Low rank tensor approximation refers to the idea of transferring the useful theoretical and practical properties of low rank matrix approximation to objects of higher order. Tensors, which in many applications may be seen as a multivariate function, can be given explicitly, e.g., as data points, or implicitly, e.g., as the solution to some physical equation. The reasons to seek for an approximation of a tensor by one of lower rank include estimation of computational complexity of bilinear operations, interpretable models for data analysis, and low-parametric solutions of high-dimensional problems. It is a widely accepted view that most techniques related to low-rank matrices have no clear counterpart for tensors, which is illustrated by the lack of an analog to the singular value decomposition. Given these theoretical challenges on the one hand, and the modern applications on the other hand, this mini-symposium features topics from multilinear algebra, nonlinear optimization, algebraic geometry, and system identification.
Monday 11/07, 10:30–12:30
- Mon 10:30–11:00, Room AV 00.17The Alternating Steepest Descent Method for Solving Linear Systems in Tensor Format Representations, Mike Espig (RWTH Aachen).
- Mon 11:00–11:30, Room AV 00.17Tensors and Volterra series, Mariya Ishteva (Vrije Universiteit Brussel).
- Mon 11:30–12:00, Room AV 00.17Fast Iterative Methods for Hierarchical Low-Rank Approximations, Benjamin Huber (TU Berlin).
- Mon 12:00–12:30, Room AV 00.17Low rank tensor recovery via iterative hard thresholding, Željka Stojanac (RWTH Aachen University).
Tuesday 12/07, 10:30–12:30
- Tue 10:30–11:00, Room AV 00.17Recursive blocked algorithms for triangular linear systems with tensor product structure, Daniel Kressner (EPFL).
- Tue 11:00–11:30, Room AV 00.17Low-rank techniques in PDE-constrained optimization, Martin Stoll (MPI Magdeburg).
- Tue 11:30–12:00, Room AV 00.17Optimization on low-rank manifold: what we know and what we do not know yet., Ivan Oseledets (Skolkovo Institute of Science and Technology).
- Tue 12:00–12:30, Room AV 00.17Parametric model reduction with hierarchical low rank tensors, Lars Grasedyck (RWTH Aachen).
Wednesday 13/07, 10:30–12:30
- Wed 10:30–11:00, Room AV 00.17Connectedness of tensor rank and multilinear rank, Yang Qi (CNRS and University Grenoble Alpes).
- Wed 11:00–11:30, Room AV 00.17Perron-Frobenius theory for nonnegative tensors, Antoine Gautier (Saarland University).
- Wed 11:30–12:00, Room AV 00.17A condition number for the tensor rank decomposition, Nick Vannieuwenhoven (KU Leuven).
- Wed 12:00–12:30, Room AV 00.17Tensor decompositions in $(L,L,1)$-terms with ones in different modes, Nico Vervliet (KU Leuven).