基于奇异值分解的一类广义特征值反问题

A Class of Generalized Eigenvalue Inverse Problem Based on Singular Value Decomposition

本文考虑了中心对称矩阵和反中心对称矩阵的广义特征值反问题及其最佳逼近问题,给出了解的一般表达式,进而对任意给定的矩阵[A,B]求出了最佳逼近解,并给出了数值算例.

In this paper, the generalized inverse eigenvalue problem of centrosymmetric and anticentrosymmetric matrices and relevant optimal approximation problem are considered. A general representation of the solution is derived. Furthermore,for any given matrices [A ,B] ,an expression of solution for its approximation, algorithm and numerical example are presented.