On the iterative bisymmetric solution of general coupled matrix equations

matrix A = (ai;j) 2 Rn×n is called bisymmetric matrix if ai;j = aj;i =an+1-j;n+1-i holds for all 1≤i; j≤n. In this paper, an efficient algorithm is presented to find the bisymmetric solution of the general coupled matrix equations. When the general coupled matrix equations is consistent on bisymmetric solutions, then for any initial bisymmetric matrix group, a group of bisymmetric solution can be obtained within finite iterative steps in the absence of round off errors, and the least norm bisymmetric solution can be obtained by choosing a group of special kind of initial matrices. Finally, we test the algorithm and show it is effectiveness by a numerical example.