Improved convergence analysis for the Secant method based on a certain type of recurrence relations

Abstract

We provide new sufficient conditions for the local as well as semilocal convergence of the secant method in a Banach space. Using a certain type of recurrence relations, we provide a finer convergence analysis than before. Moreover, our conditions compare favourably with earlier ones, which allow us to apply our results in cases not covered before.

Keywords:

• Secant method
• Banach space
• Divided difference of order one
• Fréchet-derivative
• Semilocal/local convergence