Local convergence theorems for Newton's method from data at one point
Volume 29 / 2002
Applicationes Mathematicae 29 (2002), 481-486
MSC: 65B05, 47H17, 49D15, 65G99, 65J15, 65N30, 65N35.
DOI: 10.4064/am29-4-7
Abstract
We provide local convergence theorems for the convergence of Newton's method to a solution of an equation in a Banach space utilizing only information at one point. It turns out that for analytic operators the convergence radius for Newton's method is enlarged compared with earlier results. A numerical example is also provided that compares our results favorably with earlier ones.
