Author, as appears in the article.: Gardini, Laura; Garijo, Antonio; Jarque, Xavier;
Department: Enginyeria Informàtica i Matemàtiques
URV's Author/s: Garijo Real, Antonio
Keywords: Secant method Root finding algorithms Rational iteration Plane maps Periodic orbits Denominator
Abstract: We study the discrete dynamical system defined on a subset of R-2 given by the iterates of the secant method applied to a real polynomial p. Each simple real root a of p has associated its basin of attraction A(alpha) formed by the set of points converging towards the fixed point (alpha, alpha) of S. We denote by A* (alpha) its immediate basin of attraction, that is, the connected component of A( a) which contains (alpha, alpha). We focus on some topological properties of A* (alpha), when a is an internal real root of p. More precisely, we show the existence of a 4-cycle in. A* (alpha) and we give conditions on p to guarantee the simple connectivity of A* (alpha).
Thematic Areas: Mathematics, applied Mathematics (miscellaneous) Mathematics (all) Mathematics Matemática / probabilidade e estatística General mathematics Ensino Engenharias iv
licence for use: https://creativecommons.org/licenses/by/3.0/es/
Author's mail: antonio.garijo@urv.cat
Author identifier: 0000-0002-1503-7514
Record's date: 2024-07-27
Papper version: info:eu-repo/semantics/publishedVersion
Link to the original source: https://link.springer.com/article/10.1007/s00009-021-01845-y
Licence document URL: https://repositori.urv.cat/ca/proteccio-de-dades/
Papper original source: Mediterranean Journal Of Mathematics. 18 (5):
APA: Gardini, Laura; Garijo, Antonio; Jarque, Xavier; (2021). Topological Properties of the Immediate Basins of Attraction for the Secant Method. Mediterranean Journal Of Mathematics, 18(5), -. DOI: 10.1007/s00009-021-01845-y
Article's DOI: 10.1007/s00009-021-01845-y
Entity: Universitat Rovira i Virgili
Journal publication year: 2021
Publication Type: Journal Publications
Repositori URV