An Improved Semilocal Convergence Analysis for the Halley's Method

摘要

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].