Ball Convergence of an Efficient Eighth Order Iterative Method Under Weak Conditions

Abstract

The convergence order of numerous iterative methods is obtained using derivatives of a higher order, although these derivatives are not involved in the methods. Therefore, these methods cannot be used to solve equations with functions that do not have such high-order derivatives, since their convergence is not guaranteed. The convergence in this paper is shown, relying only on the first derivative. That is how we expand the applicability of some popular methods.

Keywords

• local convergence
• nonlinear systems
• Banach space
• Fréchet-derivative