An Iterative Method for Bisymmetric Solutions and Optimal Approximation Solution of AXB=C
Yaxin Peng, Xi-Yan Hu, Lei Zhang · 2007
The bisymmetric solutions of the matrix equationAXB=Care 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 equationAXB=Cover 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 equationAXcircB=Ccirc.