79 citations · 407 across the 53 of their papers we have counts for
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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…
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…
A numerical method for solving elliptic equations on real closed algebraic curves and surfaces
Wenrui Hao, Jonathan D. Hauenstein, Margaret H. Regan +1
There are many numerical methods for solving partial different equations (PDEs) on manifolds such as classical implicit, finite difference, finite element, and isogeometric analysi…
Max-convolution through numerics and tropical geometry
Taylor Brysiewicz, Jonathan D. Hauenstein, Caroline Hills
The maximum function, on vectors of real numbers, is not differentiable. Consequently, several differentiable approximations of this function are popular substitutes. We survey thr…
Singular value decomposition of complexes
Danielle A. Brake, Jonathan D. Hauenstein, Frank-Olaf Schreyer +2
Singular value decompositions of matrices are widely used in numerical linear algebra with many applications. In this paper, we extend the notion of singular value decompositions t…
Adaptive strategies for solving parameterized systems using homotopy continuation
Jonathan D. Hauenstein, Margaret H. Regan
Three aspects of applying homotopy continuation, which is commonly used to solve parameterized systems of polynomial equations, are investigated. First, for parameterized systems w…