次对称三对角矩阵特征值反问题

Inverse Eigenvalue Problem for Persymmetric Tridiagonal Matrix

文章讨论了由两个特征对构造次对称三对角矩阵的特征值反问题。结合次对称矩阵中属于不同特征值的特征向量的次正交性,研究了解的存在性以及存在解的充要条件,并给出了相应的算法及数值例子。

In this paper, a kind of inverse eigenvalue problem which is the reconstuction of persymmetric tridiagonal matrix by two eigenvalues and corresponding eigenvectors is proposed. Integrated with the sub - orthogonal of the eigenvectors which belonged to the different eigenvalues, the solvability of the problem is discussed and some sufficient and necessary conditions of solution are given. Furthermore, numerical algorithm and the example are given.