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Mathematics 2019, 7(2), 164; https://doi.org/10.3390/math7020164

Optimal Derivative-Free Root Finding Methods Based on Inverse Interpolation

Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan 60800, Pakistan
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Received: 12 December 2018 / Revised: 20 January 2019 / Accepted: 22 January 2019 / Published: 12 February 2019
(This article belongs to the Section Mathematics and Computers Science)
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Abstract

Finding a simple root for a nonlinear equation f ( x ) = 0 , f : I R R has always been of much interest due to its wide applications in many fields of science and engineering. Newton’s method is usually applied to solve this kind of problems. In this paper, for such problems, we present a family of optimal derivative-free root finding methods of arbitrary high order based on inverse interpolation and modify it by using a transformation of first order derivative. Convergence analysis of the modified methods confirms that the optimal order of convergence is preserved according to the Kung-Traub conjecture. To examine the effectiveness and significance of the newly developed methods numerically, several nonlinear equations including the van der Waals equation are tested. View Full-Text
Keywords: nonlinear equations; simple roots; inverse interpolation; optimal iterative methods; higher order of convergence nonlinear equations; simple roots; inverse interpolation; optimal iterative methods; higher order of convergence
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Junjua, M.-U.-D.; Zafar, F.; Yasmin, N. Optimal Derivative-Free Root Finding Methods Based on Inverse Interpolation. Mathematics 2019, 7, 164.

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