85 citations · 449 across the 28 of their papers we have counts for
21 papers · 1 filter
An Efficient Randomized Hierarchical Tucker Decomposition
Bram Leys, Karl Meerbergen, Nick Vannieuwenhoven +1
We introduce randomized algorithms for computing the hierarchical Tucker decomposition of high-order tensors. Unlike traditional algorithms performed in a sequential leaves-to-root…
Minimality of Tree Tensor Network Ranks
Jana Jovcheva, Tim Seynnaeve, Nick Vannieuwenhoven
For a given tree tensor network , we call a tuple of bond dimensions minimal if there exists a tensor that can be represented by this network but not on the same tree topolo…
Manifold-valued function approximation from multiple tangent spaces
Hang Wang, Raf Vandebril, Joeri Van der Veken +1
Approximating a manifold-valued function from samples of input-output pairs consists of modeling the relationship between an input from a vector space and an output on a Riemannian…
A chiseling algorithm for low-rank Grassmann decomposition of skew-symmetric tensors
Nick Vannieuwenhoven
A numerical algorithm to decompose an exact low-rank skew-symmetric tensor into a sum of elementary (rank-) skew-symmetric tensors is introduced. The algorithm uncovers this Gra…
Warped geometries of Segre-Veronese manifolds
Simon Jacobsson, Lars Swijsen, Joeri Van der Veken +1
Segre-Veronese manifolds are smooth submanifolds of tensors comprising the partially symmetric rank-1 tensors. We investigate a one-parameter family of warped geometries of Segre-V…
Approximating maps into manifolds with lower curvature bounds
Simon Jacobsson, Raf Vandebril, Joeri van der Veken +1
Many interesting functions arising in applications map into Riemannian manifolds. We present an algorithm, using the manifold exponential and logarithm, for approximating such func…
Which constraints of a numerical problem cause ill-conditioning?
Nick Dewaele, Nick Vannieuwenhoven
Many numerical problems with input and output can be formulated as a system of equations where the goal is to solve for . The condition number measures the…
The condition number of singular subspaces, revisited
Nick Vannieuwenhoven
I revisit the condition number of computing left and right singular subspaces from [J.-G. Sun, Perturbation analysis of singular subspaces and deflating subspaces, Numer. Math. 73(…
Three decompositions of symmetric tensors have similar condition numbers
Nick Dewaele, Paul Breiding, Nick Vannieuwenhoven
We relate the condition numbers of computing three decompositions of symmetric tensors: the canonical polyadic decomposition, the Waring decomposition, and a Tucker-compressed Wari…
When can forward stable algorithms be composed stably?
Carlos Beltrán, Vanni Noferini, Nick Vannieuwenhoven
We state some widely satisfied hypotheses, depending only on two functions and , under which the composition of a stable algorithm for and a stable algorithm for is…
Algebraic compressed sensing
Paul Breiding, Fulvio Gesmundo, Mateusz Michałek +1
We introduce the broad subclass of algebraic compressed sensing problems, where structured signals are modeled either explicitly or implicitly via polynomials. This includes, for i…
The condition number of many tensor decompositions is invariant under Tucker compression
Nick Dewaele, Paul Breiding, Nick Vannieuwenhoven
We characterise the sensitivity of several additive tensor decompositions with respect to perturbations of the original tensor. These decompositions include canonical polyadic deco…
A Normal Form Algorithm for Tensor Rank Decomposition
Simon Telen, Nick Vannieuwenhoven
We propose a new numerical algorithm for computing the tensor rank decomposition or canonical polyadic decomposition of higher-order tensors subject to a rank and genericity constr…
Sensitivity of low-rank matrix recovery
Paul Breiding, Nick Vannieuwenhoven
We characterize the first-order sensitivity of approximately recovering a low-rank matrix from linear measurements, a standard problem in compressed sensing. A special case covered…
The condition number of Riemannian approximation problems
Paul Breiding, Nick Vannieuwenhoven
We consider the local sensitivity of least-squares formulations of inverse problems. The sets of inputs and outputs of these problems are assumed to have the structures of Riemanni…
The average condition number of most tensor rank decomposition problems is infinite
Carlos Beltrán, Paul Breiding, Nick Vannieuwenhoven
The tensor rank decomposition, or canonical polyadic decomposition, is the decomposition of a tensor into a sum of rank-1 tensors. The condition number of the tensor rank decomposi…
Pencil-based algorithms for tensor rank decomposition are not stable
Carlos Beltrán, Paul Breiding, Nick Vannieuwenhoven
We prove the existence of an open set of tensors of rank on which a popular and efficient class of algorithms for computing tensor rank decomposition…
On the average condition number of tensor rank decompositions
Paul Breiding, Nick Vannieuwenhoven
We compute the expected value of powers of the geometric condition number of random tensor rank decompositions. It is shown in particular that the expected value of the condition n…
A Riemannian Trust Region Method for the Canonical Tensor Rank Approximation Problem
Paul Breiding, Nick Vannieuwenhoven
The canonical tensor rank approximation problem (TAP) consists of approximating a real-valued tensor by one of low canonical rank, which is a challenging non-linear, non-convex, co…
Convergence analysis of Riemannian Gauss-Newton methods and its connection with the geometric condition number
Paul Breiding, Nick Vannieuwenhoven
We obtain estimates of the multiplicative constants appearing in local convergence results of the Riemannian Gauss-Newton method for least squares problems on manifolds and relate…
The condition number of join decompositions
Paul Breiding, Nick Vannieuwenhoven
The join set of a finite collection of smooth embedded submanifolds of a mutual vector space is defined as their Minkowski sum. Join decompositions generalize some ubiquitous decom…