- D. Bates and T. Hodges,

Heuristic path choice to avoid ill-conditioning in homotopy continuation (pdf). - D. Bates, D. Brake, J. Hauenstein, A. Sommese, and C. Wampler,

Homotopies for connected components of algebraic sets with application to computing critical sets (pdf). - Daniel J. Bates, Daniel A. Brake, and Matthew E. Niemerg,

Paramotopy: Parameter homotopies in parallel (pdf). - D. Bates, E. Gross, A. Leykin, and J. Rodriguez,

Bertini.m2: A Bertini interface to Macaulay2 (arXiv).

### Accepted or appeared (in reverse chronological order by date of acceptance)

- D. Brake, D. Bates, W. Hao, J. Hauenstein, A. Sommese, and C. Wampler,

Bertini_real: Numerical decomposition of real algebraic curves and surfaces.

A version of this article will appear in*ACM Transactions of Mathematical Software*, 2016. - E. Gross, B. Davis, K.L. Ho, D.J. Bates, and H.A. Harrington

Numerical algebraic geometry for model selection and its application to the life sciences.

A version of this article will appear in*Journal of the Royal Society Interface*, 2016. (arXiv). - D. Bates, J. Hauenstein, M. Niemerg, and F. Sottile,

Software for the Gale transform of fewnomial systems and a Descartes rule for fenomials.

A version of this article will appear in*Numerical Algorithms*, 2016. Here's a link. - D. Brake, D. Bates, V. Putkaradze, and T. Maciejewski,

Workspace multiplicity and fault tolerance of cooperating robots.

A version of this article will appear in*Lecture Notes in Computer Science*, 2016. - D. Bates, A. Newell, and M. Niemerg,

Decoupling highly structured polynomial systems (pdf).

A version of this article will appear in*J. Symbolic Computation*, 2016. - D. Bates, A. Newell, and M. Niemerg,

BertiniLab: A MATLAB interface for solving systems of polynomial equations.

A version of this article appeared in*Numerical Algorithms*, 71(1):229-244, 2016.

Software available at Matlab Central File Exchange. - D. Bates, B. Davis, M. Kirby, J. Marks, and C. Peterson,

The max-length-vector line of best fit to a set of vector subspaces and an optimization problem over a set of hyperellipsoids (pdf). Computation page.

A version of this article appeared in*Numerical Linear Algebra with Applications*22(3):453-464, 2015. - D. Brake, D. Bates, W. Hao, J. Hauenstein, A. Sommese, and C. Wampler

Bertini_real: Software for One- and Two-Dimensional Real Algebraic Sets (pdf).

A version of this**extended abstract**appeared in the Proceedings of ICMS 2014. - D. Brake, D. Bates, J. Hauenstein, A. Sommese, and C. Wampler

On computing a cell decomposition of a real surface containing innitely many singularities (pdf).

A version of this**extended abstract**appear ed in the Proceedings of ICMS 2014. - D. Bates, B. Davis, D. Eklund, E. Hanson, and C. Peterson,

Perturbed homotopies for finding all isolated solutions of polynomial systems (pdf).

A version of this article appeared in*Applied Mathematics and Computation*247:301-311, 2014. - D. Bates and M. Niemerg,

Using monodromy to avoid high precision in homotopy continuation (pdf).

A version of this article appeared in*Mathematics in Computer Science*8(2):253-262, 2014. Computation page. - D. Bates, W. Decker, J. Hauenstein, C. Peterson, G. Pfister, F. Schreyer, A. Sommese,
and C. Wampler.

Comparison of probabilistic algorithms for analyzing the componentsof an algebraic variety.

A version of this article appeared in*Applied Mathematics and Computation*231:619-633, 2014. - Daniel J. Bates, Jonathan D. Hauenstein, Andrew J. Sommese, and Charles W. Wampler,

Numerically Solving Polynomial Systems with Bertini. 400 page**book**published by SIAM, available November 2013. - Daniel J. Bates, David Eklund, and Chris Peterson,

Computing intersection numbers of Chern classes (pdf). Computation page.

A version of this article appeared in*Journal of Symbolic Computation*50:493-507, 2013. - Daniel J. Bates, Jonathan D. Hauenstein, Timothy McCoy, Chris Peterson, and Andrew J. Sommese,

Recovering exact results from inexact numerical data in algebraic geometry (pdf). Computation page.

A version of this article appeared in*Experimental Mathematics*22(1):38-50, 2013. - Luke Oeding and Daniel J. Bates,

Toward a salmon conjecture (pdf coming soon). Computation page.

A version of this article appeared in*Experimental Mathematics*20(3):358-370, 2011. - D. Bates, J. Hauenstein, and A. Sommese,

A parallel endgame (pdf).

A version of this article appeared in*Randomization, Relaxation, and Complexity in Polynomial Equation Solving*, volume 556 of*Contemporary Mathematics*, 25-35, 2011. - D. Bates, J. Hauenstein, and A. Sommese,

Efficient path tracking methods (pdf).

A version of this article appeared in*Numerical Algorithms*58(4):451-459,2011. - D. Bates and F. Sottile,

Khovanskii-Rolle continuation for real solutions (dvi, ps, pdf).

A version of this article appeared in*Foundations of Computational Mathematics*11(5):563-587, 2011. - Daniel J. Bates, Chris Peterson, Andrew J. Sommese, and Charles W. Wampler,

Numerical computation of the genus of an irreducible curve within an algebraic set (dvi, ps, pdf).

A version of this article appeared in*Journal of Pure and Applied Algebra*215(8):1844-1851, 2011. - P. Rostalski, I. Fotiou, D. Bates, A. Beccuti, and M. Morari,

Numerical algebraic geometry for optimal control applications (pdf).

A version of this article appeared in*SIAM Journal on Optimization*21(2):417-437, 2011. - D. Brake, D. Bates, V. Putkaradze, and T. Maciejewski,

An illustration of numerical algebraic methods for workspace estimation of cooperating robots after joint failure (pdf).

A version of this article appeared in the*Proceedings of the IASTED Robotics and Applications (RA) 2010*conference. - D. Bates, J. Hauenstein, C. Peterson, and A. Sommese,

Numerical decomposition of the rank-deficiency set of a polynomial matrix. (dvi, ps, pdf).

A version of this article appeared as the first chapter in*Approximate Commutative Algebra*in the series Texts and Monographs in Symbolic Computation, 2010. - D. Bates, J. Hauenstein, C. Peterson, and A. Sommese,

A local dimension test for numerically approximated points on algebraic sets. (dvi, ps, pdf).

A version of this article appeared in*SIAM Journal on Numerical Analysis*47:3608-3623, 2009. - D. Bates, J. Hauenstein, A. Sommese, and C. Wampler.

Stepsize control for adaptive multiprecision path tracking. (dvi, ps, pdf).

A version of this article appeared in*Contemporary Mathematics*496:21-31, 2009. - Daniel J. Bates, A. Giovanni Beccuti, Ioannis A. Fotiou, and Manfred Morari,

An optimal control application in power electronics using numerical algebraic geometry (abstract).

A version of this article appeared in the Proceedings of the 2008 American Control Conference (ACC 2008). - Daniel J. Bates, Jonathan D. Hauenstein, Andrew J. Sommese, and Charles W. Wampler,

Software for numerical algebraic geometry: a paradigm and progress towards its implementation (dvi, ps, pdf).

A version of this article appeared in*IMA Volumes in Mathematics and its Applications*148:1-14, 2008. - Daniel J. Bates, Chris Peterson, and Andrew J. Sommese,

Applications of numerical terracini's lemma (dvi, ps, pdf).

A version of this article appeared in*IMA Volumes in Mathematics and its Applications*146:1-14, 2008. - Daniel J. Bates, Jonathan D. Hauenstein, Andrew J. Sommese, and Charles W. Wampler,

Adaptive multiprecision path tracking (dvi, ps, pdf).

A version of this article appeared in*SIAM Journal on Numerical Analysis*46(2):722-746, 2008. - Daniel J. Bates, Frédéric Bihan, and Frank Sottile,

Bounds on the number of real solutions to polynomial equations (pdf).

This article appeared in*International Mathematics Research Notices*, 2007(114):rnm114-7, 2007. - Daniel J. Bates, Ioannis A. Fotiou, and Philipp Rostalski,

A numerical algebraic geometry approach to nonlinear constrained optimal control (abstract).

A version of this article appeared in the Proceedings of the 2007 IEEE Conference on Decision and Control, 2007. - Ye Lu, Daniel J. Bates, Andrew J. Sommese, and Charles W. Wampler,

Finding all real points of a complex curve (dvi, ps, pdf).

A version of this article appeared in*Contemporary Mathematics*448:183-205, 2007. - Daniel J. Bates, Chris Peterson, and Andrew J. Sommese,

A numerical-symbolic algorithm for computing the multiplicity of a component of an algebraic set (dvi, ps, pdf).

A version of this article appeared in*Journal of Complexity*, 22(4): 475-489, 2006. - Eugene L. Allgower, Daniel J. Bates, Andrew J. Sommese, and Charles W. Wampler,

Solution of polynomial systems derived from differential equations (dvi, ps, pdf).

A version of this article appeared in*Computing*, 76(1-2): 1-10, 2006.

- Daniel J. Bates, GianMario Besana, Sandra Di Rocco, and Charles W. Wampler,

Interactions of Classical and Numerical Algebraic Geometry (AMS page).

*Contemporary Mathematics*496, 2009.

- Here is the final version of my Ph.D. thesis, titled "Theory and Applications in Numerical Algebraic Geometry" and completed in April 2006 (dvi, ps, pdf).