Kutschan, Benjamin (2019)
Subject of the attached dissertation are the sets of tensors of bounded hierarchical rank. They are algebraic varieties. The central result is a parametrization of the tangent cones of these varieties. Using this result a Riemannian gradient method is constructed. The global convergence of this gradient method is proven using a Lojasiewicz inequality.Low rank tensor decompositions for high dimensional data approximation, recovery and prediction
Wolf, Alexander Sebastian Johannes Wolf (2019)
In this thesis, we examine different approaches for efficient high dimensional data acquisition and reconstruction using low rank tensor decomposition techniques. High dimensional here refers to the order of the ambient tensor space in which the data is contained. Examples of such data include tomographic videos, solutions to parametric differential equations and quantum states of many particle...Exact and soft recovery of structured signals from atomic and total variation norm regularization
Flinth, Axel (2018)
This thesis treats regularization techniques of inverse problems using TV- and atomic norms. In the first part of the thesis, the two concepts are connected, making a unified treatment in the rest of the thesis possible. Concretely, it is proven that for reasonable dictionaries, atomic norms can be calculated with the help of TV -minimization, and that the TV -norm can be considered as an atomi...Singular analysis and coupled cluster theory
Flad, Heinz-Jürgen ; Harutyunyan, Gohar ; Schulze, Bert-Wolfgang (2015)
The primary motivation for systematic bases in first principles electronic structure simulations is to derive physical and chemical properties of molecules and solids with predetermined accuracy. This requires a detailed understanding of the asymptotic behaviour of many-particle Coulomb systems near coalescence points of particles. Singular analysis provides a convenient framework to study the ...