Dynamics and Fractal Dimension of Steffensen-Type Methods

Algorithms

Francisco I. Chicharro²  Alicia Cordero¹  Juan R. Torregrosa¹ 

[1] Institute of Multidisciplinary Mathematics, Universitat Politècnica de València, Camino de Vera, s/n, 46022-Valencia, Spain; E-Mail:;Institute of Telecommunications and Multimedia Applications (iTEAM), Universitat Politècnica de Valencia, Camino de Vera, s/n, 46022-Valencia, Spain; E-Mail:

关键词: nonlinear equation;    derivative-free;    dynamical plane;    fractal dimension;    Padé-like approximant;   

DOI  :  10.3390/a8020271

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
© 2015 by the authors; licensee MDPI, Basel, Switzerland