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

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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.

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FUNDING

This work was supported by the Foundation of Science and Technology of Mongolia, project no. SST_18/2018 and by the program JINR–Romania–Hulubei–Meshcheryakov of the Joint Institute for Nuclear Research.

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Authors and Affiliations

  1. Institute of Mathematics, National University of Mongolia, 14201, Ulan-Bator, Mongolia

    T. Zhanlav & O. Chuluunbaatar

  2. Division of Applied Sciences, Mongolian University of Science and Technology, 14191, Ulan-Bator, Mongolia

    Kh. Otgondorj

  3. Joint Institute for Nuclear Research, 141980, Dubna, Moscow oblast, Russia

    O. Chuluunbaatar

Authors
  1. T. Zhanlav
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  2. Kh. Otgondorj
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  3. O. Chuluunbaatar
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Correspondence to T. Zhanlav, Kh. Otgondorj or O. Chuluunbaatar.

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Translated by A. Klimontovich

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Zhanlav, T., Otgondorj, K. & Chuluunbaatar, O. Families of Optimal Derivative-Free Two- and Three-Point Iterative Methods for Solving Nonlinear Equations. Comput. Math. and Math. Phys. 59, 864–880 (2019). https://doi.org/10.1134/S0965542519060149

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  • DOI: https://doi.org/10.1134/S0965542519060149

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