6 papers · 1 filter
On low-rank tensor train approximability for linear nearest neighbor systems
Patrick GelÃ, 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 \s…
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…