Fractal Dimension of the Universal Julia Sets for the Chebyshev-Halley Family of Methods

被引：2

作者：

Gutierrez, J. M. ^{[1
]}

Magrenan, A. A. ^{[1
]}

Varona, J. L. ^{[1
]}

机构：

[1] Univ La Rioja, Dept Matemat & Computac, La Rioja, Spain

来源：

NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS, VOLS A-C | 2011年 / 1389卷

关键词：

fractal dimension; Julia set; Chebyshev-Halley methods; box-counting;

D O I：

10.1063/1.3637794

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The concept of universal Julia set introduced in [5] allows us to conclude that the dynamics of a root-finding algorithm applied to any quadratic polynomial can be understood through the analysis of a particular rational map. In this study we go a step beyond in this direction. In particular, we can define the universal fractal dimension of the aforementioned algorithms as the fractal dimension of they corresponding universal Julia sets.

引用

页数：4

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