A faster King–Werner-type iteration and its convergence analysis.

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 + 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. [ABSTRACT FROM AUTHOR]