36 citations · 61 across the 23 of their papers we have counts for
14 papers · 1 filter
A stable rank-adaptive step-and-truncate finite volume method for Vlasov transport on domains with piecewise linear boundaries
André Uschmajew, Andreas Zeiser
We consider the numerical solution of the linear Vlasov transport equation on bounded spatial domains with inflow boundary conditions based on low-rank approximation. We combine a…
On low-rank tensor train approximability for linear nearest neighbor systems
Patrick Gelß, Sebastian Matera, Reinhold Schneider +1
Low-rank tensor methods are an important tool in the numerical treatment of equations with a high-dimensional state space. Nearest neighbor interaction systems like the Ising model…
On the randomized SVD in infinite dimensions
Daniel Kressner, David Persson, André Uschmajew
Randomized methods, such as the randomized SVD (singular value decomposition) and Nyström approximation, are an effective way to compute low-rank approximations of large matrices.…
Discontinuous Galerkin discretization of conservative dynamical low-rank approximation schemes for the Vlasov-Poisson equation
André Uschmajew, Andreas Zeiser
A numerical dynamical low-rank approximation (DLRA) scheme for the solution of the Vlasov-Poisson equation is presented. Based on the formulation of the DLRA equations as Friedrich…
Dynamical low-rank tensor approximations to high-dimensional parabolic problems: existence and convergence of spatial discretizations
Markus Bachmayr, Henrik Eisenmann, André Uschmajew
We consider dynamical low-rank approximations to parabolic problems on higher-order tensor manifolds in Hilbert spaces. In addition to existence of solutions and their stability wi…
On the approximation of vector-valued functions by volume sampling
Daniel Kressner, Tingting Ni, André Uschmajew
Given a Hilbert space and a finite measure space , the approximation of a vector-valued function by a -dimensional subspace $\mathcal U \sub…
Dynamical low-rank approximation of the Vlasov-Poisson equation with piecewise linear spatial boundary
André Uschmajew, Andreas Zeiser
We consider dynamical low-rank approximation (DLRA) for the numerical simulation of Vlasov--Poisson equations based on separation of space and velocity variables, as proposed in se…
Local convergence of alternating low-rank optimization methods with overrelaxation
Ivan V. Oseledets, Maxim V. Rakhuba, André Uschmajew
The local convergence of alternating optimization methods with overrelaxation for low-rank matrix and tensor problems is established. The analysis is based on the linearization of…
Existence of dynamical low-rank approximations to parabolic problems
Markus Bachmayr, Henrik Eisenmann, Emil Kieri +1
The existence and uniqueness of weak solutions to dynamical low-rank evolution problems for parabolic partial differential equations in two spatial dimensions is shown, covering al…
Alternating least squares as moving subspace correction
Ivan Oseledets, Maxim Rakhuba, André Uschmajew
In this note we take a new look at the local convergence of alternating optimization methods for low-rank matrices and tensors. Our abstract interpretation as sequential optimizati…
On orthogonal tensors and best rank-one approximation ratio
Zhening Li, Yuji Nakatsukasa, Tasuku Soma +1
As is well known, the smallest possible ratio between the spectral norm and the Frobenius norm of an matrix with is and is (up to scalar scaling…
Tensor Networks for Latent Variable Analysis. Part I: Algorithms for Tensor Train Decomposition
Anh-Huy Phan, Andrzej Cichocki, Andre Uschmajew +3
Decompositions of tensors into factor matrices, which interact through a core tensor, have found numerous applications in signal processing and machine learning. A more general ten…
Finding a low-rank basis in a matrix subspace
Yuji Nakatsukasa, Tasuku Soma, André Uschmajew
For a given matrix subspace, how can we find a basis that consists of low-rank matrices? This is a generalization of the sparse vector problem. It turns out that when the subspace…
On low-rank approximability of solutions to high-dimensional operator equations and eigenvalue problems
Daniel Kressner, André Uschmajew
Low-rank tensor approximation techniques attempt to mitigate the overwhelming complexity of linear algebra tasks arising from high-dimensional applications. In this work, we study…