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Tikhonov regularisation for non-linear ill-posed problems: optimal convergence rates and finite-dimensional approximation

The author studies Tikhonov regularisation as a stable method for approximating the solutions of non-linear ill-posed problems. The authors gives conditions that guarantee the best possible rate O( delta 23/) for the regularised solutions, where delta is a norm bound for the noise in the data, in the infinite-dimensional setting, and illustrates these conditions for several examples including parameter estimation. The author also presents results on convergence and convergence rates for Tikhonov regularisation combined with the finite-dimensional approximation.