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

  • Identification data

    Identifier: imarina:9291710
    Handle: https://hdl.handle.net/20.500.11797/imarina9291710
    Authors:
    Canela, JEvdoridou, VGarijo, AJarque, X
    Abstract:
    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.

  • Others:

    Author, as appears in the article.: Canela, J; Evdoridou, V; Garijo, A; Jarque, X
    Department: Enginyeria Informàtica i Matemàtiques
    URV's Author/s: Canela Gracia, Joan / Garijo Real, Antonio
    Project code: PID2020-118281GB-C33
    Keywords: 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
    Abstract: 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.
    Thematic Areas: Mathematics (miscellaneous) Mathematics (all) Mathematics Matemática / probabilidade e estatística General mathematics
    licence for use: https://creativecommons.org/licenses/by/3.0/es/
    Author's mail: joan.canela@urv.cat antonio.garijo@urv.cat
    Author identifier: 0000-0002-1503-7514
    Record's date: 2024-08-03
    Papper version: info:eu-repo/semantics/publishedVersion
    Link to the original source: https://link.springer.com/article/10.1007/s00209-023-03215-8
    Funding program: Herramientas para el análisis de diagramas de bifurcación en sistemas dinámicos
    Papper original source: Mathematische Zeitschrift. 303 (3):
    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
    Licence document URL: https://repositori.urv.cat/ca/proteccio-de-dades/
    Acronym: ATBiD
    Article's DOI: 10.1007/s00209-023-03215-8
    Entity: Universitat Rovira i Virgili
    Journal publication year: 2023
    Funding program action: Proyectos I+D Generación de Conocimiento
    Publication Type: Journal Publications

  • Keywords:

    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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