Improved ball convergence of Newton's method under general conditions
Volume 39 / 2012
Applicationes Mathematicae 39 (2012), 365-375
MSC: 65G99, 65K10, 47H17, 49M15, 90C30
DOI: 10.4064/am39-3-9
Abstract
We present ball convergence results for Newton's method in order to approximate a locally unique solution of a nonlinear operator equation in a Banach space setting. Our hypotheses involve very general majorants on the Fréchet derivatives of the operators involved. In the special case of convex majorants our results, compared with earlier ones, have at least as large radius of convergence, no less tight error bounds on the distances involved, and no less precise information on the uniqueness of the solution.
