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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 DjellitDépartement 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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