54 citations · 71 across the 10 of their papers we have counts for
12 papers · 1 filter
Bayesian inversion for electromyography using low-rank tensor formats
Anna Rörich, Tim A. Werthmann, Dominik Göddeke +1
The reconstruction of the structure of biological tissue using electromyographic data is a non-invasive imaging method with diverse medical applications. Mathematically, this proce…
A parameter-dependent smoother for the multigrid method
Lars Grasedyck, Maren Klever, Christian Löbbert +1
The solution of parameter-dependent linear systems, by classical methods, leads to an arithmetic effort that grows exponentially in the number of parameters. This renders the multi…
Low-rank tensor methods for Markov chains with applications to tumor progression models
Peter Georg, Lars Grasedyck, Maren Klever +3
Continuous-time Markov chains describing interacting processes exhibit a state space that grows exponentially in the number of processes. This state-space explosion renders the com…
Rank Bounds for Approximating Gaussian Densities in the Tensor-Train Format
Paul B. Rohrbach, Sergey Dolgov, Lars Grasedyck +1
Low-rank tensor approximations have shown great potential for uncertainty quantification in high dimensions, for example, to build surrogate models that can be used to speed up lar…
Finding entries of maximum absolute value in low-rank tensors
Lars Grasedyck, Lukas Juschka, Christian Löbbert
We present an iterative method for the search of extreme entries in low-rank tensors which is based on a power iteration combined with a binary search. In this work we use the HT-f…
Proper orthogonal decomposition (POD) combined with hierarchical tensor approximation (HTA) in the context of uncertain parameters
Steffen Kastian, Dieter Moser, Stefanie Reese +1
The evaluation of robustness and reliability of realistic structures in the presence of uncertainty involves costly numerical simulations with a very high number of evaluations. Th…
Distributed Hierarchical SVD in the Hierarchical Tucker Format
Lars Grasedyck, Christian Löbbert
We consider tensors in the Hierarchical Tucker format and suppose the tensor data to be distributed among several compute nodes. We assume the compute nodes to be in a one-to-one c…
Stable ALS Approximation in the TT-Format for Rank-Adaptive Tensor Completion
Lars Grasedyck, Sebastian Krämer
Low rank tensor completion is a highly ill-posed inverse problem, particularly when the data model is not accurate, and some sort of regularization is required in order to solve it…
Alternating Least Squares Tensor Completion in The TT-Format
Lars Grasedyck, Melanie Kluge, Sebastian Krämer
We consider the problem of fitting a low rank tensor , , to a given set of data points $\{M_i\in\mathbb{R}\mid i\in…
A Nearly Optimal Multigrid Method for General Unstructured Grids
Lars Grasedyck, Lu Wang, Jinchao Xu
In this paper, we develop a multigrid method on unstructured shape-regular grids. For a general shape-regular unstructured grid of elements, we present a construction…
Tensor-Sparsity of Solutions to High-Dimensional Elliptic Partial Differential Equations
Wolfgang Dahmen, Ronald DeVore, Lars Grasedyck +1
A recurring theme in attempts to break the curse of dimensionality in the numerical approximations of solutions to high-dimensional partial differential equations (PDEs) is to empl…
A literature survey of low-rank tensor approximation techniques
Lars Grasedyck, Daniel Kressner, Christine Tobler
During the last years, low-rank tensor approximation has been established as a new tool in scientific computing to address large-scale linear and multilinear algebra problems, whic…