Optimal Approximation of Centrosymmetric Matrix Pencil with a Submatrix Pencil Constraint

This paper deals with the centrosymmetric solution of a generalized inverse eigenvalue problem with a submatrix pencil constraint.By using the generalized singular value decomposition(GSVD) of matrix pencils,the suffcient and necessary conditions for the problem having a centrosymmetric solution are obtained,and the general solution is presented.The best approximation for a given matrix pencil under a given spectral constraint and a submatrix pencil constraint is also considered.The existence and the uniqueness of the optimal approximation are proved,and the expression of the best approximation are derived.A numerical algorithm for solving the problems is prensented.