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Convergence of the Newton–Kurchatov Method Under Weak Conditions

  • S. M. Shakhno
  • H. P. Yarmola
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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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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • S. M. Shakhno
    • 1
  • H. P. Yarmola
    • 1
  1. 1.I. Franko Lviv National UniversityLvivUkraine

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