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Global dynamics of the real secant method

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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.

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(c) IOP Publishing & London Mathematical Society , 2019

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Articles publicats en revistes (Matemàtiques i Informàtica)

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Funcions de diverses variables complexes

# metadata.dc.title[].value
Global dynamics of the real secant method