학술저널
A STUDY ON CONVERGENCE OF EXTENDED LEAP-FROGGING NEWTON S METHOD LOCATING MULTIPLE ZEROS
- 충청수학회
- Journal of the Chungcheong Mathematical Society
- Volume 22, No. 2
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2009.06217 - 227 (11 pages)
- 0
Assuming that a given nonlinear function f : R ! R has a zero ？？ with integer multiplicity m ¸ 1 and is su±ciently smooth in a small neighborhood of ？？, we de¯ne extended leap- frogging Newton s method. We investigate the order of conver- gence and the asymptotic error constant of the proposed method as a function of multiplicity m. Numerical experiments for various test functions show a satisfactory agreement with the theory pre-sented in this paper and are throughly veri¯ed via Mathematica programming with its high-precision computability.
1. Introduction
2. Convergence analysis
3. Algorithm, numerical results and discussions
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