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Title: Global dynamics of the real secant method
Author: Garijo Real, Antonio
Jarque i Ribera, Xavier
Keywords: Teoria de la bifurcació
Funcions de diverses variables complexes
Bifurcation theory
Functions of several complex variables
Issue Date: 14-Oct-2019
Publisher: IOP Publishing
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 $\mathbb{R}^{2}$ . 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 $\mathbb{T}_{\infty}^{2}$ which allow us to better understand the dynamics of the secant method near $\infty$ and facilitate the use of the secant map as a method to find all roots of a polynomial.
Note: Versió postprint del document publicat a:
It is part of: Nonlinearity, 2019, vol. 32, num. 11, p. 4557-4578
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ISSN: 0951-7715
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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