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arXiv · 0911.0410

Universality of Newton's method

A. G. Ramm
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Abstract

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.

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A. G. Ramm. 2009-11-02. Universality of Newton's method. https://arxiv.org/abs/0911.0410

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