On the semilocal convergence of derivative free methods for solving nonlinear equations

Abstract

We introduce a Derivative Free Method (DFM) for solving nonlinear equations in a Banach space setting. We provide a semilocal convergence analysis for DFM using recurrence relations. Numerical examples validating our theoretical results are also provided in this study to show that DFM is faster than other derivative free methods [9] using similar information.

Keywords

• Banach space
• derivative free method
• Newton's method
• divided difference
• recurrence relations