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
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/
Entity: Universitat Rovira i Virgili
Journal publication year: 2019
Publication Type: Journal Publications
Repositori URV