On Newton's Method for Solving Nonlinear Equations and Function Splitting

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Abstract

We provided in [14] and [15] a semilocal convergence analysis for Newton's method on a Banach space setting, by splitting the given operator. In this study, we improve the error bounds, order of convergence, and simplify the sufficient convergence conditions. Our results compare favorably with the Newton-Kantorovich theorem for solving equations.

Keywords:

Newton's method Banach space majorizing sequence semilocal convergence splitting of an operator.
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DOI

10.4208/nmtma.2011.m99009