On Newton's Method for Solving Nonlinear Equations and Function Splitting
DOI:
https://doi.org/10.4208/nmtma.2011.m99009Keywords:
Newton's method, Banach space, majorizing sequence, semilocal convergence, splitting of an operator.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.