A new Kantorovich-type theorem for Newton's method

Volume 26 / 1999

Ioannis Argyros Applicationes Mathematicae 26 (1999), 151-157 DOI: 10.4064/am-26-2-151-157


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.


  • Ioannis Argyros

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