79 citations · 407 across the 53 of their papers we have counts for
70 papers
Geometry of Newton homotopies: bivariate case
Jennifer Buettner, Jonathan D. Hauenstein, Caroline Hills +3
A standard question in computational real algebraic geometry is to compute all real solutions to a system of polynomial equations with real coefficients. One classical and promisin…
Spiral Endgames for Computing Singular Endpoints of Homotopy Paths
Emma R. Cobian, Jonathan D. Hauenstein, Charles W. Wampler
We develop a new endgame for numerically computing singular solutions to complex analytic systems by means of a homotopy path whose endpoint is the solution to be computed. When th…
Common Real Secants to Pairs of Real Twisted Cubic Curves
Saima Aslam, Matthew Faust, Jonathan D. Hauenstein +5
It is well established that a general pair of twisted cubic curves in complex projective space has ten common secant lines. As an initial investigation, we show that the monodromy…
On computing local monodromy and the numerical local irreducible decomposition
Parker B. Edwards, Jonathan D. Hauenstein
Similarly to the global case, the local structure of a holomorphic subvariety at a given point is described by its local irreducible decomposition. Following the paradigm of numeri…
Smooth connectivity in real algebraic varieties
Joseph Cummings, Jonathan D. Hauenstein, Hoon Hong +1
A standard question in real algebraic geometry is to compute the number of connected components of a real algebraic variety in affine space. By adapting an approach for determining…
Robust Numerical Algebraic Geometry
Emma R. Cobian, Jonathan D. Hauenstein, Charles W. Wampler
The field of numerical algebraic geometry consists of algorithms for numerically solving systems of polynomial equations. When the system is exact, such as having rational coeffici…