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Dynamics of a Family of Rational Operators of Arbitrary Degree

  • Dades identificatives

    Identificador: imarina:9216841
    Handle: https://hdl.handle.net/20.500.11797/imarina9216841
    Autors:
    Campos, BeatrizCanela, JordiGarijo, AntonioVindel, Pura
    Resum:
    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 O-a,O-n,O-k of degree n + k operators, which includes several other families of maps obtained from other numerical methods. We study the dynamics of O-a,O-n,O-k and discuss for which parameters n and k these operators would be suitable from the numerical point of view.

  • Altres:

    Codi de projecte: PID2020-118281GB-C33
    Paraules clau: Complex dynamics of rational functions Iterative methods Parameter planes Stability
    Data d'alta del registre: 2024-07-27
    Versió de l'article dipositat: info:eu-repo/semantics/publishedVersion
    Referència a l'article segons font original: Mathematical Modelling And Analysis. 26 (2): 188-208
    Referència de l'ítem segons les normes APA: Campos, Beatriz; Canela, Jordi; Garijo, Antonio; Vindel, Pura; (2021). Dynamics of a Family of Rational Operators of Arbitrary Degree. Mathematical Modelling And Analysis, 26(2), 188-208. DOI: 10.3846/mma.2021.12642
    URL Document de llicència: https://repositori.urv.cat/ca/proteccio-de-dades/
    Acrònim: ATBiD
    Pàgina inicial: 188
    Tipus de publicació: Journal Publications
    Autor segons l'article: Campos, Beatriz; Canela, Jordi; Garijo, Antonio; Vindel, Pura;
    Departament: Enginyeria Informàtica i Matemàtiques
    Autor/s de la URV: Garijo Real, Antonio
    Resum: 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 O-a,O-n,O-k of degree n + k operators, which includes several other families of maps obtained from other numerical methods. We study the dynamics of O-a,O-n,O-k and discuss for which parameters n and k these operators would be suitable from the numerical point of view.
    Àrees temàtiques: Analysis Mathematics Modeling and simulation
    Accès a la llicència d'ús: https://creativecommons.org/licenses/by/3.0/es/
    Adreça de correu electrònic de l'autor: antonio.garijo@urv.cat
    Identificador de l'autor: 0000-0002-1503-7514
    Pàgina final: 208
    Volum de revista: 26
    Enllaç font original: https://journals.vgtu.lt/index.php/MMA/article/view/12642
    Programa de finançament: Herramientas para el análisis de diagramas de bifurcación en sistemas dinámicos
    DOI de l'article: 10.3846/mma.2021.12642
    Entitat: Universitat Rovira i Virgili
    Any de publicació de la revista: 2021
    Acció del programa de finançament: Proyectos I+D Generación de Conocimiento

  • Paraules clau:

    Analysis,Mathematics,Modeling and Simulation
    Complex dynamics of rational functions
    Iterative methods
    Parameter planes
    Stability
    Analysis
    Mathematics
    Modeling and simulation

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