Numerische Mathematik

, Volume 98, Issue 1, pp 167–176

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

• Linzhang Lu
• Michael K.  Ng
Article

## 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.

## Keywords

Differential Equation Eigenvalue Problem Jacobi Matrix Vary Cross Section Inverse Eigenvalue Problem
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