EXTENDING THE APPLICABILITY OF A SECANT-TYPE METHOD OF ORDER TWO USING RECURRENT FUNCTIONS

Abstract

We approximate a locally unique solution of an equation in a Banach space setting by using a quadratically convergent Secant-type method studied in [4]-[6]. Using our new idea of recurrent functions, we extend the applicability of this method, and also simlify the existing sucffient convergence conditions for this method [4]-[6].
Numerical examples, where the method is compared favorably to the Secant and Newton's methods are also provided in this study.