Convergence of the Newton–Kurchatov Method Under Weak Conditions
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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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- 4.S. M. Shakhno and G. P. Yarmola, “Convergence of the Newton–Kurchatov method under the classical Lipschitz conditions,” Zh. Obchysl. Prykl. Mat., No. 1 (121), 89–97 (2016).Google Scholar
- 13.S. M. Shakhno, “Combined Newton–Kurchatov method under the generalized Lipschitz conditions for the derivatives and divided differences,” Zh. Obchysl. Prykl. Mat., No. 2 (119), 78–89 (2015).Google Scholar