Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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AN IMPROVED COMPUTATION OF COMPONENT CENTERS IN THE DECREE-n BIFURCATION SET

  • Published : 2002.09.01

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Abstract

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.

Keywords

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