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Algorithms 2015, 8(2), 271-279; doi:10.3390/a8020271

Dynamics and Fractal Dimension of Steffensen-Type Methods

1
Institute of Telecommunications and Multimedia Applications (iTEAM), Universitat Politècnica de Valencia, Camino de Vera, s/n, 46022-Valencia, Spain
2
Institute of Multidisciplinary Mathematics, Universitat Politècnica de València, Camino de Vera, s/n,46022-Valencia, Spain
*
Author to whom correspondence should be addressed.
Academic Editor: Stefano Mariani
Received: 20 March 2015 / Accepted: 25 May 2015 / Published: 1 June 2015
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Abstract

In this paper, the dynamical behavior of different optimal iterative schemes for solving nonlinear equations with increasing order, is studied. The tendency of the complexity of the Julia set is analyzed and referred to the fractal dimension. In fact, this fractal dimension can be shown to be a powerful tool to compare iterative schemes that estimate the solution of a nonlinear equation. Based on the box-counting algorithm, several iterative derivative-free methods of different convergence orders are compared. View Full-Text
Keywords: nonlinear equation; derivative-free; dynamical plane; fractal dimension; Padé-like approximant nonlinear equation; derivative-free; dynamical plane; fractal dimension; Padé-like approximant
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Chicharro, F.I.; Cordero, A.; Torregrosa, J.R. Dynamics and Fractal Dimension of Steffensen-Type Methods. Algorithms 2015, 8, 271-279.

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