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

Linzhang Lu; Michael K. Ng

doi:10.1007/s00211-004-0525-x

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

Linzhang Lu^*
, Michael K. Ng

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

10 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	167-176
Number of pages	10
Journal	Numerische Mathematik
Volume	98
Issue number	1
DOIs	https://doi.org/10.1007/s00211-004-0525-x
Publication status	Published - Jul 2004

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abstract = "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.",

author = "Linzhang Lu and Ng, \{Michael K.\}",

note = "Research supported in part by National Natural Science Foundation of China. Research supported in part by RGC Grant Nos. 7130/02P and 7046/03P, and HKU CRCG Grant Nos 10203501, and 10204437. Publisher Copyright: {\textcopyright} Springer-Verlag 2004",

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AU - Lu, Linzhang

AU - Ng, Michael K.

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PY - 2004/7

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N2 - 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.

AB - 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.

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UR - https://link.springer.com/article/10.1007/s00211-004-0525-x#article-info

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DO - 10.1007/s00211-004-0525-x

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AN - SCOPUS:3543036984

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SP - 167

EP - 176

JO - Numerische Mathematik

JF - Numerische Mathematik

IS - 1

ER -

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

Abstract

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