A new semilocal convergence theorem for Newton's method
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Universidad de La Rioja
info
ISSN: 0377-0427
Ano de publicación: 1997
Volume: 79
Número: 1
Páxinas: 131-145
Tipo: Artigo
Outras publicacións en: Journal of Computational and Applied Mathematics
Resumo
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.