On the Fractal Characteristics of
نویسندگان
چکیده
In this report, we present a complete theory for the fractal that is obtained when applying Newton's Method to nd the roots of a complex cubic. We show that a modiied Newton's Method improves convergence and does not yield a fractal, but basins of attraction with smooth borders. Extensions to higher-order polynomials and the numerical relevance of this fractal analysis are discussed. M. Drexler would like to acknowledge the nancial support of the German Academic Exchange Service (DAAD) through the programme HSPII/AUFE.
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