On the local convergence of fast two-step Newton-like methods for solving nonlinear equations

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• 作者：I.K. Argyros^a ; ^{iargyros@cameron.edu} ; S. Hilout^b ; ^{said.hilout@math.univ-poitiers.fr}
• 关键词：65J15 ; 65G99 ; 47H99 ; 49M15
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2013
• 出版时间：June, 2013
• 年：2013
• 卷：245
• 期：Complete
• 页码：1-9
• 全文大小：228 K

文摘

A local convergence analysis is presented for a fast two-step Newton-like method (TSNLM) for solving nonlinear equations in a Banach space setting. The TSNLM unifies earlier methods such as Newton¡¯s, Secant, Newton-like, Chebyshev-Secant, Chebyshev-Newton, Steffensen, Stirling¡¯s and other single or multistep methods. Numerical examples and a comparative study of these methods validating our theoretical results are also given in the concluding section of this paper.