7 citations · 7 across the 1 of their papers we have counts for
4 papers
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…
Paramotopy: Parameter homotopies in parallel
Daniel J. Bates, Danielle Brake, Matthew Niemerg
Numerical algebraic geometry provides a number of efficient tools for approximating the solutions of polynomial systems. One such tool is the parameter homotopy, which can be an ex…
Computing complex and real tropical curves using monodromy
Daniel A. Brake, Jonathan D. Hauenstein, Cynthia Vinzant
Tropical varieties capture combinatorial information about how coordinates of points in a classical variety approach zero or infinity. We present algorithms for computing the rays…
Numerically validating the completeness of the real solution set of a system of polynomial equations
Daniel A. Brake, Jonathan D. Hauenstein, Alan C. Liddell
Computing the real solutions to a system of polynomial equations is a challenging problem, particularly verifying that all solutions have been computed. We describe an approach tha…