815 citations · 1k across the 11 of their papers we have counts for
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Streaming Tensor Train Approximation
Daniel Kressner, Bart Vandereycken, Rik Voorhaar
Tensor trains are a versatile tool to compress and work with high-dimensional data and functions. In this work we introduce the Streaming Tensor Train Approximation (STTA), a new c…
The leapfrog algorithm as nonlinear Gauss-Seidel
Marco Sutti, Bart Vandereycken
Several applications in optimization, image, and signal processing deal with data that belong to the Stiefel manifold St(n,p), that is, the set of n-by-p matrices with orthonormal…
Automatic rational approximation and linearization of nonlinear eigenvalue problems
Pieter Lietaert, Javier Pérez, Bart Vandereycken +1
We present a method for solving nonlinear eigenvalue problems using rational approximation. The method uses the AAA method by Nakatsukasa, Sète, and Trefethen to approximate the no…
Time integration of rank-constrained Tucker tensors
Christian Lubich, Bart Vandereycken, Hanna Walach
Dynamical low-rank approximation in the Tucker tensor format of given large time-dependent tensors and of tensor differential equations is the subject of this paper. In particular,…
Preconditioned low-rank Riemannian optimization for linear systems with tensor product structure
Daniel Kressner, Michael Steinlechner, Bart Vandereycken
The numerical solution of partial differential equations on high-dimensional domains gives rise to computationally challenging linear systems. When using standard discretization te…
Time integration of tensor trains
Christian Lubich, Ivan Oseledets, Bart Vandereycken
A robust and efficient time integrator for dynamical tensor approximation in the tensor train or matrix product state format is presented. The method is based on splitting the proj…