Solving polynomial systems via symbolic-numeric reduction to geometric involutive form
type: Item
instance of: scholarly article
title: Solving polynomial systems via symbolic-numeric reduction to geometric involutive form
zbMATH Open document ID: 1177.13065
author: Greg Reid
author: Lihong Zhi
published in: Journal of Symbolic Computation
publication date: 2009-03-25T00:00:00Z
review text: As the title suggests, this article introduces a new symbolic-numeric method for solving zero-dimensional polynomial systems with inexact coefficients. The authors use the correspondence between polynomial systems and PDE systems in the following way: the corresponding PDE system is brought to involutive form (abundant literature is cited in reference to this). The authors use a criterion for involutiveness that involves computing dimensions of certain null spaces. After this, the solutions are computed by solving an eigenvalue/vector problem constructed from it. The constructed problem is a modification of a similar one in the literature.
reviewed by: David Sevilla
Mathematics Subject Classification ID: 13P10
Mathematics Subject Classification ID: 68W30
Mathematics Subject Classification ID: 65F15
zbMATH DE Number: 5532874
zbMATH Keywords: solving approximate polynomial systems
zbMATH Keywords: numerical linear algebra
zbMATH Keywords: numeric elimination
zbMATH Keywords: partial differential equations
zbMATH Keywords: jet spaces
zbMATH Keywords: involutive bases
zbMATH Keywords: numeric jet geometry
MaRDI profile type: Publication
full work available at URL: j.jsc.2007.10.013
OpenAlex ID: W2115204962
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DOI: 10.1016/J.JSC.2007.10.013
description: scientific article; zbMATH DE number 5532874