Free access article

ESAIM: Proc., 2007, Vol. 20, pp. 208-216
DOI: 10.1051/proc:072018

Fractalisation du bassin d'attraction dans l'algorithme de Newton Modifié

Mohamed Lamine Sahari and Ilhem Djellit

Département de Mathématiques, Université Badji-Mokhtar. B.P. 12, Annaba 23.000. Algérie;

mlsahari@yahoo.fr
i_djellit@hotmail.com

(Published online: 13 October 2007)

Abstract
Newton's method is a root-finding algorithm and Newton basins is the set of initial guesses that lead to one root of polynomial on the complex plane. A boundary of Newton basins are fractals and called Julia set. In this work we introduce a modification on the algorithm and we show that the fractal aspect of basins is preserved.

Résumé
L'algorithme de Newton appliqué à la ré solution d'équations algébriques à variable complexe gén ère une suite dotée d'un comportement chaotique qui se traduit par la "fractalisation" de la frontière du bassin d'attraction des solutions. Dans ce travail on introduit une modification sur l'algorithme et on montre que l'aspect fractal des bassins est preservé.

Mathematics Subject Classification. 37N30. 65F10. 30C15

Key words: Algorithme de Newton, Bassin d'attraction, Chaos, Fractal, Problème de Cayley.


© EDP Sciences, ESAIM 2007

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