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On the basins of attraction of a one-dimensional family of root finding algorithms: from Newton to Traub

  • Datos identificativos

    Identificador: imarina:9291710
    Handle: https://hdl.handle.net/20.500.11797/imarina9291710
    Autores:
    Canela, JEvdoridou, VGarijo, AJarque, X
    Resumen:
    In this paper we study the dynamics of damped Traub’s methods Tδ when applied to polynomials. The family of damped Traub’s methods consists of root finding algorithms which contain both Newton’s (δ= 0) and Traub’s method (δ= 1). Our goal is to obtain several topological properties of the basins of attraction of the roots of a polynomial p under T1, which are used to determine a (universal) set of initial conditions for which convergence to all roots of p can be guaranteed. We also numerically explore the global properties of the dynamical plane for Tδ to better understand the connection between Newton’s method and Traub’s method.

  • Otros:

    Autor según el artículo: Canela, J; Evdoridou, V; Garijo, A; Jarque, X
    Departamento: Enginyeria Informàtica i Matemàtiques
    Autor/es de la URV: Canela Gracia, Joan / Garijo Real, Antonio
    Código de proyecto: PID2020-118281GB-C33
    Palabras clave: Unboundedness Simple connectivity Root finding algorithms Rational maps Julia and fatou sets Holomorphic dynamics Basins of attraction unboundedness simple connectivity root finding algorithms polynomials julia and fatou sets dynamics connectivity basins of attraction
    Resumen: In this paper we study the dynamics of damped Traub’s methods Tδ when applied to polynomials. The family of damped Traub’s methods consists of root finding algorithms which contain both Newton’s (δ= 0) and Traub’s method (δ= 1). Our goal is to obtain several topological properties of the basins of attraction of the roots of a polynomial p under T1, which are used to determine a (universal) set of initial conditions for which convergence to all roots of p can be guaranteed. We also numerically explore the global properties of the dynamical plane for Tδ to better understand the connection between Newton’s method and Traub’s method.
    Áreas temáticas: Mathematics (miscellaneous) Mathematics (all) Mathematics Matemática / probabilidade e estatística General mathematics
    Acceso a la licencia de uso: https://creativecommons.org/licenses/by/3.0/es/
    Direcció de correo del autor: joan.canela@urv.cat antonio.garijo@urv.cat
    Identificador del autor: 0000-0002-1503-7514
    Fecha de alta del registro: 2024-08-03
    Versión del articulo depositado: info:eu-repo/semantics/publishedVersion
    Programa de financiación: Herramientas para el análisis de diagramas de bifurcación en sistemas dinámicos
    Referencia al articulo segun fuente origial: Mathematische Zeitschrift. 303 (3):
    Referencia de l'ítem segons les normes APA: Canela, J; Evdoridou, V; Garijo, A; Jarque, X (2023). On the basins of attraction of a one-dimensional family of root finding algorithms: from Newton to Traub. Mathematische Zeitschrift, 303(3), -. DOI: 10.1007/s00209-023-03215-8
    URL Documento de licencia: https://repositori.urv.cat/ca/proteccio-de-dades/
    Acrónimo: ATBiD
    Entidad: Universitat Rovira i Virgili
    Año de publicación de la revista: 2023
    Acción del progama de financiación: Proyectos I+D Generación de Conocimiento
    Tipo de publicación: Journal Publications

  • Palabras clave:

    Mathematics,Mathematics (Miscellaneous)
    Unboundedness
    Simple connectivity
    Root finding algorithms
    Rational maps
    Julia and fatou sets
    Holomorphic dynamics
    Basins of attraction
    unboundedness
    simple connectivity
    root finding algorithms
    polynomials
    julia and fatou sets
    dynamics
    connectivity
    basins of attraction
    Mathematics (miscellaneous)
    Mathematics (all)
    Mathematics
    Matemática / probabilidade e estatística
    General mathematics

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