Acknowledgement
Supported by : Dankook University
Journal of the Chungcheong Mathematical Society (충청수학회지)
- Volume 21 Issue 4
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- Pages.483-492
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- 2008
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- 1226-3524(pISSN)
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- 2383-6245(eISSN)
ASYMPTOTIC ERROR ANALYSIS OF k-FOLD PSEUDO-NEWTON'S METHOD LOCATING A SIMPLE ZERO
- Kim, Young Ik (Department of Applied Mathematics Dankook University)
- Received : 2008.09.06
- Accepted : 2008.11.20
- Published : 2008.12.30
Abstract
The k-fold pseudo-Newton's method is proposed and its convergence behavior is investigated near a simple zero. The order of convergence is proven to be at least k + 2. The asymptotic error constant is explicitly given in terms of k and the corresponding simple zero. High-precison numerical results are successfully implemented via Mathematica and illustrated for various examples.