We study the semilocal convergence of the combined Newton–Kurchatov method to a locally unique solution of the nonlinear equation under weak conditions imposed on the derivatives and first-order divided differences. The radius of the ball of convergence is established and the rate of convergence of the method is estimated. As a special case of these conditions, we consider the classical Lipschitz conditions.
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 60, No. 2, pp. 7–13, April–June, 2017.
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Shakhno, S.M., Yarmola, H.P. Convergence of the Newton–Kurchatov Method Under Weak Conditions. J Math Sci 243, 1–10 (2019). https://doi.org/10.1007/s10958-019-04521-5
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DOI: https://doi.org/10.1007/s10958-019-04521-5