THE NEAREST BISYMMETRIC SOLUTIONS OF LINEAR MATRIX EQUATIONS
Zhen-yunPeng, Xi-yanHu, LeiZhang · Acta Scientiarum Naturalium Universitatis Sunyatseni · 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 neaxest solutions axe also provided.