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A faster King-Werner-type iteration and its convergence analysis. (English) Zbl 07250981
Summary: We introduce a new faster two-step King-Werner-type iterative method for solving nonlinear equations. The methodology is based on rational Hermite interpolation. The local as well as semi-local convergence analyses are presented under weak center Lipschitz and Lipschitz conditions. The convergence order is increased from $$1 + \sqrt{2}$$ to 3 without any additional function calculations. Another advantage is the convenient fact that this method does not use derivatives. Numerical examples further validate the theoretical results.
##### MSC:
 65H10 Numerical computation of solutions to systems of equations 65J10 Numerical solutions to equations with linear operators (do not use 65Fxx) 41A25 Rate of convergence, degree of approximation
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