79 citations · 407 across the 53 of their papers we have counts for
7 papers · 1 filter
Tensor decomposition and homotopy continuation
Alessandra Bernardi, Noah S. Daleo, Jonathan D. Hauenstein +1
A computationally challenging classical elimination theory problem is to compute polynomials which vanish on the set of tensors of a given rank. By moving away from computing polyn…
A hybrid symbolic-numerical approach to the center-focus problem
Adam Mahdi, Claudio Pessoa, Jonathan D. Hauenstein
We propose a new hybrid symbolic-numerical approach to the center-focus problem. The method allowed us to obtain center conditions for a three-dimensional system of differential eq…
Multiprojective witness sets and a trace test
Jonathan D. Hauenstein, Jose Israel Rodriguez
In the field of numerical algebraic geometry, positive-dimensional solution sets of systems of polynomial equations are described by witness sets. In this paper, we define multipro…
Software for the Gale transform of fewnomial systems and a Descartes rule for fewnomials
Daniel J. Bates, Jonathan D. Hauenstein, Matthew E. Niemerg +1
We give a Descartes'-like bound on the number of positive solutions to a system of fewnomials that holds when its exponent vectors are not in convex position and a sign condition i…
Algebraic Geometrization of the Kuramoto Model: Equilibria and Stability Analysis
Dhagash Mehta, Noah Daleo, Florian Dörfler +1
Finding equilibria of the finite size Kuramoto model amounts to solving a nonlinear system of equations, which is an important yet challenging problem. We translate this into an al…
Certifying isolated singular points and their multiplicity structure
Jonathan D. Hauenstein, Bernard Mourrain, Agnes Szanto
This paper presents two new constructions related to singular solutions of polynomial systems. The first is a new deflation method for an isolated singular root. This construc-tion…