• Title/Summary/Keyword: pseudo-Halley's method

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ERROR ANALYSIS OF k-FOLD PSEUDO-HALLEY'S METHOD FINDING A SIMPLE ZERO

  • Kim, Young Ik
    • Journal of the Chungcheong Mathematical Society
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    • v.20 no.1
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    • pp.11-21
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    • 2007
  • Given a nonlinear function f : $\mathbb{R}{\rightarrow}\mathbb{R}$ that has a simple real zero ${\alpha}$, a new numerical method to be called k-fold pseudo- Halley's method is proposed and it's error analysis is under investigation to confirm the convergence behavior near ${\alpha}$. Under the assumption that f is sufficiently smooth in a small neighborhood of ${\alpha}$, the order of convergence is found to be at least k+3. In addition, the corresponding asymptotic error constant is explicitly expressed in terms of k, ${\alpha}$ and f as well as the derivatives of f. A zero-finding algorithm is written and has been successfully implemented for numerous examples with Mathematica.

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