An improved semilocal convergence analysis for the Halley's method

Abstract

We expand the applicability of the Halley's method for approximating a locally unique solution of nonlinear equations in a Banach space setting. Our majorizing sequences are finer than in earlier studies such as [1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 19, 20, 21, 23] and furthermore developed convergence criteria can be weaker. Finally numerical work is reported that compares favorably to the existing approaches in the literature [6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 24, 25, 26, 28].