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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 δ we propose a stopping rule that yields the convergence rate O(δ 1/2 ) under appropriate conditions. We illustrate these conditions for a few examples.Mathematics Subject Classification (1991): 65J15, 65J20, 47H17

In this paper we consider non-linear ill-posed problems in a Hilbert space setting. We show that Tikhonov regularisation is a stable method for solving non-linear illposed problems and give conditions that guarantee the convergence rate O(d\/B) for the regularised solutions, where cE is a norm bound for the noise in the data. We illustrate these conditions for several examples including parameter estimation problems. In an appendix, we study the connection between the ill-posedness of a non-linear problem and its linearisation and show that this connection is rather weak. A sufficient condition for illposedness is given in the case that the non-linear operator is compact.

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