47 citations · 232 across the 39 of their papers we have counts for
5 papers · 1 filter
Random points on an algebraic manifold
Paul Breiding, Orlando Marigliano
Consider the set of solutions to a system of polynomial equations in many variables. An algebraic manifold is an open submanifold of such a set. We introduce a new method for compu…
On the geometry of the set of symmetric matrices with repeated eigenvalues
Paul Breiding, Khazhgali Kozhasov, Antonio Lerario
We investigate some geometric properties of the real algebraic variety of symmetric matrices with repeated eigenvalues. We explicitly compute the volume of its intersection wit…
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…
Learning Algebraic Varieties from Samples
Paul Breiding, Sara Kalisnik Verovsek, Bernd Sturmfels +1
We seek to determine a real algebraic variety from a fixed finite subset of points. Existing methods are studied and new methods are developed. Our focus lies on aspects of topolog…
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…