Higher-Order Root-Finding Algorithms and Their Basins of Attraction
نویسندگان
چکیده
منابع مشابه
Higher Order Methods for Nonlinear Equations and Their Basins of Attraction
Abstract: In this paper, we have presented a family of fourth order iterative methods, which uses weight functions. This new family requires three function evaluations to get fourth order accuracy. By the Kung–Traub hypothesis this family of methods is optimal and has an efficiency index of 1.587. Furthermore, we have extended one of the methods to sixth and twelfth order methods whose efficien...
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Given a complex polynomial p(z) with at least three distinct roots, we first prove no rational iteration function exists where the basin of attraction of a root coincides with its Voronoi cell. In spite of this negative result, we prove the Voronoi diagram of the roots can be well approximated through a high order sequence of iteration functions, the Basic Family, Bm(z), m ≥ 2. Let θ be a simpl...
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ژورنال
عنوان ژورنال: Journal of Mathematics
سال: 2020
ISSN: 2314-4785,2314-4629
DOI: 10.1155/2020/5070363