ON APPLICATION OF GENERALIZED DISCREPANCY PRINCIPLE TO ITERATIVE METHODS FOR NONLINEAR ILL-POSED PROBLEMS

摘要

In this paper, we consider generalized Gauss–Newton's scheme for solving nonlinear unstable operator equation F(x) = f in a Hilbert space. In case of noisy data, we propose a novel a posteriori stopping rule and prove a convergence theorem under a source type condition on the solution. As a consequence of this theorem, we obtain convergence rates for various generating functions, θ = θ(θ, α), of a spectral parameter θ and α > 0.