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For solving linear ill-posed problems regularization methods are required when the right hand side and the operator is with some noise. In the present paper regularized approximations are obtained by Tikhonov regularization, by regularized total least squares (RTLS) and by dual regularized total...
This paper addresses the regularization by sparsity constraints by means of weighted ℓ p penalties for 0 ≤ p ≤ 2. For 1 ≤ p ≤ 2 special attention is payed to convergence rates in norm and to source conditions. As main results it is proven that one gets a convergence rate of in the...
We introduce and analyze moduli of continuity for specific classes of Nemytskii operators on spaces of continuous functions, which are given by kernels, strictly monotone in their second argument. Such operators occur as non-linear (outer) mappings for certain problems of option pricing within...
In a model situation the problem of parallel identification of two parameters in an elliptic equation was examined. Here, coefficients were considered which are piecewise constant. In a numerical study we deal with various questions. The main focal point is on additional ill-posedness phenomena...
In this article we investigate and prove relationships between metric and Bregman projections induced by powers of the norm of a Banach space. We consider Bregman projections onto affine subspaces of Banach spaces and deduce some interesting analogies to results which are well known for Hilbert...
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