Characterization and construction of the nearest defective matrix via coalescence of pseudospectral components
type: Item
instance of: scholarly article
title: Characterization and construction of the nearest defective matrix via coalescence of pseudospectral components
zbMATH Open document ID: 1228.65062
author: Rafikul Alam
author: Shreemayee Bora
author: Ralph Byers
author: Michael L. Overton
published in: Linear Algebra and its Applications
publication date: 2011-06-08T00:00:00Z
review text: This paper deals with the distance (in 2-norm or Frobenius norm) \(w(A)\) of a complex matrix \(A\) to the nearest defective matrix. Considering that the distance of a matrix to the set of matrices having a defective eigenvalue is the same as the distance to the set of matrices having multiple eigenvalues, this problem is equivalent to the relationship between \(w(A)\) and \(c(A)\), where \(c(A)\) is the supremum of the pseudo spectra of \(A\), with distinct elements. It is classical that in general \(w(A)\geq c(A)\). Via coalescence of the pseudospectral components the authors extend a previous result that \(w(A)=c(A)\) with the 2-norm to be valid also with the Frobenius norm. In addition a variant of the Newton's method to compute the nearest defective matrix and a respective backward error analysis are presented.
reviewed by: Edgar Pereira
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 65F15
zbMATH DE Number: 5905215
zbMATH Keywords: nearest defective matrix
zbMATH Keywords: multiple eigenvalues
zbMATH Keywords: pseudospectrum
zbMATH Keywords: Newton's method
zbMATH Keywords: backward error analysis
describes a project that uses: Eigtool
describes a project that uses: Seigtool
MaRDI profile type: Publication
full work available at URL: j.laa.2010.09.022
OpenAlex ID: W2156023353
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DOI: 10.1016/J.LAA.2010.09.022
description: scientific article; zbMATH DE number 5905215