A new semilocal convergence theorem for Newton's method
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1
Universidad de La Rioja
info
ISSN: 0377-0427
Argitalpen urtea: 1997
Alea: 79
Zenbakia: 1
Orrialdeak: 131-145
Mota: Artikulua
Beste argitalpen batzuk: Journal of Computational and Applied Mathematics
Laburpena
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.