A numerical-symbolic algorithm for computing the multiplicity of a component of an algebraic set. - Daniel J. Bates; Chris Peterson 001; Andrew J. Sommese (J. Complex., 2006)

A numerical algebraic geometry approach to nonlinear constrained optimal control. - Daniel J. Bates; Ioannis A. Fotiou; Philipp Rostalski (CDC, 2007)

An optimal control application in power electronics using numerical algebraic geometry. - Daniel J. Bates; A. Giovanni Beccuti; Ioannis A. Fotiou; Manfred Morari (ACC, 2008)

Adaptive Multiprecision Path Tracking. - Daniel J. Bates; Jonathan D. Hauenstein; Andrew J. Sommese; Charles W. Wampler (SIAM J. Numer. Anal., 2008)

A Numerical Local Dimension Test for Points on the Solution Set of a System of Polynomial Equations. - Daniel J. Bates; Jonathan D. Hauenstein; Chris Peterson 001; Andrew J. Sommese (SIAM J. Numer. Anal., 2009)

Toward a Salmon Conjecture. - Daniel J. Bates; Luke Oeding (Exp. Math., 2011)

Khovanskii-Rolle Continuation for Real Solutions. - Daniel J. Bates; Frank Sottile (Found. Comput. Math., 2011)

Efficient path tracking methods. - Daniel J. Bates; Jonathan D. Hauenstein; Andrew J. Sommese (Numer. Algorithms, 2011)

Numerical Algebraic Geometry for Optimal Control Applications. - Philipp Rostalski; Ioannis A. Fotiou; Daniel J. Bates; A. Giovanni Beccuti; Manfred Morari (SIAM J. Optim., 2011)

Numerically Solving Polynomial Systems with Bertini. - Daniel J. Bates; Andrew J. Sommese; Jonathan D. Hauenstein; Charles W. Wampler (SIAM, 2013)

Bertini for Macaulay2. - Daniel J. Bates; Elizabeth Gross; Anton Leykin; Jose Israel Rodriguez (CoRR, 2013)

Recovering Exact Results from Inexact Numerical Data in Algebraic Geometry. - Daniel J. Bates; Jonathan D. Hauenstein; Timothy M. McCoy; Chris Peterson 001; Andrew J. Sommese (Exp. Math., 2013)

Computing intersection numbers of Chern classes. - Daniel J. Bates; David Eklund; Chris Peterson 001 (J. Symb. Comput., 2013)

On Computing a Cell Decomposition of a Real Surface Containing Infinitely Many Singularities. - Daniel J. Bates; Daniel A. Brake; Jonathan D. Hauenstein; Andrew J. Sommese; Charles W. Wampler (ICMS, 2014)

Bertini_real: Software for One- and Two-Dimensional Real Algebraic Sets. - Daniel A. Brake; Daniel J. Bates; Wenrui Hao; Jonathan D. Hauenstein; Andrew J. Sommese; Charles W. Wampler (ICMS, 2014)

Perturbed homotopies for finding all isolated solutions of polynomial systems. - Daniel J. Bates; Brent R. Davis; David Eklund; Eric M. Hanson; Chris Peterson 001 (Appl. Math. Comput., 2014)

Comparison of probabilistic algorithms for analyzing the components of an affine algebraic variety. - Daniel J. Bates; Wolfram Decker; Jonathan D. Hauenstein; Chris Peterson 001; Gerhard Pfister; Frank-Olaf Schreyer; Andrew J. Sommese; Charles W. Wampler (Appl. Math. Comput., 2014)

Decoupling Highly Structured Polynomial Systems. - Daniel J. Bates; Andrew J. Newell; Matthew E. Niemerg (ACM Commun. Comput. Algebra, 2014)

Using Monodromy to Avoid High Precision in Homotopy Continuation. - Daniel J. Bates; Matthew E. Niemerg (Math. Comput. Sci., 2014)

Workspace Multiplicity and Fault Tolerance of Cooperating Robots. - Daniel A. Brake; Daniel J. Bates; Vakhtang Putkaradze; Anthony A. Maciejewski (MACIS, 2015)

The max-length-vector line of best fit to a set of vector subspaces and an optimization problem over a set of hyperellipsoids. - Daniel J. Bates; Brent R. Davis; Michael Kirby; Justin Marks; Chris Peterson 001 (Numer. Linear Algebra Appl., 2015)

Software for the Gale transform of fewnomial systems and a Descartes rule for fewnomials. - Daniel J. Bates; Jonathan D. Hauenstein; Matthew E. Niemerg; Frank Sottile (Numer. Algorithms, 2016)

BertiniLab: A MATLAB interface for solving systems of polynomial equations. - Daniel J. Bates; Andrew J. Newell; Matthew E. Niemerg (Numer. Algorithms, 2016)

Homotopies for Connected Components of Algebraic Sets with Application to Computing Critical Sets. - Daniel J. Bates; Daniel A. Brake; Jonathan D. Hauenstein; Andrew J. Sommese; Charles W. Wampler (MACIS, 2017)

Algorithm 976: Bertini_real: Numerical Decomposition of Real Algebraic Curves and Surfaces. - Daniel A. Brake; Daniel J. Bates; Wenrui Hao; Jonathan D. Hauenstein; Andrew J. Sommese; Charles W. Wampler (ACM Trans. Math. Softw., 2017)

Paramotopy: Parameter Homotopies in Parallel. - Daniel J. Bates; Danielle A. Brake; Matt Niemerg (ICMS, 2018)

Robustness and parameter geography in post-translational modification systems. - Kee-Myoung Nam; Benjamin M. Gyori; Silviana V. Amethyst; Daniel J. Bates; Jeremy Gunawardena (PLoS Comput. Biol., 2020)

Excess intersections and numerical irreducible decompositions. - Daniel J. Bates; David Eklund; Jonathan D. Hauenstein; Chris Peterson 001 (SYNASC, 2021)

Numerical Nonlinear Algebra. - Daniel J. Bates; Paul Breiding; Tianran Chen; Jonathan D. Hauenstein; Anton Leykin; Frank Sottile (CoRR, 2023)