79 citations · 407 across the 53 of their papers we have counts for
10 papers · 1 filter
Certified counting of roots of random univariate polynomials
Joseph Cleveland, Jeffrey Dzugan, Jonathan D. Hauenstein +5
A challenging problem in computational mathematics is to compute roots of a high-degree univariate random polynomial. We combine an efficient multiprecision implementation for solv…
Energy Landscape of the Finite-Size Mean-field 2-Spin Spherical Model and Topology Trivialization
Dhagash Mehta, Jonathan D. Hauenstein, Matthew Niemerg +2
Motivated by the recently observed phenomenon of topology trivialization of potential energy landscapes (PELs) for several statistical mechanics models, we perform a numerical stud…
Certifying solutions to overdetermined and singular polynomial systems over Q
Tulay Ayyildiz Akoglu, Jonathan D. Hauenstein, Agnes Szanto
This paper is concerned with certifying that a given point is near an exact root of an overdetermined or singular polynomial system with rational coefficients. The difficulty lies…
Global Structure of Curves from Generalized Unitarity Cut of Three-loop Diagrams
Jonathan D. Hauenstein, Rijun Huang, Dhagash Mehta +1
This paper studies the global structure of algebraic curves defined by generalized unitarity cut of four-dimensional three-loop diagrams with eleven propagators. The global structu…
Computations and Equations for Segre-Grassmann hypersurfaces
Noah S. Daleo, Jonathan D. Hauenstein, Luke Oeding
In 2013, Abo and Wan studied the analogue of Waring's problem for systems of skew-symmetric forms and identified several defective systems. Of particular interest is when a certain…
Certification and the Potential Energy Landscape
Dhagash Mehta, Jonathan D. Hauenstein, David J. Wales
Typically, there is no guarantee that a numerical approximation obtained using standard nonlinear equation solvers is indeed an actual solution, meaning that it lies in the quadrat…