A Note on Necessary and Sufficient Conditions for the Jacobi Matrix Inverse Eigenvalue Problem
Yin Qing-xiang · Journal of Mathematical Research and Exposition · 2007
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 3.