A New Method for the Bisymmetric Minimum Norm Solution of the Consistent Matrix Equations A1XB1=C1, A2XB2=C2

Abstract

We propose a new iterative method to find the bisymmetric minimum norm solution of a pair of consistent matrix equations $A_{1}X{B}_1=C_1$, $A_{2}X{B}_2=C_2$. The algorithm can obtain the bisymmetric solution with minimum Frobenius norm in finite iteration steps in the absence of round-off errors. Our algorithm is faster and more stable than Algorithm 2.1 by Cai et al. (2010).