Convergence rates for Tikhonov regularisation of non-linear ill-posed problems

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Abstract
The authors consider non-linear ill-posed problems in a Hilbert space setting, they show that Tikhonov regularisation is a stable method for solving non-linear ill-posed problems and give conditions that guarantee the convergence rate O( square root delta ) for the regularised solutions, where delta is a norm bound for the noise in the data. They illustrate these conditions for several examples including parameter estimation problems. In an appendix, they 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.