Computing the isolated roots by matrix methods
type: Item
instance of: scholarly article
title: Computing the isolated roots by matrix methods
zbMATH Open document ID: 0934.68136
published in: Journal of Symbolic Computation
publication date: 2000-04-03T00:00:00Z
review text: One approach to compute the roots of a zero-dimensional polynomial system is based on resultant formulations and can be performed with floating point arithmetic. In this paper, reinvestigating the resultant approach from the linear algebra point of view the author handles the problem of genericity and presents a new algorithm for computing the isolated roots of an algebraic variety. The author analyses two types of resultant formulations, transforms them into eigenvector problems, and describes special linear algebra operations on the matrix pencils in order to reduce the root computation to a non-singular eigenvector problem. This new algorithm, based on pencil decompositions, has a good complexity even in the non-generic situations and can be executed with floating point arithmetic.
reviewed by: Yueh-er Kuo
Mathematics Subject Classification ID: 68W30
Mathematics Subject Classification ID: 13P05
zbMATH DE Number: 1268450
zbMATH Keywords: roots of a zero-dimensional polynomial system
zbMATH Keywords: resultant
zbMATH Keywords: floating point arithmetic
zbMATH Keywords: non-singular eigenvector problem
zbMATH Keywords: complexity
author: Bernard Mourrain
describes a project that uses: LAPACK
MaRDI profile type: Publication
full work available at URL: jsco.1998.0236
OpenAlex ID: W2048961297
DOI: 10.1006/JSCO.1998.0236
description: scientific article; zbMATH DE number 1268450