A new matrix based iterative method is presented to compute common symmetric solution or common symmetric least-squares solution of the pair of matrix equations AXB = E and CXD = F. By this iterative method, for any initial matrix X0, a solution X* can be obtained within finite iteration steps if exact arithmetic was used, and the solution X * with the minimum Frobenius norm can be obtained by choosing a special kind of initial matrix. In addition, the unique nearest common symmetric solution or common symmetric least-squares solution X to give...
