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

Hoang, N. S.; Ramm, Alexander G.

doi:10.1016/j.jmaa.2010.01.062

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

Hoang, N. S.; Ramm, Alexander G.

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

Journal: Journal of Mathematical Analysis and Applications, Volume: 367, Issue: 2, Starting Page: 508, Ending Page: 515

Date: 2010

Publisher URL: http://doi.org/10.1016/j.jmaa.2010.01.062

Article (author version)

Record URL: http://hdl.handle.net/2097/8521

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