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

URL Documento de licencia: http://repositori.urv.cat/ca/proteccio-de-dades/

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

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