Symmetric homotopy construction
type: Item
instance of: scholarly article
title: Symmetric homotopy construction
zbMATH Open document ID: 0806.65055
DOI: 10.1016/0377-0427(94)90329-8
author: J. Verschelde
author: Ronald Cools
published in: Journal of Computational and Applied Mathematics
publication date: 1994-09-22T00:00:00Z
review text: Numerical homotopy continuation methods may be applied to compute all of the finite complex solutions to a system of polynomial equations, say \(P(x)= 0\). For systems which are in addition, symmetric, i.e., invariant under a group \(G\) of permutations of the variables and equations, the determination of the zeros can be greatly simplified, since then for each solution \(x\), also \(P(\gamma x)= 0\) for all \(\gamma\in G\), i.e., \(P\) vanishes on the orbit of \(x\) for the group \(G\). In this paper the authors investigate the construction of homotopies which carry the symmetry of the system \(P\). This reduces correspondingly the number of homotopy paths which need to be traversed.
Mathematics Subject Classification ID: 65H20
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 30C15
zbMATH DE Number: 643784
zbMATH Keywords: numerical homotopy continuation methods
zbMATH Keywords: complex solutions
zbMATH Keywords: system of polynomial equations
zbMATH Keywords: orbit
zbMATH Keywords: group
zbMATH Keywords: symmetry
zbMATH Keywords: number of homotopy paths
Wikidata QID: Q57779005
reviewed by: Eugene L. Allgower
describes a project that uses: HOMPACK
MaRDI profile type: Publication
full work available at URL: 0377-0427(94)90329-8
OpenAlex ID: W2024630469
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description: scientific article; zbMATH DE number 643784