Extreme eigenvalues of real symmetric Toeplitz matrices
type: Item
instance of: scholarly article
zbMATH Open document ID: 0968.65018
DOI: 10.1090/S0025-5718-00-01258-8
published in: Mathematics of Computation
publication date: 2001-02-19T00:00:00Z
Mathematics Subject Classification ID: 65F15
zbMATH DE Number: 1566124
zbMATH Keywords: Toeplitz matrix
zbMATH Keywords: extreme eigenvalues
zbMATH Keywords: odd and even spectra
zbMATH Keywords: spectral equation
zbMATH Keywords: secular equation
zbMATH Keywords: rational approximation
zbMATH Keywords: numerical results
zbMATH Keywords: error analysis
author: Aaron Melman
MaRDI profile type: Publication
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full work available at URL: s0025-5718-00-01258-8
OpenAlex ID: W2080178953
title: Extreme eigenvalues of real symmetric Toeplitz matrices
review text: Spectral equations (with possibly unknown singularities) are used for computing the smallest and largest eigenvalues of real symmetric Toeplitz matrices (other papers on this problem are quoted) from two equations, one for the even and one for the odd eigenvalues, that have already been used by others. The present paper presents a shorter analysis of the rootfinder used in two other works. This also leads to a better stopping rule, based on rational rather than on polynomial approximation. The paper also presents an error analysis not contained in those other works. Numerical results given concern positive semidefinite Toeplitz matrices earlier considered by G. Szegő, Cybenko, and others.
reviewed by: Erwin O. Kreyszig
description: scientific article