42 citations · 88 across the 8 of their papers we have counts for
10 papers
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…
Geolocation with FDOA Measurements via Polynomial Systems and RANSAC
Karleigh J. Cameron, Daniel J. Bates
The problem of geolocation of a transmitter via time difference of arrival (TDOA) and frequency difference of arrival (FDOA) is given as a system of polynomial equations. This allo…
Numerical algebraic geometry for model selection and its application to the life sciences
Elizabeth Gross, Brent Davis, Kenneth L. Ho +2
Researchers working with mathematical models are often confronted by the related problems of parameter estimation, model validation, and model selection. These are all optimization…
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…
Multiprecision path tracking
Daniel J. Bates, Andrew J. Sommese, Charles W. Wampler
A path tracking algorithm that adaptively adjusts precision is presented. By adjusting the level of precision in accordance with the numerical conditioning of the path, the algorit…