, Volume 72, Issue 1, pp 21-37

A convergence analysis of the Landweber iteration for nonlinear ill-posed problems

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In this paper we prove that the Landweber iteration is a stable method for solving nonlinear ill-posed problems. For perturbed data with noise level \(\delta \) we propose a stopping rule that yields the convergence rate\(O (\delta ^{1/2}\) ) under appropriate conditions. We illustrate these conditions for a few examples.