Finding a cluster of zeros of univariate polynomials
type: Item
instance of: scholarly article
title: Finding a cluster of zeros of univariate polynomials
zbMATH Open document ID: 0974.65045
author: Jean-Claude Yakoubsohn
published in: Journal of Complexity
publication date: 2001-07-05T00:00:00Z
review text: A method to compute an accurate approximation for a zero cluster of a complex univariate polynomial is presented. The methodology is based on homotopy. Newton's method, and Rouché's theorem. The homotopy method provides a point close to the cluster. The Newton method in the neighborhood of a zero cluster gives the number of zeros in the cluster, where it is sufficient to know three points of the Newton sequence in order to generate an open disk susceptible to contain all zeros of the cluster. An inclusion test based on a punctual version of the Rouché theorem validates the previous step. Numerical examples illustrate the effectiveness of the algorithm.
Mathematics Subject Classification ID: 65H05
Mathematics Subject Classification ID: 12Y05
Mathematics Subject Classification ID: 26C10
Mathematics Subject Classification ID: 30C15
zbMATH DE Number: 1558137
zbMATH Keywords: polynomial roots
zbMATH Keywords: Newton's method
zbMATH Keywords: numerical examples
zbMATH Keywords: zero cluster
zbMATH Keywords: homotopy method
reviewed by: F. Szidarovszky
MaRDI profile type: Publication
full work available at URL: jcom.2000.0555
OpenAlex ID: W2055700385
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DOI: 10.1006/JCOM.2000.0555
description: scientific article; zbMATH DE number 1558137