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Resultats globals: 5 registres trobats en 0.02 segons.
Articles, 5 registres trobats

Articles	5 registres trobats

13 p, 622.2 KB

Dynamics of the Secant map near infinity / Garijo, Antoni (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques) ; Jarque i Ribera, Xavier (Centre de Recerca Matemàtica)
We investigate the root finding algorithm given by the Secant method applied to a real polynomial p of degree k as a discrete dynamical system defined on R2. We extend the Secant map to the real projective plane RP2. [...]
2022 - DOI (Digital Object Identifier)

10.1080/10236198.2022.2044476
Journal of Difference Equations and Applications, Vol. 28, Issue 10 (2022) , p. 1334-1347

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22 p, 2.1 MB

On the basins of attraction of a one-dimensional family of root finding algorithms : from Newton to Traub / Canela Sánchez, Jordi (Universitat Jaume I. Institut Universitari de Matemátiques i Aplicacions de Castelló) ; Evdoridou, Vasiliki (The Open University. School of Mathematics and Statistics (UK)) ; Garijo, Antoni (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques) ; Jarque i Ribera, Xavier (Universitat de Barcelona. Departament de Matemàtiques i Informàtica)
In this paper we study the dynamics of damped Traub's methods T when applied to polynomials. The family of damped Traub's methods consists of root finding algorithms which contain both Newton's (δ= 0) and Traub's method (δ= 1). [...]
2023 - DOI (Digital Object Identifier)

10.1007/s00209-023-03215-8
Mathematische Zeitschrift, Vol. 303, Issue 3 (March 2023) , art. 55

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27 p, 2.6 MB

Topological properties of the immediate basins of attraction for the secant method / Gardini, Laura (University of Urbino. Department of Economics, Society and Politics) ; Garijo, Antoni (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques) ; Jarque i Ribera, Xavier (Universitat de Barcelona. Departament de Matemàtiques i Informàtica)
We study the discrete dynamical system defined on a subset of R given by the iterates of the secant method applied to a real polynomial p. Each simple real root α of p has associated its basin of attraction A(α) formed by the set of points converging towards the fixed point (α, α) of S. [...]
2021 - DOI (Digital Object Identifier)

10.1007/s00009-021-01845-y
Mediterranean Journal of Mathematics, Vol. 18, Issue 5 (October 2021) , art. 221

2 documents

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12 p, 514.1 KB

The secant map applied to a real polynomial with multiple roots / Garijo, Antoni (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques) ; Jarque i Ribera, Xavier (Universitat de Barcelona. Departament de Matemàtica Aplicada i Anàlisi)
We investigate the plane dynamical system given by the secant map applied to a polynomial p having at least one multiple root of multiplicity d > 1. We prove that the local dynamics around the ﬁxed points associated to the roots of p depend on the parity of d.
2019 - DOI (Digital Object Identifier)

10.3934/dcds.2020133
Discrete and Continuous Dynamical Systems. Series A, vol. 40 12 2019, p. 6783-6794

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26 p, 1.4 MB

Global dynamics of the real secant method / Garijo, Antoni (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques) ; Jarque i Ribera, Xavier (Universitat de Barcelona. Departament de Matemàtiques i Informàtica)
We investigate the root finding algorithm given by the secant method applied to a real polynomial p as a discrete dynamical system defined on R2. 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. [...]
2019 - DOI (Digital Object Identifier)

10.1088/1361-6544/ab2f55
Nonlinearity, Vol. 32, Issue 11 (November 2019) , p. 4557-4578

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