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Mathematics 2019, 7(3), 306; https://doi.org/10.3390/math7030306

Improving the Computational Efficiency of a Variant of Steffensen’s Method for Nonlinear Equations

1
Department of Mathematics, College of Science, Salahaddin University, Erbil, Iraq
2
Department of Mathematics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 45137-66731, Iran
*
Author to whom correspondence should be addressed.
Received: 21 January 2019 / Revised: 10 March 2019 / Accepted: 18 March 2019 / Published: 26 March 2019
(This article belongs to the Special Issue Iterative Methods for Solving Nonlinear Equations and Systems)
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Abstract

Steffensen-type methods with memory were originally designed to solve nonlinear equations without the use of additional functional evaluations per computing step. In this paper, a variant of Steffensen’s method is proposed which is derivative-free and with memory. In fact, using an acceleration technique via interpolation polynomials of appropriate degrees, the computational efficiency index of this scheme is improved. It is discussed that the new scheme is quite fast and has a high efficiency index. Finally, numerical investigations are brought forward to uphold the theoretical discussions. View Full-Text
Keywords: iterative methods; Steffensen’s method; R-order; with memory; computational efficiency iterative methods; Steffensen’s method; R-order; with memory; computational efficiency
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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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Khdhr, F.W.; Saeed, R.K.; Soleymani, F. Improving the Computational Efficiency of a Variant of Steffensen’s Method for Nonlinear Equations. Mathematics 2019, 7, 306.

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