An improved semilocal convergence analysis for the midpoint method

Abstract

We expand the applicability of the midpoint method for approximating a locally unique solution of nonlinear equations in a Banach space setting. Our majorizing sequences are finer than the known results in scientific literature [1,3,4,5,6,7,8,9,10,11,19,20,21,23] and the convergence criteria can be weaker. Finally, numerical work is reported that compares favorably to the existing approaches in the literature [6, 8-16, 24-26,28].