Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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A STUDY ON CONVERGENCE OF EXTENDED LEAP-FROGGING NEWTON'S METHOD LOCATING MULTIPLE ZEROS

  • Received : 2009.03.23
  • Accepted : 2009.05.21
  • Published : 2009.06.30
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Abstract

Assuming that a given nonlinear function f : $\mathbf{R}{\rightarrow}\mathbf{R}$ has a zero $\alpha$with integer multiplicity $m{\geq}1$ and is sufficiently smooth in a small neighborhood of $\alpha$, we define extended leap-frogging Newton's method. We investigate the order of convergence 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 presented in this paper and are throughly verified via Mathematica programming with its high-precision computability.

Keywords

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