Articles producció científica> Enginyeria Informàtica i Matemàtiques

Global dynamics of the real secant method

  • Identification data

    Identifier: imarina:6170411
    Authors:
    Garijo, AntonioJarque, Xavier
    Abstract:
    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.
  • Others:

    Author, as appears in the article.: Garijo, Antonio; Jarque, Xavier;
    Department: Enginyeria Informàtica i Matemàtiques
    URV's Author/s: Garijo Real, Antonio
    Keywords: 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
    Abstract: 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.
    Thematic Areas: 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
    licence for use: https://creativecommons.org/licenses/by/3.0/es/
    ISSN: 09517715
    Author's mail: antonio.garijo@urv.cat
    Author identifier: 0000-0002-1503-7514
    Record's date: 2023-02-19
    Papper version: info:eu-repo/semantics/submittedVersion
    Link to the original source: https://iopscience.iop.org/article/10.1088/1361-6544/ab2f55
    Papper original source: Nonlinearity. 32 (11): 4557-4578
    APA: Garijo, Antonio; Jarque, Xavier; (2019). Global dynamics of the real secant method. Nonlinearity, 32(11), 4557-4578. DOI: 10.1088/1361-6544/ab2f55
    Licence document URL: https://repositori.urv.cat/ca/proteccio-de-dades/
    Article's DOI: 10.1088/1361-6544/ab2f55
    Entity: Universitat Rovira i Virgili
    Journal publication year: 2019
    Publication Type: Journal Publications
  • Keywords:

    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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