Stefan Kindermann

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There are numerous applications of tensor analysis in signal processing, such as, blind multiuser separation-equalization-detection and blind identification. As the applicability of tensor analysis widens, the numerical techniques must improve to accommodate new data. We present a new numerical method for tensor analysis. The method is based on the iterated(More)
We consider the reconstruction of complex obstacles from few farfield acoustic measurements. The complex obstacle is characterized by its shape and an impedance function distributed along its boundary through Robin type boundary conditions. This is done by minimizing an objective functional, which is the L distance between the given far field information g∞(More)
We study the least-squares functional of the canonical polyadic tensor decomposition for third order tensors by eliminating one factor matrix, which leads to a reduced functional. An analysis of the reduced functional leads to several equivalent optimization problem, like a Rayleigh quotient or a projection. These formulations are the basis of several new(More)
We study the stability in the Cauchy Problem for the Helmholtz equation in dependence of the wave number k. For simple geometries, we show analytically that this problem is getting more stable with increasing k. In more detail, there is a subspace of the data space on which the Cauchy Problem is well posed, and this subspace grows with larger k. We call(More)
Recently, the metric of Ky Fan was successfully applied to assess uncertainty in linear inverse problems. In this work, we present an extension of these results to nonlinear problems. More precisely, we derive results on convergence and convergence rates for Tikhonov regularization applied to nonlinear stochastic ill-posed problems, and discuss strategies(More)
Regularization is an important aspect whenever a matrix inversion during the training phase is required, as this inversion may lead to an unstable (ill-posed) problem, usually simply because of a matrix with a high condition or even a singular matrix, guiding the learning algorithm to wrong solutions. In this paper we present regularization issues applied(More)