Iterative Regularization and Generalized Discrepancy Principle for Monotone Operator Equations

In this paper, we propose two novel algorithms for solving a nonlinear ill-posed operator equation F(x) = f δ , ||f − f δ || ≤ δ, in a real Hilbert space H under the following basic assumption: The first algorithm is a combination of iteratively regularized Newton's scheme (IRNS) with a posteriori stopping rule The second algorithm is a modified version of IRNS with simultaneous updates of the operator [F′(x n ) + ϵ n I] −1 : combined with ( 1 ). A rigorous theoretical analysis of both methods is conducted.