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

  • Dades identificatives

    Identificador: imarina:9291710
    Handle: https://hdl.handle.net/20.500.11797/imarina9291710
    Autors:
    Canela, JEvdoridou, VGarijo, AJarque, X
    Resum:
    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.

  • Altres:

    Autor segons l'article: Canela, J; Evdoridou, V; Garijo, A; Jarque, X
    Departament: Enginyeria Informàtica i Matemàtiques
    Autor/s de la URV: Canela Gracia, Joan / Garijo Real, Antonio
    Codi de projecte: PID2020-118281GB-C33
    Paraules clau: 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
    Resum: 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.
    Àrees temàtiques: Mathematics (miscellaneous) Mathematics (all) Mathematics Matemática / probabilidade e estatística General mathematics
    Accès a la llicència d'ús: https://creativecommons.org/licenses/by/3.0/es/
    Adreça de correu electrònic de l'autor: joan.canela@urv.cat antonio.garijo@urv.cat
    Identificador de l'autor: 0000-0002-1503-7514
    Data d'alta del registre: 2024-08-03
    Versió de l'article dipositat: info:eu-repo/semantics/publishedVersion
    Programa de finançament: Herramientas para el análisis de diagramas de bifurcación en sistemas dinámicos
    Referència a l'article segons font original: Mathematische Zeitschrift. 303 (3):
    Referència 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 Document de llicència: https://repositori.urv.cat/ca/proteccio-de-dades/
    Acrònim: ATBiD
    Entitat: Universitat Rovira i Virgili
    Any de publicació de la revista: 2023
    Acció del programa de finançament: Proyectos I+D Generación de Conocimiento
    Tipus de publicació: Journal Publications

  • Paraules clau:

    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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