Regularization by projection: Approximation theoretic aspects and distance functions

Abstract The authors study regularization of non-linear inverse problems by projection methods. Non-linearity is controlled by some range invariance assumption. Emphasis is on approximation theoretic properties of the discretization which determine the convergence rates. Instead of using source conditions for the true solution to represent the error, the authors show how distance functions with respect to some benchmark smoothness are able to replace this. Some examples indicate how the results can be applied.

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