42 citations · 88 across the 8 of their papers we have counts for
7 papers · 1 filter
Numerical Nonlinear Algebra
Daniel J. Bates, Paul Breiding, Tianran Chen +3
Numerical nonlinear algebra is a computational paradigm that uses numerical analysis to study polynomial equations. Its origins were methods to solve systems of polynomial equation…
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…
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…
Bertini for Macaulay2
Daniel J. Bates, Elizabeth Gross, Anton Leykin +1
Numerical algebraic geometry is the field of computational mathematics concerning the numerical solution of polynomial systems of equations. Bertini, a popular software package for…
Toward a salmon conjecture
Daniel J. Bates, Luke Oeding
By using a result from the numerical algebraic geometry package Bertini we show that (up to high numerical accuracy) a specific set of degree 6 and degree 9 polynomials cut out the…
Khovanskii-Rolle continuation for real solutions
Dan Bates, Frank Sottile
We present a new continuation algorithm to find all nondegenerate real solutions to a system of polynomial equations. Unlike homotopy methods, it is not based on a deformation of t…
Bounds on the number of real solutions to polynomial equations
Daniel J. Bates, Frédéric Bihan, Frank Sottile
We use Gale duality for polynomial complete intersections and adapt the proof of the fewnomial bound for positive solutions to obtain the bound (e^4+3) 2^(k choose 2) n^k/4 for the…