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International Journal of Computer Mathematics Volume 86, 2009 - Issue 4
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Section B

On the dynamics of some Newton's type iterative functions

S. Amat Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, SpainCorrespondence[email protected]
,
C. Bermúdez Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Spain
,
S. Busquier Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Spain
,
P. Leauthier Ecole Généraliste d'Ingénieurs de Marseille (EGIM), Marseille, Cedex, France
&
S. Plaza Departmento de Matemáticas, Facultad de Ciencias, Universidad de Santiago de Chile, Santiago, Chile
Pages 631-639 | Received 12 Dec 2005, Accepted 24 Apr 2007, Published online: 24 Mar 2009
 
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Abstract

The dynamics of a family of Newton's type iterative methods for second- and third-degree complex polynomials is studied. The conjugacy classes of these methods are presented. Classical properties of rational maps are used.

AMS(MOS) subject Classifications :

Acknowledgements

We would like to thank the referees and the editor for their comments and suggestions. S.A. and S.B. were supported in part by the Spanish grants MTM2004-07114 and 00675/PI/04. S.P. was supported by Fondecyt grant # 1020711 and Dicyt grant #0433.

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