A new semilocal convergence theorem for Newton's method
-
1
Universidad de La Rioja
info
ISSN: 0377-0427
Year of publication: 1997
Volume: 79
Issue: 1
Pages: 131-145
Type: Article
More publications in: Journal of Computational and Applied Mathematics
Abstract
A new semilocal convergence theorem for Newton's method is established for solving a nonlinear equation F(x)=0, defined in Banach spaces. It is assumed that the operator F is twice Fréchet differentiable, and F″ satisfies a Lipschitz type condition. Results on uniqueness of solution and error estimates are also given. Finally, these results are compared with those that use Kantorovich conditions.