子矩阵约束下广义反中心对称矩阵的广义特征值反问题

摘要

This paper deals with the generalized anti-centrosymmetric solution of a generalized inverse eigen-value problem with a submatrix pencil constraint. By using the quotient singular value decomposition( QSVD) of matrix pencil,the sufficient and necessary conditions for the problem having a generalized 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 u-niqueness of the optimal approximation are proved,and the expression of the best approximation are derived. A numerical algorithm for solving the problems is prensented.%讨论了广义特征值反问题在子矩阵束约束下的广义反中心对称解及其最佳逼近问题。应用矩阵对的商奇异值分解，导出了该问题有广义反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。