815 citations · 1k across the 11 of their papers we have counts for
13 papers
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…
TTML: tensor trains for general supervised machine learning
Bart Vandereycken, Rik Voorhaar
This work proposes a novel general-purpose estimator for supervised machine learning (ML) based on tensor trains (TT). The estimator uses TTs to parametrize discretized functions,…
Distributed Principal Component Analysis with Limited Communication
Foivos Alimisis, Peter Davies, Bart Vandereycken +1
We study efficient distributed algorithms for the fundamental problem of principal component analysis and leading eigenvector computation on the sphere, when the data are randomly…
A note on the optimal convergence rate of descent methods with fixed step sizes for smooth strongly convex functions
André Uschmajew, Bart Vandereycken
Based on a result by Taylor, Hendrickx, and Glineur (J. Optim. Theory Appl., 178(2):455--476, 2018) on the attainable convergence rate of gradient descent for smooth and strongly 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…
Explicit Stabilised Gradient Descent for Faster Strongly Convex Optimisation
Armin Eftekhari, Bart Vandereycken, Gilles Vilmart +1
This paper introduces the Runge-Kutta Chebyshev descent method (RKCD) for strongly convex optimisation problems. This new algorithm is based on explicit stabilised integrators for…
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…
Unifying time evolution and optimization with matrix product states
Jutho Haegeman, Christian Lubich, Ivan Oseledets +2
We show that the time-dependent variational principle provides a unifying framework for time-evolution methods and optimisation methods in the context of matrix product states. In…
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…
A Riemannian approach to low-rank algebraic Riccati equations
B. Mishra, B. Vandereycken
We propose a Riemannian optimization approach for computing low-rank solutions of the algebraic Riccati equation. The scheme alternates between fixed-rank optimization and rank-one…
Low-rank matrix completion by Riemannian optimization---extended version
Bart Vandereycken
The matrix completion problem consists of finding or approximating a low-rank matrix based on a few samples of this matrix. We propose a new algorithm for matrix completion that mi…