An algorithm for constructing a pseudo-Jacobi matrix from given spectral data

• Type: Article in International Scientific Journal
• Date: 2013

Authors

Natália Bebiano (Author) Other; Susana Borges Furtado (Author) FEP; João da Providência (Author) Other

Journal

Title: Numerical Linear Algebra with Applications

Vol. 20

Pages: 185-197

ISSN: 1070-5325

Publisher: Wiley-Blackwell

Indexing

ISI Web of Knowledge - 8 Citations

ISI Web of Science

Scopus - 8 Citations

Scientific classification

FOS: Natural sciences

Other information

Authenticus ID: P-002-087

DOI: 10.1002/nla.1855

Abstract (EN): The main purpose of this paper is the extension of the classical spectral direct and inverse analysis of Jacobi matrices for the non-self-adjoint setting. Matrices of this class appear in the context of non-Hermitian quantum mechanics. The reconstruction of a pseudo-Jacobi matrix from its spectrum and the spectra of two complementary principal matrices is investigated in the context of indefinite inner product spaces. An existence and uniqueness theorem is given, and a strikingly simple algorithm, based on the Euclidean division algorithm, to reconstruct the matrix from the spectral data is presented. A result of Friedland and Melkman stating a necessary and sufficient condition for a real sequence to be the spectrum of a non-negative Jacobi matrix is revisited and generalized. Namely, it is shown that a suitable set of prescribed eigenvalues defines a unique non-negative pseudo-Jacobi matrix, which is J-Hermitian for a fixed J. Copyright (c) 2012 John Wiley & Sons, Ltd.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 13