Bernd Hofmann

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Variable Hilbert scales are an important tool for the recent analysis of inverse problems in Hilbert spaces, as these constitute a way to describe smoothness of objects other than functions on domains. Previous analysis of such classes of Hilbert spaces focused on interpolation properties, which allows us to vary between such spaces. In the context of(More)
EEcient implementation of communication software is of critical importance for high-speed networks. We analyze performance bottlenecks in existing implementations and propose two techniques for improvements: The rst exploits parallelism not only in the actions of the FSMs, but also in the runtime system of the protocol stack. The second integrates adjacent(More)
Correct pricing of options and other financial derivatives is of great importance to financial markets and one of the key subjects of mathematical finance. Usually, parameters specifying the underlying stochastic model are not directly observable, but have to be determined indirectly from observable quantities. The identification of local volatility(More)
Dedicated to Ulrich Tautenhahn, a friend and co-author, who passed away too early at the age of 60. Abstract. The regularization of linear ill-posed problems is based on their conditional well-posedness when restricting the problem to certain classes of solutions. Given such class one may consider several related real-valued functions, which measure the(More)
In this paper we deal with aspects of characterizing the ill-posedness of nonlinear inverse problems based on the discussion of speciic examples. In particular, a parameter identiication problem to a second order diierential equation and its ill-posed linear components are under consideration. A new approach to the classiication of ill-posedness degrees for(More)
In this paper, we are going to improve the enhanced convergence rates for Tikhonov regularization of nonlinear ill-posed problems in Banach spaces presented by Neubauer in [14]. The new message is that rates are shown to be independent of the residual norm exponents 1 ≤ p < ∞ in the functional to be minimized for obtaining regularized solutions. However, on(More)