Least-squares Solutions of Matrix Equation AX-BY=Z over Centrosymmetric Matrices and Its Optimal Approximation
Bing Gui, Hua Dai · Gongcheng shuxue xuebao · 2006
The least-squares solutions of the matrix equation AX－BY＝Z with respect to cen- trosymmetric matrices A and B is considered.The general expression of the solution is given and some necessary and sufficient conditions are derived for the solvability of the matrix equation AX－BY＝Z. The optimal approximation to given matrices from the least-squares solution set of AX－BY＝Z is provided.These results are applied to solve an class of inverse generalized eigenvalue problem for centrosymmetric matrices.