Mathematical and Computer Modelling, ( ISI ), Volume (56), No (5), Year (2012-9) , Pages (97-104)

Title : ( An optimized derivative-free form of the Potra–Pták method )

Authors: F.soleymani , Rajni Sharma , Xiaowu Li , EMRAN TOHIDI ,

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Abstract

Abstract In this paper, we discuss iterative methods for solving univariate nonlinear equations. First of all, we construct a family of methods with optimal convergence rate 4 based upon the Potra–Pták scheme and provide its error equation theoretically. Second, by using this derivative-involved family, a novel derivative-free family of two-step iterations without memory is derived. This derivative-free family agrees with the Kung–Traub conjecture (1974) for building optimal multi-point iterations without memory, since it is proven that each derivative-free method of the family reaches the convergence rate 4 requiring only three function evaluations per full iteration. Finally, numerical test problems are also provided to confirm the theoretical results.

Keywords

, Optimal iterations; Derivative, free; Without memory; Nonlinear equations; The Potra–Pták method; Kung–Traub conjecture
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@article{paperid:1029817,
author = {F.soleymani and Rajni Sharma and Xiaowu Li and TOHIDI, EMRAN},
title = {An optimized derivative-free form of the Potra–Pták method},
journal = {Mathematical and Computer Modelling},
year = {2012},
volume = {56},
number = {5},
month = {September},
issn = {0895-7177},
pages = {97--104},
numpages = {7},
keywords = {Optimal iterations; Derivative-free; Without memory; Nonlinear equations; The Potra–Pták method; Kung–Traub conjecture},
}

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%0 Journal Article
%T An optimized derivative-free form of the Potra–Pták method
%A F.soleymani
%A Rajni Sharma
%A Xiaowu Li
%A TOHIDI, EMRAN
%J Mathematical and Computer Modelling
%@ 0895-7177
%D 2012

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