47 citations · 232 across the 39 of their papers we have counts for
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HomotopyContinuation.jl: A package for homotopy continuation in Julia
Paul Breiding, Sascha Timme
We present the Julia package HomotopyContinuation.jl, which provides an algorithmic framework for solving polynomial systems by numerical homotopy continuation. We introduce the ba…
Random spectrahedra
Paul Breiding, Khazhgali Kozhasov, Antonio Lerario
Spectrahedra are affine-linear sections of the cone of positive semidefinite symmetric -matrices. We consider random spectrahedra that are obtained by in…
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…
How Many Eigenvalues of a Random Symmetric Tensor are Real?
Paul Breiding
This article answers a question posed by Draisma and Horobet, who asked for a closed formula for the expected number of real eigenvalues of a random real symmetric tensor drawn fro…