Related bounds for the extreme eigenvalues
type: Item
instance of: scholarly article
title: Related bounds for the extreme eigenvalues
zbMATH Open document ID: 0947.15013
DOI: 10.1016/S0898-1221(99)00253-9
author: Yanyan Li
publication date: 2000-11-01T00:00:00Z
review text: Let \({\mathbf A}\) be a matrix with real eigenvalues \(\lambda _1\geq \lambda _2\geq ...\geq \lambda _n\). The authors present a method to construct an increasing (respectively, decreasing) sequence of lower (respectively, upper) bounds for \(\lambda _n\) (respectively, \(\lambda _1\)) in the case where \(\lambda _1\) (respectively, \(\lambda _n\)) is known. This situation occurs for example if \({\mathbf A}\) is an irreducible stochastic matrix with real spectrum, and in this case \(\lambda _1=1\). A method to construct a decreasing sequence of upper bounds for the largest singular value of an \(m\times n\) complex matrix is obtained as an application of the main result.
reviewed by: Nicolae Cotfas
Mathematics Subject Classification ID: 15A42
Mathematics Subject Classification ID: 15B51
Mathematics Subject Classification ID: 65F15
zbMATH DE Number: 1429547
zbMATH Keywords: eigenvalue bounds
zbMATH Keywords: singular value bounds
zbMATH Keywords: irreducible stochastic matrix
MaRDI profile type: Publication
cites work: Inertia characteristics of self-adjoint matrix polynomials
cites work: A decreasing sequence of eigenvalue localization regions
cites work: An approach to nonlinear programming
cites work: Q5185900
full work available at URL: s0898-1221(99)00253-9
OpenAlex ID: W2083921388
published in: Computers & Mathematics with Applications
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description: scientific article; zbMATH DE number 1429547