A construction of attracting periodic orbits for some classical third-order iterative methods

Authors:
S. Amat;Sonia Busquier;S. Plaza
Affiliations:
Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Spain;Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Spain;Departamento de Matemáticas, Facultad de Ciencias, Universidad de Santiago de Chile, Casilla 307, Correo 2, Santiago, Chile
Venue:
Journal of Computational and Applied Mathematics
Year:
2006

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Abstract

We use a family of root-finding iterative methods for finding roots of nonlinear equations. We present a procedure for constructing polynomials so that superattracting periodic orbits of any prescribed period occur when these methods are applied. This family includes Chebyshev's method, Halley's method, the super-Halley method, and the c-methods, as particular cases.