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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2021, Volume 61, Number 1, Pages 32–46
DOI: https://doi.org/10.31857/S0044466920120182 (Mi zvmmf11182) 		 
Optimal control

On the optimal choice of parameters in two-point iterative methods for solving nonlinear equations

T. Zhanlava, Kh. Otgondorjb

a Institute of Mathematics and Digital Technology, Mongolian Academy of Sciences
b Mongolian University of Science and Technology
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DOI: https://doi.org/10.31857/S0044466920120182
Abstract: A new optimal two-parameter class of derivative-free iterative methods with the application to the Hansen–Patrick type iterations is developed. Using self-accelerating parameters, new higher order methods with memory are obtained. Exact analytical formulas for the optimal values of the parameters are found for the first time. The convergence order is increased from four to seven without any additional computations. Thus, the proposed methods with memory have a high computational efficiency. Numerical examples and comparison with some other available methods confirm the theoretical results and high computational efficiency.
Key words: nonlinear equations, two-point iterations, methods with memory, optimal methods.
Funding agency Grant number
Foundation of Science and Technology of Mongolia SST_18 /2018
This work was supported by the Foundation of Science and Technology of Mongolia, project no. SST_18 /2018.
Received: 05.11.2019
Revised: 07.07.2020
Accepted: 18.09.2020
English version:
Computational Mathematics and Mathematical Physics, 2021, Volume 61, Issue 1, Pages 29–42
DOI: https://doi.org/10.1134/S0965542520120180
Bibliographic databases:
Document Type: Article
UDC: 519.615
Language: Russian
Citation: T. Zhanlav, Kh. Otgondorj, “On the optimal choice of parameters in two-point iterative methods for solving nonlinear equations”, Zh. Vychisl. Mat. Mat. Fiz., 61:1 (2021), 32–46; Comput. Math. Math. Phys., 61:1 (2021), 29–42
Citation in format AMSBIB
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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