Universality of Newton's method

Details Universality of Newton's method Universality of Newton's method

2009-11-02

arxiv.org/abs/0911.0410v1

Mathematics

Functional Analysis

Scientific paper

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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