47 citations · 232 across the 39 of their papers we have counts for
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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…
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…
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…