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

Producción científica: Contribución a una revista › Artículo › revisión exhaustiva

23 Citas (Scopus)

Resumen

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.

Idioma original	Inglés
Páginas (desde-hasta)	699-708
Número de páginas	10
Publicación	Computers and Mathematics with Applications
Volumen	54
N.º	5
DOI	https://doi.org/10.1016/j.camwa.2006.12.035
Estado	Publicada - sept 2007
Publicado de forma externa	Sí

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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 - Soto, Ricardo L.

AU - Egaña, J.

AU - Salas, Mario

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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

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DO - 10.1016/j.camwa.2006.12.035

M3 - Article

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JO - Computers and Mathematics with Applications

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An inverse eigenvalue problem for symmetrical tridiagonal matrices

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