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Young Hee Geum, Young Ik Kim : A STUDY ON COMPUTATION OF COMPONENT CENTERS IN THE DEGREE- n BIFURCATION SET.
International Journal of Computer Mathematics, Volume 80, Issue 2 February 2003 , pages 223 - 232
The governing equation locating component centers in the degree- n bifurcation set is a polynomial with a very high degree and its root-finding lacks numerical accuracy. The equation is transformed to have its degree reduced by a factor (n - 1) . Newton's method applied to the transformed equation improves the accuracy with properly chosen initial values. The numerical implementation is done with Maple V using a large number of computational precision digits. Many cases are studied for 2\leq n \leq 25 and show a remarkably improved computation. Our study extends the results given by Peitgen and Richter .
Keywords: Bifurcation; Component Centers; Degree- n Bifurcation Set; Mandelbrot Set; Newton's Method
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Author: Adam Majewski adammaj1-at-o2-dot-pl