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A family of optimal iterative methods with fifth and tenth order convergence for solving nonlinear equations

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Author(s): Mashallah Matinfar | Mohammad Aminzadeh

Journal: Journal of Interpolation and Approximation in Scientific Computing
ISSN 2194-3907

Volume: 2012;
Start page: 1;
Date: 2012;
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Keywords: Nonlinear equation | Iterative method | Three-step | Convergence order | Efficiency index

ABSTRACT
In this paper, we propose a two-step method with fifth-order convergence and a family of optimal three-step method with tenth-order convergence for finding the simple roots of nonlinear equations. The optimal efficiency indices are all found to be $5^{frac{1}{3}}approx1.71$ and $10^{frac{1}{4}}approx1.78.$ Some numerical examples illustrate that the algorithms are more efficient and performs better than other methods.
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