Dynamics of a higher-order family of iterative methods

Authors:
Gerardo Honorato;Sergio Plaza;Natalia Romero
Affiliations:
Departamento de Matemáticas, Facultad de Ciencias, Universidad de Santiago de Chile, Chile;Departamento de Matemáticas, Facultad de Ciencias, Universidad de Santiago de Chile, Casilla 307, Correo 2. Santiago, Chile;Departamento de Matemáticas y Computación, C/Luis de Ulloa s/n, Edificio Vives 26006, Logroño, La Rioja, Spain
Venue:
Journal of Complexity
Year:
2011

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Abstract

We study the dynamics of a higher-order family of iterative methods for solving non-linear equations. We show that these iterative root-finding methods are generally convergent when extracting radicals. We examine the Julia sets of these methods with particular polynomials. The examination takes place in the complex plane.