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

ABSTRACT

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.

KEYWORDS:

• King–Werner method
• local convergence
• semi-local convergence
• Banach space
• Euclidean space

AMS CLASSIFICATIONS:

• 65H10
• 65J10
• 41A25

Disclosure statement

No potential conflict of interest was reported by the authors.