A new Kantorovich-type theorem for Newton's method
Tom 26 / 1999
Applicationes Mathematicae 26 (1999), 151-157
DOI: 10.4064/am-26-2-151-157
Streszczenie
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.
