Geodesic
A new Kantorovich-type theorem for Newton's method
Applicationes Mathematicae, Tome 26 (1999) no. 2, pp. 151-157

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

A new Kantorovich-type convergence theorem for Newton's method is established for approximating a locally unique solution of an equation F(x)=0 defined on a Banach space. It is assumed that the operator F is twice Fréchet differentiable, and that F', F'' satisfy Lipschitz conditions. Our convergence condition differs from earlier ones and therefore it has theoretical and practical value.
DOI : 10.4064/am-26-2-151-157
Keywords: Newton's method, Lipschitz-Hölder condition, Kantorovich hypothesis, Banach space

Ioannis Argyros 1

1 
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Ioannis Argyros. A new Kantorovich-type theorem for Newton's method. Applicationes Mathematicae, Tome 26 (1999) no. 2, pp. 151-157. doi: 10.4064/am-26-2-151-157

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