一类次对称矩阵的广义特征值反问题

Inverse Problem of Gerneralized Eigenvalue for a Persymmetric Matrix

在矩阵广义特征值反问题实际应用中,提供全部的广义特征值有时存在较大困难。本文讨论了已知两组特征对的一类次对称矩阵的广义特征直反问题,通过对次对称矩阵广义特征向量性质的研究,得出该问题有唯一解、多解和无解的充分条件,并给出唯一解的具体表达式及其算法。

In the practical use of generalized inverse eigenvalue problem,it is difficult to provide all the generalized eigenvalues.In this paper,a generalized inverse eigenvalue problem with two eigenvalues and corresponding eigenvectors of persymmetric matrix is discussed.With a thorough study of the characteristic of generalized eigenvector,the conditions of the existence of its unique solution,multiple solutions and no solution are obtained.The expressions and the numerical algorithm of the unique solution are given.