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Zh. Vychisl. Mat. Mat. Fiz., 2019, Volume 59, Number 6, Pages 920–936 (Mi zvmmf10904)  

Families of optimal derivative-free two- and three-point iterative methods for solving nonlinear equations

T. Zhanlava, Kh. Otgondorjb, O. Chuluunbaatarac

a Institute of Mathematics, National University of Mongolia, Ulan-Bator, 14201 Mongolia
b Division of Applied Sciences, Mongolian University of Science and Technology, Ulan-Bator, 14191 Mongolia
c Joint Institute for Nuclear Research, Dubna, Moscow oblast, 141980 Russia

Abstract: Necessary and sufficient conditions for derivative-free two- and three-point iterative methods to have the optimal convergence order are obtained. These conditions can be effectively used not only for determining the order of convergence of iterative methods but also for designing new methods. Furthermore, the use of the method of generating functions makes it possible to construct a wide class of optimal derivative-free two- and three-point methods that includes many well-known methods as particular cases. An analytical formula for the optimal choice of the parameter of iterations improving the order of convergence is derived.

Key words: nonlinear equations, two- and three-point iterations, necessary and sufficient conditions, optimal methods.

Funding Agency Grant Number
Фонд науки и технологии Монголии SST_18/2018
JINR-Romania program
This work was supported by the Foundation of Science and Technology of Mongolia, project no.В SST_18/2018 and and by the program JINR–Romania–Hulubei–Meshcheryakov of the Joint Institute for Nuclear Research.


DOI: https://doi.org/10.1134/S0044466919060140


English version:
Computational Mathematics and Mathematical Physics, 2019, 59:6, 864–880

Bibliographic databases:

UDC: 519.615
Received: 09.09.2018
Revised: 16.01.2019
Accepted:08.02.2019

Citation: T. Zhanlav, Kh. Otgondorj, O. Chuluunbaatar, “Families of optimal derivative-free two- and three-point iterative methods for solving nonlinear equations”, Zh. Vychisl. Mat. Mat. Fiz., 59:6 (2019), 920–936; Comput. Math. Math. Phys., 59:6 (2019), 864–880

Citation in format AMSBIB
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