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.
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Funding
This work was supported by the Foundation of Science and Technology of Mongolia, project no. SST_18 /2018.
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Translated by A. Klimontovich
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Zhanlav, T., Otgondorj, K. On the Optimal Choice of Parameters in Two-Point Iterative Methods for Solving Nonlinear Equations. Comput. Math. and Math. Phys. 61, 29–42 (2021). https://doi.org/10.1134/S0965542520120180
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DOI: https://doi.org/10.1134/S0965542520120180