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Dynamics of a family of rational operators of arbitrary degree

    Beatriz Campos   Affiliation
    ; Jordi Canela   Affiliation
    ; Antonio Garijo   Affiliation
    ; Pura Vindel   Affiliation

Abstract

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 unboundedness 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.

Keyword : iterative methods, parameter planes, complex dynamics of rational functions

How to Cite
Campos, B., Canela, J., Garijo, A., & Vindel, P. (2021). Dynamics of a family of rational operators of arbitrary degree. Mathematical Modelling and Analysis, 26(2), 188-208. https://doi.org/10.3846/mma.2021.12642
Published in Issue
May 26, 2021
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