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Open AccessArticle

Sixteenth-Order Optimal Iterative Scheme Based on Inverse Interpolatory Rational Function for Nonlinear Equations

by Mehdi Salimi 1,2 and Ramandeep Behl 3,*
1
Center for Dynamics and Institute for Analysis, Department of Mathematics, Technische Universität Dresden, 01062 Dresden, Germany
2
Department of Law, Economics and Human Sciences, University Mediterranea of Reggio Calabria, 89125 Reggio Calabria, Italy
3
Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(5), 691; https://doi.org/10.3390/sym11050691
Received: 30 April 2019 / Revised: 14 May 2019 / Accepted: 14 May 2019 / Published: 19 May 2019
(This article belongs to the Special Issue Symmetry with Operator Theory and Equations)
The principal motivation of this paper is to propose a general scheme that is applicable to every existing multi-point optimal eighth-order method/family of methods to produce a further sixteenth-order scheme. By adopting our technique, we can extend all the existing optimal eighth-order schemes whose first sub-step employs Newton’s method for sixteenth-order convergence. The developed technique has an optimal convergence order regarding classical Kung-Traub conjecture. In addition, we fully investigated the computational and theoretical properties along with a main theorem that demonstrates the convergence order and asymptotic error constant term. By using Mathematica-11 with its high-precision computability, we checked the efficiency of our methods and compared them with existing robust methods with same convergence order. View Full-Text
Keywords: simple roots; Newton’s method; computational convergence order; nonlinear equations simple roots; Newton’s method; computational convergence order; nonlinear equations
MDPI and ACS Style

Salimi, M.; Behl, R. Sixteenth-Order Optimal Iterative Scheme Based on Inverse Interpolatory Rational Function for Nonlinear Equations. Symmetry 2019, 11, 691.

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