On \(\varepsilon\)-spectra and stability radii
type: Item
instance of: scholarly article
title: On \(\varepsilon\)-spectra and stability radii
zbMATH Open document ID: 1016.65014
DOI: 10.1016/S0377-0427(02)00480-6
author: Laurence Grammont
author: Alain Largillier
published in: Journal of Computational and Applied Mathematics
publication date: 2003-02-23T00:00:00Z
review text: The authors suggest that for large matrices \(A\) (one of illustrative examples of which is the Wilkinson matrix), the analysis of the epsilon spectra (= sets where the resolvent is large) should be done, in parallel, also for certain diagonal submatrices of \(A\). Within this framework they analyse the simplest case (of a two-by-two partitioning) and study its details (new upper bound for the resolvent and its consequences, the influence of the off-diagonal components, a lower bound for a stability radius etc). Consequences are discussed for the Lyapunov stability (illustration: Orr-Sommerfeld operator) and for the reliability of the Krylov-subspace iteration techniques.
reviewed by: Miloslav Znojil
Mathematics Subject Classification ID: 65F15
zbMATH DE Number: 1872867
zbMATH Keywords: epsilon-spectrum
zbMATH Keywords: Lyapunov stability
zbMATH Keywords: partitioning two by two
zbMATH Keywords: stability
zbMATH Keywords: Orr-Sommerfeld operator
zbMATH Keywords: Krylov-subspace iteration
describes a project that uses: mctoolbox
describes a project that uses: testmatrix
MaRDI profile type: Publication
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full work available at URL: s0377-0427(02)00480-6
OpenAlex ID: W2062511235
description: scientific article; zbMATH DE number 1872867