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Dynamics of a Family of Rational Operators of Arbitrary Degree

  • Identification data

    Identifier: imarina:9216841
    Handle: https://hdl.handle.net/20.500.11797/imarina9216841
    Authors:
    Campos, BeatrizCanela, JordiGarijo, AntonioVindel, Pura
    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 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.

  • Others:

    Project code: PID2020-118281GB-C33
    Keywords: Complex dynamics of rational functions Iterative methods Parameter planes Stability
    Record's date: 2024-07-27
    Papper version: info:eu-repo/semantics/publishedVersion
    Papper original source: Mathematical Modelling And Analysis. 26 (2): 188-208
    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
    Licence document URL: https://repositori.urv.cat/ca/proteccio-de-dades/
    Acronym: ATBiD
    First page: 188
    Publication Type: Journal Publications
    Author, as appears in the article.: Campos, Beatriz; Canela, Jordi; Garijo, Antonio; Vindel, Pura;
    Department: Enginyeria Informàtica i Matemàtiques
    URV's Author/s: Garijo Real, Antonio
    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 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.
    Thematic Areas: Analysis Mathematics Modeling and simulation
    licence for use: https://creativecommons.org/licenses/by/3.0/es/
    Author's mail: antonio.garijo@urv.cat
    Author identifier: 0000-0002-1503-7514
    Last page: 208
    Journal volume: 26
    Link to the original source: https://journals.vgtu.lt/index.php/MMA/article/view/12642
    Funding program: Herramientas para el análisis de diagramas de bifurcación en sistemas dinámicos
    Article's DOI: 10.3846/mma.2021.12642
    Entity: Universitat Rovira i Virgili
    Journal publication year: 2021
    Funding program action: Proyectos I+D Generación de Conocimiento

  • Keywords:

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

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