ASYMPTOTIC ERROR ANALYSIS OF k-FOLD PSEUDO-NEWTON'S METHOD LOCATING A SIMPLE ZERO

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Published: Nov 15, 2008
DOI: https://doi.org/10.14403/jcms.2008.21.4.483
Keywords:
pseudo-Newton's method, order of convergence, asymptotic error constant
Mathematics Subject Classification (2020):
Primary 65H05, 65H99

Main Article Content

Young Ik Kim
Department of Applied Mathematics, Dankook University

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.





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Article Details

Issue
Vol. 21 No. 4 (2008)
Section
Articles