The Inverse Problem of Centrosymmetric Matrices with a Submatrix Constraint

By using Moore-Penrose generalized inverse and the general singular value decomposition of matrices, this paper establishes the necessary and sufficient conditions for the existence of and the expressions for the centrosymmetric solutions with a submatrix constraint of matrix inverse problem $AX = B$. In addition, in the solution set of corresponding problem, the expression of the optimal approximation solution to a given matrix is derived.