Authors: Heinz W. Engl, Karl Kunisch, and Andreas Neubauer
Abstract: In this paper we consider non-linear ill-posed problems in a Hilbert space setting. We show that Tikhonov regularization is a stable method for solving non-linear ill-posed problems and give conditions that guarantee the convergence rate O(srt(delta)) for the regularised solutions, where delta is a norm bound for the noise in the data. We illustrate the 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 ill-posedness is given in the case that the non-linear operator is compact.