A heuristic method for certifying isolated zeros of polynomial systems
type: Item
instance of: scholarly article
title: A heuristic method for certifying isolated zeros of polynomial systems
zbMATH Open document ID: 1405.65073
author: Xiaojie Dou~
author: Jin-San Cheng
published in: Mathematics
publication date: 2018-12-18T00:00:00Z
review text: By transforming the given over-determined system into a square one, the authors provide necessary and sufficient conditions to certify the simple roots of the over-determined system by certifying the simple roots of the square system. Based on their previous research, the authors propose a heuristic method for certifying not only the isolated singular zeros of polynomial systems, but also the multiplicity structures of the isolated singular zeros. Various numerical examples are presented.
reviewed by: Nikolay Kyurkchiev
Mathematics Subject Classification ID: 65H10
zbMATH DE Number: 6994730
zbMATH Keywords: over-determined polynomial system
zbMATH Keywords: isolated zeros
zbMATH Keywords: minimum point
zbMATH Keywords: sum of squares
zbMATH Keywords: interval methods
describes a project that uses: SOS.m2
describes a project that uses: MultRoot
describes a project that uses: Macaulay2
describes a project that uses: alphaCertified
MaRDI profile type: Publication
full work available at URL: math6090166
OpenAlex ID: W2883255855
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DOI: 10.3390/MATH6090166
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description: scientific article; zbMATH DE number 6994730