Pseudospectra for matrix pencils and stability of equilibria
type: Item
instance of: scholarly article
title: Pseudospectra for matrix pencils and stability of equilibria
zbMATH Open document ID: 0894.65022
DOI: 10.1007/BF02510354
author: Jos L. M. van Dorsselaer
published in: BIT
publication date: 1998-02-11T00:00:00Z
review text: The \(\varepsilon\)-pseudospectra studied by \textit{N. M. Nachtigal}, \textit{S. C. Reddy} and \textit{L. N. Trefethen} [SIAM J. Matrix Anal. Appl. 13, No. 3, 778-795 (1992; Zbl 0754.65036)] are considered for matrix pencils. It is shown how the \(\varepsilon\)-pseudospectra for matrix pencils can be used to investigate the asymptotic stability of stationary solutions to systems of time-dependent ordinary or partial differential equations, when inexact Jacobian matrices are used. This approach is illustrated by the study of two systems of ordinary differential equations. Both systems are obtained from a semidiscretization of Burgers' equation, applying a finite difference and a finite element method, respectively.
Mathematics Subject Classification ID: 65H17
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 65M20
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 15A21
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 65L07
zbMATH DE Number: 1117810
zbMATH Keywords: spectral methods
zbMATH Keywords: eigenvalue problems
zbMATH Keywords: eigenvalues
describes a project that uses: Eigtool
describes a project that uses: JDQZ
describes a project that uses: JDQR
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02510354
OpenAlex ID: W2106533107
description: scientific article; zbMATH DE number 1117810