Families of Optimal Derivative-Free Two- and Three-Point Iterative Methods for Solving Nonlinear Equations


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Resumo

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.

Sobre autores

T. Zhanlav

Institute of Mathematics, National University of Mongolia

Autor responsável pela correspondência
Email: tzhanlav@yahoo.com
Mongólia, Ulan-Bator, 14201

Kh. Otgondorj

Division of Applied Sciences, Mongolian University of Science and Technology

Autor responsável pela correspondência
Email: otgondorj@gmail.com
Mongólia, Ulan-Bator, 14191

O. Chuluunbaatar

Institute of Mathematics, National University of Mongolia; Joint Institute for Nuclear Research

Autor responsável pela correspondência
Email: chuka@jinr.ru
Mongólia, Ulan-Bator, 14201; Dubna, Moscow oblast, 141980

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