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Dynamics of a Family of Rational Operators of Arbitrary Degree

  • Datos identificativos

    Identificador: imarina:9216841
    Handle: https://hdl.handle.net/20.500.11797/imarina9216841
    Autores:
    Campos, BeatrizCanela, JordiGarijo, AntonioVindel, Pura
    Resumen:
    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.

  • Otros:

    Código de proyecto: PID2020-118281GB-C33
    Palabras clave: Complex dynamics of rational functions Iterative methods Parameter planes Stability
    Fecha de alta del registro: 2024-07-27
    Versión del articulo depositado: info:eu-repo/semantics/publishedVersion
    Referencia al articulo segun fuente origial: Mathematical Modelling And Analysis. 26 (2): 188-208
    Referencia 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 Documento de licencia: https://repositori.urv.cat/ca/proteccio-de-dades/
    Acrónimo: ATBiD
    Página inicial: 188
    Tipo de publicación: Journal Publications
    Autor según el artículo: Campos, Beatriz; Canela, Jordi; Garijo, Antonio; Vindel, Pura;
    Departamento: Enginyeria Informàtica i Matemàtiques
    Autor/es de la URV: Garijo Real, Antonio
    Resumen: 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.
    Áreas temáticas: Analysis Mathematics Modeling and simulation
    Acceso a la licencia de uso: https://creativecommons.org/licenses/by/3.0/es/
    Direcció de correo del autor: antonio.garijo@urv.cat
    Identificador del autor: 0000-0002-1503-7514
    Página final: 208
    Volumen de revista: 26
    Enlace a la fuente original: https://journals.vgtu.lt/index.php/MMA/article/view/12642
    Programa de financiación: Herramientas para el análisis de diagramas de bifurcación en sistemas dinámicos
    DOI del artículo: 10.3846/mma.2021.12642
    Entidad: Universitat Rovira i Virgili
    Año de publicación de la revista: 2021
    Acción del progama de financiación: Proyectos I+D Generación de Conocimiento

  • Palabras clave:

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

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