Solution of bordered singular systems in numerical continuation and bifurcation
type: Item
instance of: scholarly article
title: Solution of bordered singular systems in numerical continuation and bifurcation
zbMATH Open document ID: 0806.65023
DOI: 10.1016/0377-0427(94)90311-5
published in: Journal of Computational and Applied Mathematics
publication date: 1994-09-22T00:00:00Z
review text: Linear systems with coefficient matrices in block form \(M=\left({A\atop C^ T}{B\atop D}\right)\) are considered in situations, where a specialized solver can be used for \(A\) (for example, if \(A\) is sparse, banded, etc.) but where \(C^ T\), \(B\) and \(D\) are dense. The author considers the additional difficulty of \(A\) being nearly singular and thus ill-conditioned. Numerical tests are described using the mixed block elimination method of the author and \textit{J. D. Pryce} [IMA J. Numer. Anal. 13, No. 2, 161-180 (1993; Zbl 0778.65017)]. The tests indicate that such linear systems can be solved in a stable way even if a black-box solver is used for the nearly singular matrix.
reviewed by: Thomas Sonar
Mathematics Subject Classification ID: 65F05
zbMATH DE Number: 643765
zbMATH Keywords: bordered singular systems
zbMATH Keywords: ill-conditioned matrix
zbMATH Keywords: numerical tests
zbMATH Keywords: mixed block elimination method
zbMATH Keywords: nearly singular matrix
author: Willy J. F. Govaerts
describes a project that uses: PITCON
MaRDI profile type: Publication
full work available at URL: 0377-0427(94)90311-5
OpenAlex ID: W2011330314
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description: scientific article; zbMATH DE number 643765