THE NEAREST BISYMMETRIC SOLUTIONS OF LINEAR MATRIX EQUATIONS ∗1)
Zhenyun Peng, Xi-Yan Hu, Lei Zhang · 2004
The necessary and sufficient conditions for the existence of and the expressions for the bisymmetric solutions of the matrix equations (I) A1X1B1 +A2X2B2 +···+AkXkBk = D, (II) A1XB1 + A2XB2 + ···+ AkXBk = D and (III) (A1XB1,A2XB2,···,AkXBk )= (D1,D2,···,Dk) are derived by using Kronecker product and Moore-Penrose generalized inverse of matrices. In addition, in corresponding solution set of the matrix equations, the explicit expression of the nearest matrix to a given matrix in the Frobenius norm is given. Numerical methods and numerical experiments of finding the nearest solutions are also provided.