关于Jacobi矩阵的特征值反问题可解的充分必要条件的一个注记

A Note on Necessary and Sufficient Conditions for the Jacobi Matrix Inverse Eigenvalue Problem

本文讨论一类具有特殊结构的Jacobi矩阵的特征值反问题,该问题由描述变截面杆的微分方程离散化得到．我们得到了这个问题有解的一些必要条件,并且通过一些数值例子,说明了L．Lu和K．Michael给出的充分条件和算法在矩阵的阶数高于3的时候是错误的。

This paper deals with an inverse eigenvalue problem of a specially structured Jacobi matrix, which arises from the discretization of the differential equation governing the axial of a rod with varying cross section. This problem was also studied by Lu L. Z. and Sun W.W.. We give some necessary conditions for such inverse eigenvalue problem to have solutions, and present some numerical examples to show that the sufficient conditions and algorithm presented by Lu is incorrect when the order of matrix is greater than З.