Dynamics of a family of rational operators of arbitrary degree

In this paper we analyse the dynamics of a family of rational operators coming from a fourth-order family of root-finding algorithms. We first show that it may be convenient to redefine the parameters to prevent redundancies and un-boundedness of problematic parameters. After reparametrization, we o...

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Hauptverfasser:	Campos, B, Canela, J, Garijo, A, Vindel, P
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Sprache:	eng
Schlagworte:	Complex dynamics of rational functions Iterative methods Parameter planes
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creator	Campos, B Canela, J Garijo, A Vindel, P
description	In this paper we analyse the dynamics of a family of rational operators coming from a fourth-order family of root-finding algorithms. We first show that it may be convenient to redefine the parameters to prevent redundancies and un-boundedness of problematic parameters. After reparametrization, we observe that these rational maps belong to a more general family Oa,n,k of degree n + k operators, which includes several other families of maps obtained from other numerical methods. We study the dynamics of Oa,n,k and discuss for which parameters n and k these operators would be suitable from the numerical point of view. © 2021 The Author(s). Published by Vilnius Gediminas Technical University.
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subjects	Complex dynamics of rational functions Iterative methods Parameter planes
title	Dynamics of a family of rational operators of arbitrary degree
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