new algorithm is higher speed and lower computational cost at each step compared with existing numerical algorithms. We state the solutions of these matrix equations as the intersection point of some closed convex sets, and then we use the alternating projection method to solve them. Finally, we use some numerical examples to show that the new algorithm is feasible and effective.