Letter to the Editor: Super-attracting periodic orbits for a classical third order method

Authors:
S. Amat;C. Bermúdez;S. Busquier;J. Carrasco;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 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:
2007

Citing 3
Cited 1

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SIAM Review
Geometric constructions of iterative functions to solve nonlinear equations

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

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Dynamics of a new family of iterative processes for quadratic polynomials

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Abstract

We use a classical third order root-finding iterative method for approximating roots of nonlinear equations. We present a procedure for constructing polynomials so that super-attracting periodic orbits of any prescribed period occur when this method is applied. This note can be considered as the second part of our previous study [S. Amat, S. Busquier, S. Plaza, A construction of attracting periodic orbits for some classical third order iterative methods, J. Comput. Appl. Math. 189(1-2) (2006) 22-33].