Dynamical Systems Method (DSM) for solving equations with monotone operators without smoothness assumptions on F′(u) - Hoang, N. S.; Ramm, Alexander G. (My University, 2010)
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.
Keywords: Dynamical Systems Method (DMS); Nonlinear operator equations; Monotone operators; Discrepancy principle