Finite-dimensional approximation of tikhonov regularized solutions of non-linear ill-posed problems

In this paper we consider non-linear ill-posed problems F(x)=y0 in a Hilbert space setting. We solve these problems with Tikhonov regularization combined with finite-dimensional approximation where the data y0 and the non-linear operator F are assumed to be known only approximately. Conditions are given that guarantee optimal convergence rates with respect to both, the data noise and the finite-dimensional approximation. Finally, we present some numerical results for parameter estimation problems that verify the theoretical results.