%0 Journal Article
%T Universality of Newton's method
%A A. G. Ramm
%J Mathematics
%D 2009
%I arXiv
%X Convergence of the classical Newton's method and its DSM version for solving operator equations $F(u)=h$ is proved without any smoothness assumptions on $F'(u)$. It is proved that every solvable equation $F(u)=f$ can be solved by Newton's method if the initial approximation is sufficiently close to the solution and $||[F'(y)]^{-1}||\leq m$, where $m>0$ is a constant.
%U http://arxiv.org/abs/0911.0410v1