ILAS2016 — 11–15 July 2016 — KU Leuven, Belgium

20th Conference of the International Linear Algebra Society (ILAS)

20th ILAS Conference

In minisymposium: Low Rank Tensor Approximation

Mon 11:30–12:00, Room AV 00.17
Fast Iterative Methods for Hierarchical Low-Rank Approximations
Benjamin Huber (TU Berlin)
Joint work with Reinhold Schneider (TU Berlin); Sebastian Wolf (TU Berlin)

In recent years low-rank approximations of high-dimensional tensors, most notably the Hierarchical Tucker and Tensor Train decompositions, have become increasingly relevant in the mathematical community in a variety of applications. In particular the Alternating Least Squares or DMRG algorithms and Riemannian algorithms constitute two very different approaches to optimizing on specific manifolds of low-rank tensors.

In the present talk we look at methods in-between these two approaches, in particular the Alternating Steepest Descent algorithm that sparked a lot of interest recently as well as an application of the Johnson-Lindstrauss lemma to the setting of high dimensional tensors to achieve fast iterative hard- or soft-thresholding algorithms.