Polynomial Root-Finding Methods Whose Basins of Attraction Approximate Voronoi Diagram
نویسندگان
چکیده
منابع مشابه
Polynomial Root-Finding Methods Whose Basins of Attraction Approximate Voronoi Diagram
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: Discrete & Computational Geometry
سال: 2011
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-011-9330-3