The complex dynamics of Newton's method for a double root
type: Item
instance of: scholarly article
title: The complex dynamics of Newton's method for a double root
zbMATH Open document ID: 0753.65039
DOI: 10.1016/0898-1221(91)90198-D
author: William J. Gilbert
publication date: 1992-09-27T00:00:00Z
review text: The autor shows that the relaxed Newton's method for finding the roots of a cubic with one double root is conjugate, by a linear fractional transformation on the Riemann sphere, to the iterations of the quadratic \(p(z)=z^ 2-0.75\).
Mathematics Subject Classification ID: 65H05
Mathematics Subject Classification ID: 65E05
Mathematics Subject Classification ID: 30C15
zbMATH DE Number: 60622
zbMATH Keywords: relaxed Newton's method
zbMATH Keywords: roots of a cubic
zbMATH Keywords: double root
zbMATH Keywords: linear fractional transformation
zbMATH Keywords: Riemann sphere
zbMATH Keywords: iterations
reviewed by: Plamen Yalamov
MaRDI profile type: Publication
cites work: Newton's method and complex dynamical systems
cites work: Complex analytic dynamics on the Riemann sphere
cites work: Q3993502
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published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 60622