Monday Lecture Series


May 25, 2009: Jin Cheng, Fudan University, Shanghai China

Heat Transfer in Composite Materials and Related Inverse Problems
In this talk, we will present some results about the heat transfer in a composite materials with Stefan-Boltzmann interface conditions. The related inverse problems with the applications in the steel industry are also discussed.

June 8, 2009: Victor Isakov, Wichita State University, USA

On the inverse doping profile problem in semiconductors theory
We consider the problem of determining doping profile in semiconductors from standard voltage boundary measurements. We derive a dual inverse problem, obtain its asymptotic simplification (for large contrast of conductivities), and prove first uniqueness results in the important unipolar case.

June 15, 2009: William Rundell, Texas A & M University, USA

June 22, 2009: Ulrich Tautenhahn, University of Applied Sciences Zittau/Görlitz, Germany

Regularization with differential operators -- some old and some new results
Regularization with differential operators became in particular attractive after Natterer's paper on Error bounds for Tikhonov regularization in Hilbert scales, Appl. Anal. 18 (1984). Since that time, many aspects in the regularization theory with differential operators have been studied. We give a review on some old aspects and add some new aspects concerning general source conditions and additional perturbations in the forward operator.

June 29, 2009: Peter Mathe, Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany

Discretization under general smoothness assumptions
We shall study the regularizing properties of discretization, specifically projection schemes in Hilbert space. Focus is on identifying approximation theoretic characteristics and geometric properties of the chosen discretization spaces to allow for order optimal approximation.
Focus is on solution smoothness given in terms of general source sets, thus including non-traditional smoothness beyond Sobolev spaces. To do so we exhibit some calculus in variable Hilbert scales.
The results allow to compare traditional regularization schemes and discretization from a unified perspective.

July 6, 2009: Antonio Leitao, Federal University of Santa Catarina, Florianopolis, Brazil

On Kaczmarz type methods for regularizing systems of nonlinear ill-posed equations
We investigate modified iterative methods (namely Landweber, steepest-descent, EM, Levenberg-Marquardt and iterated Tikhonov) coupled with a loping Kaczmarz strategy for obtaining stable solutions of nonlinear systems of ill-posed operator equations. We show that the proposed methods are convergent regularization methods and present some numerical tests.

July 13, 2009: Bernd Hofmann, Chemnitz University of Technology, Germany

An extended approach to source conditions and variational inequalities in regularization with general residual term
This is joint work with Jens Geissler (Chemnitz) which addresses Tikhonov like regularization methods with convex penalty functionals for solving nonlinear ill-posed operator equations formulated in Banach or, more general, topological spaces. We present an approach for proving convergence rates that combines advantages of approximate source conditions and variational inequalities. Precisely, our technique provides both a wide range of convergence rates and the capability to handle general and not necessarily convex residual terms as well as nonsmooth operators. The approach is extensively discussed for Banach and Hilbert space situations, showing that it generalizes some well-known convergence rates results.

Time: 13:30
Room: HF 136