We study the problem of local convergence of the accelerated Newton method for the solution of nonlinear functional equations under generalized Lipschitz conditions for the first- and second-order Fréchet derivatives. We show that the accelerated method is characterized by the quadratic order of convergence and compare it with the classical Newton method.
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 57, No. 1, pp. 18–25, January–March, 2014.
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Shakhno, S.М. On Convergence of the Accelerated Newton Method Under Generalized Lipschitz Conditions. J Math Sci 212, 16–26 (2016). https://doi.org/10.1007/s10958-015-2645-5
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DOI: https://doi.org/10.1007/s10958-015-2645-5