中文摘要：

本文讨论广义特征值反问题在子矩阵束约束下的中心对称解及其最佳逼近问题．应用矩阵束的广义奇异值分解，导出了该问题有中心对称解的充要条件及有解情况下的通解表达式，证明了最佳逼近问题解的存在性与唯一性，并得到了最佳逼近解的表达式．最后给出了求解最佳逼近问题的数值算法及数值例子．

英文摘要：

This paper deals with the centrosymmetric solution of a generalized inverse eigen- value problem with a submatrix pencil constraint. By using the generalized singular value decomposition（GSVD） of matrix pencils, the sufficient and necessary conditions for the prob- lem 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 approx- imation are proved, and the expression of the best approximation are derived. A numerical algorithm for solving the problems is prensented.