Bounds for the minimum eigenvalue of a symmetric Toeplitz matrix
type: Item
instance of: scholarly article
title: Bounds for the minimum eigenvalue of a symmetric Toeplitz matrix
zbMATH Open document ID: 0936.65044
author: H. Voss
publication date: 1999-09-19T00:00:00Z
full work available at URL: https://eudml.org/doc/120254
full work available at URL: pp127-137.html
review text: Upper estimates for the smallest eigenvalue of a real symmetric Toeplitz matrix \(T\) are obtained by computing eigenvalues of reduced problems obtained by projection of the matrix eigenvalue problem onto subspaces of the Krylov space of \(T^{-1}\). It is proved that eigenvalue estimates obtained by \textit{A. Melman} [Bounds on the extreme eigenvalues of real symmetric Toeplitz matrices, Stanford Univ. Report SCCM 98-7, \url{http://etna.mcs.kent.edu/vol.8.1999/pp127-137.dir/pp127-137.html} and SIAM J. Matrix Anal. Appl. 21, No. 2, 362-378 (1999)] are obtained by using projections of dimension 2 and 3. Results of computations are presented employing an algorithm based on the new projection method for dimensions 2, 3, 4, 5 using an example considered by Melman. The higher-dimensional projections have smaller average relative error than the lower ones.
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 15A42
zbMATH DE Number: 1336576
zbMATH Keywords: eigenvalue bounds
zbMATH Keywords: smallest eigenvalue
zbMATH Keywords: symmetric Toeplitz matrix
reviewed by: John B. Butler jun.
MaRDI profile type: Publication
published in: ETNA - Electronic Transactions on Numerical Analysis
description: scientific article; zbMATH DE number 1336576