Some of my preprints

    Submitted (in reverse chronological order by initial submission date)

  1. D. Bates and T. Hodges,
    Heuristic path choice to avoid ill-conditioning in homotopy continuation (pdf).

  2. 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).

  3. Daniel J. Bates, Daniel A. Brake, and Matthew E. Niemerg,
    Paramotopy: Parameter homotopies in parallel (pdf).

  4. 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)

  5. 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.

  6. 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).

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. D. Brake, D. Bates, J. Hauenstein, A. Sommese, and C. Wampler
    On computing a cell decomposition of a real surface containing in nitely many singularities (pdf).
    A version of this extended abstract appear ed in the Proceedings of ICMS 2014.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  21. 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.

  22. 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.

  23. 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.

  24. 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.

  25. 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.

  26. 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.

  27. 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.

  28. 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.

  29. 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.

  30. 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).

  31. 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.

  32. 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.

  33. 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.

  34. 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.

  35. 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.

  36. 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.

  37. 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.

  38. 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.

Edited volumes

  1. 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.

My thesis