On sufficient and necessary conditions for the Jacobi matrix inverse eigenvalue problem

Summary. In this paper, we study the 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 (Ram and Elhay 1998 Commum. Numer. Methods Engng. 14 597-608). We give a sufficient and some necessary conditions for such inverse eigenvalue problem to have solutions. Based on these results, a simple method for the reconstruction of a Jacobi matrix from eigenvalues is developed. Numerical examples are given to demonstrate our results.Research supported in part by National Natural Science Foundation of ChinaResearch supported in part by RGC Grant Nos. 7130/02P and 7046/03P, and HKU CRCG Grant Nos 10203501, and 10204437