Basins of Attraction for Various Steffensen-Type Methods
نویسندگان
چکیده
منابع مشابه
Improving the Dynamics of Steffensen-type Methods
The dynamics of Steffesen-type methods, using a graphical tool for showing the basins of attraction, is presented. The study includes as particular cases, Steffesen-type modifications of the Newton, the two-steps, the Chebyshev, the Halley and the super– Halley iterative methods. The goal is to show that if we are interesting to preserve the convergence properties we must ensure that the deriva...
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Let F be an automorphism of C which has an attracting fixed point. It is well known that the basin of attraction is biholomorphically equivalent to C. We will show that the basin of attraction of a sequence of automorphisms f1, f2, . . . is also biholomorphic to C if every fn is a small perturbation of the original map F .
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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 ...
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ژورنال
عنوان ژورنال: Journal of Applied Mathematics
سال: 2014
ISSN: 1110-757X,1687-0042
DOI: 10.1155/2014/539707