Dynamical Systems Method (DSM) for solving equations with monotone operators without smoothness assumptions on F′(u)

Abstract

A version of the Dynamical Systems Method (DSM) for solving ill-posed nonlinear equations F(u) = f with monotone operators F in a Hilbert space is studied in this paper under less restrictive assumptions on the nonlinear operators F than the assumptions used earlier. A new method of proof of the basic results is used. An a posteriori stopping rule, based on a discrepancy-type principle, is proposed and justified mathematically under weaker assumptions on the nonlinear operator F, than the assumptions used earlier.