An inverse eigenvalue problem for symmetrical tridiagonal matrices

Authors:
Hubert Pickmann;Ricardo L. Soto;J. Egaña;Mario Salas
Affiliations:
Departamento de Matemáticas, Universidad Católica del Norte, Antofagasta, Chile;Departamento de Matemáticas, Universidad Católica del Norte, Antofagasta, Chile;Departamento de Matemáticas, Universidad Católica del Norte, Antofagasta, Chile;Departamento de Matemáticas, Universidad Católica del Norte, Antofagasta, Chile
Venue:
Computers & Mathematics with Applications
Year:
2007

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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.