Bounds for the smallest singular value of a Jordan block with an application to eigenvalue perturbation
type: Item
instance of: scholarly article
title: Bounds for the smallest singular value of a Jordan block with an application to eigenvalue perturbation
zbMATH Open document ID: 0833.15016
DOI: 10.1016/0024-3795(94)90510-X
published in: Linear Algebra and its Applications
publication date: 1996-03-18T00:00:00Z
review text: The paper brings some new bounds for the smallest singular value of Jordan canonical blocks. The inequalities are given in terms of the magnitude of the smallest singular value \((s)\) and the size of the matrix block \((m)\). Three cases are considered: either \(s\) is greater, equal or smaller (but positive) than \(m/(m + 1)\). These bounds are applied to eigenvalue perturbation, giving lower bounds for more general matrices (e.g. Hessenberg matrices).
Mathematics Subject Classification ID: 15A42
zbMATH DE Number: 553982
zbMATH Keywords: bounds
zbMATH Keywords: smallest singular value
zbMATH Keywords: Jordan canonical blocks
zbMATH Keywords: eigenvalue perturbation
zbMATH Keywords: Hessenberg matrices
author: Erxiong Jiang
reviewed by: Marián Vajteršic
MaRDI profile type: Publication
cites work: Q5185900
cites work: On spectral variation of a nonnormal matrix
cites work: Residual Bounds on Approximate Eigensystems of Nonnormal Matrices
cites work: Q4171531
full work available at URL: 0024-3795(94)90510-x
OpenAlex ID: W2068169767
description: scientific article; zbMATH DE number 553982