Continuous bordering of matrices and continuous matrix decompositions
type: Item
instance of: scholarly article
title: Continuous bordering of matrices and continuous matrix decompositions
zbMATH Open document ID: 0829.15007
published in: Numerische Mathematik
publication date: 1996-01-24T00:00:00Z
review text: This paper studies the problems in continuous bordering of matrices, which are often used to compute manifolds of fold points or symmetry breaking bifurcation points. It has been concluded that for \(n \times n\) matrices, with \(n \geq 2\) and rank \(\geq n - 1\), there are no continuous vector fields that will preserve the regularity of their bordered matrices. It is also shown that there is no singular value decomposition (SVD) of a matrix depending continuously on itself, and that such branching steps in algorithms for SVD and similarly for eigenvalue decompositions are mathematically unavoidable.
Mathematics Subject Classification ID: 15A18
zbMATH DE Number: 770161
zbMATH Keywords: continuous bordering
zbMATH Keywords: manifolds of fold points
zbMATH Keywords: symmetry breaking bifurcation points
zbMATH Keywords: continuous vector fields
zbMATH Keywords: bordered matrices
zbMATH Keywords: singular value decomposition
zbMATH Keywords: eigenvalue decompositions
author: Willy J. F. Govaerts
author: Bodo Werner
MaRDI profile type: Publication
full work available at URL: s002110050121
OpenAlex ID: W1998610755
DOI: 10.1007/S002110050121
description: scientific article; zbMATH DE number 770161