A new class of optimal four-point methods with convergence order 16 for solving nonlinear equations

Somayeh Sharifi, Mehdi Salimi, Stefan Siegmund and Taher Lotfi

Mathematics and Computers in Simulation (MATCOM), 2016, vol. 119, issue C, 69-90

Abstract: We introduce a new class of optimal iterative methods without memory for approximating a simple root of a given nonlinear equation. The proposed class uses four function evaluations and one first derivative evaluation per iteration and it is therefore optimal in the sense of Kung and Traub’s conjecture. We present the construction, convergence analysis and numerical implementations, as well as comparisons of accuracy and basins of attraction between our method and existing optimal methods for several test problems.

Keywords: Simple root; Four-step iterative method; Kung and Traub conjecture; Optimal order of convergence; Computational efficiency (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:119:y:2016:i:c:p:69-90

DOI: 10.1016/j.matcom.2015.08.011

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