An improved computation of component centers in the degree-n bifurcation set

Authors:
Young Hee Geum;Young Ik Kim
Affiliations:
Department of Mathematics, Dankook University, Hannamdong, Seoul, Korea;Department of Applied Mathematics, Dankook University, Cheonan, Korea
Venue:
The Korean Journal of Computational & Applied Mathematics
Year:
2002

Citing 5
Cited 0

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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 ≤ n ≤ 25 and show a remarkably improved computation.