An inverse eigenvalue problem for symmetrical tridiagonal matrices

Hubert Pickmann; Ricardo L. Soto; J. Egaña; Mario Salas

doi:10.1016/j.camwa.2006.12.035

An inverse eigenvalue problem for symmetrical tridiagonal matrices

Hubert Pickmann
, Ricardo L. Soto
, J. Egaña
, Mario Salas

Universidad Católica del Norte
Departamento de Matemáticas

Research output: Contribution to journal › Article › peer-review

23 Scopus citations

Abstract

We consider the following inverse eigenvalue problem: to construct a symmetrical tridiagonal matrix from the minimal and maximal eigenvalues of all its leading principal submatrices. We give a necessary and sufficient condition for the existence of such a matrix and for the existence of a nonnegative symmetrical tridiagonal matrix. Our results are constructive, in the sense that they generate an algorithmic procedure to construct the matrix.

Original language	English
Pages (from-to)	699-708
Number of pages	10
Journal	Computers and Mathematics with Applications
Volume	54
Issue number	5
DOIs	https://doi.org/10.1016/j.camwa.2006.12.035
State	Published - Sep 2007
Externally published	Yes

Keywords

Matrix inverse eigenvalue problem
Symmetrical tridiagonal matrices

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10.1016/j.camwa.2006.12.035

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title = "An inverse eigenvalue problem for symmetrical tridiagonal matrices",

abstract = "We consider the following inverse eigenvalue problem: to construct a symmetrical tridiagonal matrix from the minimal and maximal eigenvalues of all its leading principal submatrices. We give a necessary and sufficient condition for the existence of such a matrix and for the existence of a nonnegative symmetrical tridiagonal matrix. Our results are constructive, in the sense that they generate an algorithmic procedure to construct the matrix.",

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AU - Pickmann, Hubert

AU - Soto, Ricardo L.

AU - Egaña, J.

AU - Salas, Mario

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Y1 - 2007/9

N2 - We consider the following inverse eigenvalue problem: to construct a symmetrical tridiagonal matrix from the minimal and maximal eigenvalues of all its leading principal submatrices. We give a necessary and sufficient condition for the existence of such a matrix and for the existence of a nonnegative symmetrical tridiagonal matrix. Our results are constructive, in the sense that they generate an algorithmic procedure to construct the matrix.

AB - We consider the following inverse eigenvalue problem: to construct a symmetrical tridiagonal matrix from the minimal and maximal eigenvalues of all its leading principal submatrices. We give a necessary and sufficient condition for the existence of such a matrix and for the existence of a nonnegative symmetrical tridiagonal matrix. Our results are constructive, in the sense that they generate an algorithmic procedure to construct the matrix.

KW - Matrix inverse eigenvalue problem

KW - Symmetrical tridiagonal matrices

UR - https://www.scopus.com/pages/publications/34447327243

U2 - 10.1016/j.camwa.2006.12.035

DO - 10.1016/j.camwa.2006.12.035

M3 - Article

AN - SCOPUS:34447327243

SN - 0898-1221

VL - 54

SP - 699

EP - 708

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

IS - 5

ER -

An inverse eigenvalue problem for symmetrical tridiagonal matrices

Abstract

Keywords

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