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Global dynamics of the real secant method

  • Datos identificativos

    Identificador: imarina:6170411
    Autores:
    Garijo, AntonioJarque, Xavier
    Resumen:
    We investigate the root finding algorithm given by the secant method applied to a real polynomial p as a discrete dynamical system defined on R-2. We study the shape and distribution of the basins of attraction associated to the roots of p, and we also show the existence of other stable dynamics that might affect the efficiency of the algorithm. Finally we extend the secant map to the punctured torus T-infinity(2) which allow us to better understand the dynamics of the secant method near infinity and facilitate the use of the secant map as a method to find all roots of a polynomial.
  • Otros:

    Autor según el artículo: Garijo, Antonio; Jarque, Xavier;
    Departamento: Enginyeria Informàtica i Matemàtiques
    Autor/es de la URV: Garijo Real, Antonio
    Palabras clave: Secant method Root finding algorithms Rational iteration on the plane Polynomial diffeomorphisms Plane maps Julia sets Henon mappings Family Entropy Dynamical systems Denominator Connectivity C2 C-2
    Resumen: We investigate the root finding algorithm given by the secant method applied to a real polynomial p as a discrete dynamical system defined on R-2. We study the shape and distribution of the basins of attraction associated to the roots of p, and we also show the existence of other stable dynamics that might affect the efficiency of the algorithm. Finally we extend the secant map to the punctured torus T-infinity(2) which allow us to better understand the dynamics of the secant method near infinity and facilitate the use of the secant map as a method to find all roots of a polynomial.
    Áreas temáticas: Statistical and nonlinear physics Physics, mathematical Physics and astronomy (miscellaneous) Physics and astronomy (all) Mathematics, applied Mathematical physics Matemática / probabilidade e estatística Interdisciplinar General physics and astronomy Astronomia / física Applied mathematics
    Acceso a la licencia de uso: https://creativecommons.org/licenses/by/3.0/es/
    ISSN: 09517715
    Direcció de correo del autor: antonio.garijo@urv.cat
    Identificador del autor: 0000-0002-1503-7514
    Fecha de alta del registro: 2023-02-19
    Versión del articulo depositado: info:eu-repo/semantics/submittedVersion
    Enlace a la fuente original: https://iopscience.iop.org/article/10.1088/1361-6544/ab2f55
    Referencia al articulo segun fuente origial: Nonlinearity. 32 (11): 4557-4578
    Referencia de l'ítem segons les normes APA: Garijo, Antonio; Jarque, Xavier; (2019). Global dynamics of the real secant method. Nonlinearity, 32(11), 4557-4578. DOI: 10.1088/1361-6544/ab2f55
    URL Documento de licencia: https://repositori.urv.cat/ca/proteccio-de-dades/
    DOI del artículo: 10.1088/1361-6544/ab2f55
    Entidad: Universitat Rovira i Virgili
    Año de publicación de la revista: 2019
    Tipo de publicación: Journal Publications
  • Palabras clave:

    Applied Mathematics,Mathematical Physics,Mathematics, Applied,Physics and Astronomy (Miscellaneous),Physics, Mathematical,Statistical and Nonlinear Physics
    Secant method
    Root finding algorithms
    Rational iteration on the plane
    Polynomial diffeomorphisms
    Plane maps
    Julia sets
    Henon mappings
    Family
    Entropy
    Dynamical systems
    Denominator
    Connectivity
    C2
    C-2
    Statistical and nonlinear physics
    Physics, mathematical
    Physics and astronomy (miscellaneous)
    Physics and astronomy (all)
    Mathematics, applied
    Mathematical physics
    Matemática / probabilidade e estatística
    Interdisciplinar
    General physics and astronomy
    Astronomia / física
    Applied mathematics
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