A. G. Ramm
Published 2009-11-02Version 1
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.
Universality and models for semigroups of operators on a Hilbert space
The universality of $\ell_1$ as a dual space
Universality for Doubly Stochastic Matrices
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