47 citations · 232 across the 39 of their papers we have counts for
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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…
Quantitative singularity theory for random polynomials
Paul Breiding, Hanieh Keneshlou, Antonio Lerario
Motivated by Hilbert's 16th problem we discuss the probabilities of topological features of a system of random homogeneous polynomials. The distribution for the polynomials is the…
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…
3264 Conics in a Second
Paul Breiding, Bernd Sturmfels, Sascha Timme
Enumerative algebraic geometry counts the solutions to certain geometric constraints. Numerical algebraic geometry determines these solutions for any given instance. This article i…