An Iterative Method for Bisymmetric Solutions and Optimal Approximation Solution of AXB=C
The bisymmetric solutions of the matrix equation AXB = C are too difficult to be obtained by applying matrices decomposition. In this paper, an iterative method is applied to solve this problem. By this, the solvability of the equation AXB = C over bisymmetric X can be determined automatically, and its solution can be obtained in finite iterative steps when it is consistent, its least-norm solution can be obtained by choosing a special kind of starting iterative matrix, furthermore, its optimal approximation solution to a given matrix can be derived by finding the least- norm solution of a new equation AXcircB = Ccirc.