Global convergence of the Durand-Kerner method applied to the equation \(z^ 3 = 0\)
type: Item
instance of: scholarly article
title: Global convergence of the Durand-Kerner method applied to the equation \(z^ 3 = 0\)
zbMATH Open document ID: 0862.65031
DOI: 10.1016/0377-0427(95)00147-6
published in: Journal of Computational and Applied Mathematics
publication date: 1996-07-23T00:00:00Z
review text: The Durand-Kerner method for finding all the roots of a polynomial is applied to the equation \(z^3=0\). It is proved that the method is globally convergent. The behaviour of orbits with real initial values is chaotic, while the convergence with complex initial values is balanced.
Mathematics Subject Classification ID: 65H05
Mathematics Subject Classification ID: 30C15
Mathematics Subject Classification ID: 12Y05
zbMATH DE Number: 908429
zbMATH Keywords: polynomial roots
zbMATH Keywords: global convergence
zbMATH Keywords: Durand-Kerner method
author: Yoshikazu Yamagishi
reviewed by: Plamen Yalamov
MaRDI profile type: Publication
full work available at URL: 0377-0427(95)00147-6
OpenAlex ID: W2049329464
cites work: Q3279563
cites work: Ein Gesamtschrittverfahren zur Berechnung der Nullstellen von Polynomen
cites work: Q4724859
cites work: Balanced convergence of iterative methods to a multiple zero of a complex polynomial
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description: scientific article; zbMATH DE number 908429