Some Preprints and Publication Links

Papers posted here are preprints which may be different from the final refereed and edited publications. You are encouraged to access the final publications to see a definitive copy. Do not repost these preprints without explicit permission.
My publication list (pdf) contains a more complete list, especially regarding older articles.
Books
  1. Daniel J. Bates, Jonathan D. Hauenstein, Andrew J. Sommese, and Charles W. Wampler,
    Numerically Solving Polynomial Systems with Bertini, (publisher's webpage) SIAM Books, Philadelphia, PA, 2013.

  2. Andrew J. Sommese and Charles W. Wampler,
    Numerical Solution of Systems of Polynomials Arising In Engineering And Science, (publisher's webpage)
    World Scientific Press, Singapore, 401+xxii pages, (2005).

Articles
  1. J.D. Hauenstein, C. Hills, A.J. Sommese, and C.W. Wampler,
    Branch points of homotopies, Part I: Distribution and probability of failure, (pdf) preprint, 2024.

  2. A.J. Sommese, J.D. Hauenstein, C. Hills, and C.W. Wampler,
    Branch points of homotopies, Part II: Enumeration and general theory, (pdf, Maple worksheets and examples) preprint, 2024.

  3. E.R. Cobain, J.D. Hauenstein, and C.W. Wampler,
    Robust Numerical Algebraic Geometry, (pdf) preprint, 2024.
    Computational files: (doi)

  4. A. Baskar, M. Plecnik, J.D. Hauenstein, and C.W. Wampler,
    A numerical continuation approach using monodromy to solve the forward kinematics of cable-driven parallel robots with sagging cables, (pdf) Mechanism & Machine Theory, Volume 195, DOI10.1016/j.mechmachtheory.2024.1056092024.

  5. A. Baskar, M. Plecnik, J.D. Hauenstein, and C.W. Wampler,
    A real-time algorithm for computing the tension force in a suspended elastic sagging cable, (pdf) Proceedings MSR-RoManSy 2024, May 22-25, 2024.

  6. M. He, C.W. Wampler, L. Hector, M. Dato, S. Kolluri, K. Amine, C.-C. Su, and M. Cai,
    Revealing the Mechanism Behind Sudden Capacity Loss in Lithium Metal Batteries, (pdf) J. Electrochem. Soc., 170 100528. DOI:10.1149/1945-7111/ad01e7
    Erratum: (pdf) J. Electrochem. Soc., 171 029001. DOI: 10.1149/1945-7111/ad1f36

  7. Silviana Amethyst, Jonathan D. Hauenstein, and Charles W. Wampler,
    Cellular decompositions and Chebyshev interpolants for real algebraic curves, (pdf).

  8. E. Baker, C. Wampler, and D. Baker,
    Triply invertible scarf sewing adventures (and instructions) (pdf) J. Mathematics and the Arts, 2023. DOI:10.1080/17513472.2023.2200897

  9. Samantha N. Sherman, Jonathan D. Hauenstein, and Charles W. Wampler,
    Advances in the theory of planar curve cognates. (pdf) J. Mechanisms and Robotics, 13(3), 031107, 2021

  10. Samantha N. Sherman, Jonathan D. Hauenstein, and Charles W. Wampler,
    A general method for constructing planar cognate mechanisms. (pdf) J. Mechanisms and Robotics, 13(3), 031107, 2021

  11. Samantha N. Sherman, Jonathan D. Hauenstein, and Charles W. Wampler,
    Curve cognate construction made easy (pdf). Proc. ASME 2020 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 10: 44th Mechanisms and Robotics Conference (MR), DETC2020-22409, V010T10A024, 2020.

  12. R. Fabbri, et al.,
    Trifocal Relative Pose from Lines at Points and its Efficient Solution: Expanded Version with Supplementary Material (pdf) Conf. Computer Vision & Pattern Recognition (CVPR 2020), Seattle, June 16-18, 2020

  13. Mark W. Verbrugge and Charles W. Wampler,
    Smoothing methods for numerical differentiation to identify electrochemical reactions from open-circuit-potential data, (pdf) J. Electrochemical Society, 165(16)A4000-A4011, 2018.
    DOI:10.1149/2.0951816jes

  14. Mark W. Verbrugge and Charles W. Wampler,
    On the optimal sizing of batteries for electric vehicles and the influence of fast charge, (pdf) J. Power Sources, 384:312-317, 2018.
    DOI:10.1016/j.jpowsour.2018.02.064

  15. Jonathan D. Hauenstein, Samantha N. Sherman, and Charles W. Wampler,
    Exceptional Stewart-Gough platforms, Segre embeddings, and the special Euclidean group, (pdf). SIAM J. Appl. Algebra Geometry, 2(1), 179--205, 2018. DOI:10.1137/17M1114284

  16. Daniel J. Bates, Daniel A. Brake, Jonathan D. Hauenstein, Andrew J. Sommese, and Charles W. Wampler,
    Homotopies for connected components of algebraic sets with application to computing critical sets, (pdf). In: Bl mer J., Kotsireas I., Kutsia T., Simos D. (eds) MACIS 2017. Lecture Notes in Computer Science, vol 10693. Springer, Cham. DOI:10.1007/978-3-319-72453-9_8

  17. Daniel A. Brake, Daniel J. Bates, Wenrui Hao, Jonathan D. Hauenstein, Andrew J. Sommese, and Charles W. Wampler,
    Bertini_real: Numerical decomposition of real algebraic curves and surfaces, (pdf). Trans. Math. Software (ToMS), accepted 2017.

  18. Jonathan D. Hauenstein, Charles W. Wampler, and Martin Pfurner,
    Synthesis of three-revolute spatial chains for body guidance, (pdf). Mechanism and Machine Theory, 110:61-72, 2017,
    http://dx.doi.org/10.1016/j.mechmachtheory.2016.12.008

  19. Daniel A. Brake, Jonathan D. Hauenstein, Andrew P. Murray, David H. Myszka, and Charles W. Wampler,
    The complete solution of Alt-Burmester synthesis problems for four-bar linkages, (pdf). ASME. J. Mechanisms Robotics. 2016;8(4):041018-041018-8.
    doi:10.1115/1.4033251.

  20. Jonathan D. Hauenstein and Charles W. Wampler,
    Unification and extension of intersection algorithms in numerical algebraic geometry (pdf). Applied Mathematics and Computation, 293:226-243, 2017,
    http://dx.doi.org/10.1016/j.amc.2016.08.023.
    (computation page)

  21. Saleh M. Almestiri, Andrew P. Murray, David H. Myszka, and Charles W. Wampler,
    Singularity traces of single degree-of-freedom planar linkages that include prismatic and revolute joints, (pdf). ASME J. Mechanism \& Robotics, 8(5):051003-051003-3, 2016.
    doi:10.1115/1.4032410.

  22. Charles W. Wampler,
    Robotics, (pdf). In N.J. Higham, et al, eds., The Princeton Companion to Applied Mathematics, pp. 767--769. Princeton University Press, Princeton, NJ, USA, 2015.

  23. Daniel J. Bates, Daniel A. Brake, Jonathan D. Hauenstein, Andrew J. Sommese, and Charles W. Wampler,
    On computing a cell decomposition of a real surface containing infinitely many singularities, (pdf). (pdf). in Mathematical Software --- ICMS 2014: 4th International Congress, Seoul, South Korea, August 5-9, 2014. Proceedings, H. Hong and C. Yap, eds., Springer, pp. 246-252,doi:10.1007/978-3-662-44199-2_39, 2014.

  24. Daniel A. Brake, Daniel J. Bates, Wenrui Hao, Jonathan D. Hauenstein, Andrew J. Sommese, and Charles W. Wampler,
    Bertini_real: Numerical decomposition of real algebraic curves and surfaces, (pdf). in Mathematical Software --- ICMS 2014: 4th International Congress, Seoul, South Korea, August 5-9, 2014. Proceedings, H. Hong and C. Yap, eds., Springer, pp. 175--182, doi:10.1007/978-3-662-44199-2_29, 2014.

  25. Daniel J. Bates, Wolfram Decker, Jonathan D. Hauenstein, Chris Peterson, Gerhard Pfister, Frank-Olaf Schreyer, Andrew J. Sommese, and Charles W. Wampler,
    Comparison of probabilistic algorithms for analyzing the components of an affine algebraic variety (pdf). Applied Mathematics and Computation, 231:619--633, http://dx.doi.org/10.1016/j.amc.2013.12.165, 2014.

  26. Mark Plecnik, J.Michael McCarthy, and Charles W. Wampler,
    Kinematic synthesis of a Watt I six-bar linkage for body guidance,'' (publisher's link) in Advances in Robot Kinematics, Springer, pp.~317--325, 2014.

  27. J.D. Hauenstein, and C.W. Wampler, Isosingular sets and deflation (pdf)
    Foundations of Computational Mathematics, 13:3:371-403, 2013.
    DOI:10.1007/s10208-013-9147-y

  28. J.D. Hauenstein and C.W. Wampler,
    Numerically Intersecting Algebraic Varieties via Witness Sets (pdf)
    Applied Math. Comp., 219:5730-5742, 2013.
    DOI:10.1016/j.amc.2012.06.034

  29. G.M Besana, S. Di Rocco, J.D. Hauenstein, A.J. Sommese, and C.W. Wampler,
    Cell decomposition of almost smooth real algebraic surfaces (pdf)
    Numerical Algorithms, 63:4:645 678, 2013.
    DOI:10.1007/s11075-012-9646-y

  30. F. Permenter, C. Wampler, and R. Tedrake,
    A numerical algebraic geometry approach to regional stability analysis of polynomial systems.(pdf)
    In American Control Conference (ACC), June 2013 (pp. 2127-2132). IEEE.

  31. Lin Li, David H. Myszka, Andrew P. Murray, and Charles W. Wampler,
    Using the singularity trace to understand linkage motion characteristics, (pdf)
    paper DETC2013-13244, Proc. ASME Int. Design Eng. Tech. Conf. (IDETC), Portland, OR, August 5--7, 2013.

  32. M. Abdallah, C.W. Wampler, and R. Platt,
    Decoupled torque control of tendon-driven fingers with tension management, (pdf)
    Int. J. Robotics Research, 32(2):247--258, 2013.
    DOI: 10.1177/0278364912468302

  33. D.H. Myszka, A.P. Murray, and C.W. Wampler,
    Mechanism branches, turning curves, and critical points, (pdf)
    paper DETC2012-70277, Proc. ASME Int. Design Eng. Tech. Conf. (IDETC), Chicago, IL, August 12--15, 2012.

  34. C.W. Wampler and A.J. Sommese,
    Applying Numerical Algebraic Geometry to Kinematics (pdf)
    Chapter 5, 21st Century Kinematics, Springer, 2012, pp. 125-159.

  35. J.D. Hauenstein, A.J. Sommese, and C.W. Wampler,
    Regenerative Cascade Homotopies for Solving Polynomial Systems (pdf)
    Applied Math. Comp., 218:4:1240--1246, 2011.
    DOI:10.1016/j.amc.2011.06.004

  36. C.W. Wampler and A.J. Sommese,
    Numerical Algebraic Geometry and Algebraic Kinematics, (pdf) (ps)
    Acta Numerica, 20:469--567, 2011.
    DOI:10.1017/S0962492911000067

  37. C.W. Wampler, J.D. Hauenstein, and A.J. Sommese,
    Mechanism Mobility and a Local Dimension Test, (pdf)
    Mech. & Machine Theory, 2011.
    DOI:10.1016/j.mechmachtheory.2011.04.011

  38. Daniel J. Bates, Christoper Peterson, Andrew J. Sommese, and Charles W. Wampler,
    Numerical Computation of the Genus of an Irreducible Curve within an Algebraic Set, (dvi) (ps) (pdf)
    J. of Pure & Applied Algebra, 215:8:1844-1851, 2011.
    DOI:10.1016/j.jpaa.2010.10.016

  39. F. Arends, J. Ouaknine, and C.W. Wampler,
    On Searching for Small Kochen-Specker Vector Systems, (pdf)
    Proc. 37th Intl. Workshop on Graph-Theoretic Concepts in Computer Science (WG'11), Tepla Monastery, Czech Republic, June 21--23, 2011.

  40. R. Platt, M.E. Abdallah, and C.W. Wampler,
    Multiple-Priority Impedance Control, (pdf)
    Proc. 2011 IEEE Conf. Robotics & Automation (ICRA), Shanghai, May 9--13, 2011.

  41. M.E. Abdallah and C.W. Wampler,
    Torque control of underactuated tendon-driven fingers, (pdf)
    Mechanism Science, 2:1:83-90, 2011, DOI:10.5194/ms-2-83-2011.
    Available at www.mech-sci.net/2/83/2011.

  42. Jonathan D. Hauenstein, Andrew J. Sommese, and Charles W. Wampler,
    Regeneration Homotopies for Solving Systems of Polynomials, (pdf)
    Mathematics of Computation, 80:273:345-377, AMS, 2011.

  43. M.E. Abdallah, R. Platt, C.W. Wampler, and B. Hargrave,
    Applied joint-space torque and stiffness control of tendon-driven fingers, (pdf)
    Proc. IEEE-RAS Intl. Conf. Humanoid Robots, Nashville, TN, Dec. 6--8, 2010.

  44. M.E. Abdallah, C.W. Wampler, and R. Platt,
    Object impedance control using a closed-chain task definition, (pdf)
    Proc. IEEE-RAS Intl. Conf. Humanoid Robots, Nashville, TN, Dec. 6--8, 2010.

  45. R. Platt, M.E. Abdallah, and C.W. Wampler,
    Multi-Priority Cartesian Impedance Control, (pdf)
    Robotics: Science & Systems Conf. (RSS), Zaragoza, Spain, June 27-30, 2010.

  46. Sandra Di Rocco, David Eklund, Andrew J. Sommese, and Charles W. Wampler,
    Algebraic C*-actions and the Inverse Kinematics of a General 6R Manipulator, (pdf)
    Applied Math. & Computation, 216:9:2512-2524, 2010.

  47. Daniel J. Bates, Jonathan D. Hauenstein, Andrew J. Sommese, and Charles W. Wampler,
    Stepsize Control for Adaptive Multiprecision Path Tracking, (dvi) (ps) (pdf)
    in Interactions of Classical and Numerical Algebraic Geometry, D. Bates, G.-M. Besana, S. Di Rocco, and C. Wampler (Eds.), Contemporary Mathematics, Vol.~496, pp.~21--31, Amer. Math. Soc., 2009.

  48. D. Gao, and C.W. Wampler
    Head Injury Criterion: Assessing the Danger of Robot Impact, (pdf)
    IEEE Robotics & Automation Magazine, pp. 71--74, Dec. 2009.

  49. 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)
    in Software for Algebraic Geometry, IMA Volumes in Math. and its Applications, Vol. 148, eds. M. Stillman, N. Takayama, and J. Verschelde, Springer, 2008.

  50. Daniel J. Bates, Jonathan D. Hauenstein, Andrew J. Sommese, and Charles W. Wampler,
    Adaptive Multiprecision Path Tracking, (dvi) (ps) (pdf)
    SIAM Journal on Numerical Mathematics, 46:2:722-746, 2008.

  51. Andrew J. Sommese and Charles W. Wampler,
    Exceptional Sets and Fiber Products, (dvi) (ps) (pdf)
    Foundations of Computational Mathematics, 8:2:171-196, 2008.

  52. Andrew J. Sommese, Jan Verschelde, and Charles W. Wampler,
    Solving Polynomial Systems Equation by Equation, (dvi) (ps) (pdf) (abstract)
    in Algorithms in Algebraic Geometry, IMA Volumes in Math. and its Applications, Vol. 146, eds. A. Dickenstein, F.-O. Schreyer, and A.J. Sommese, Springer, 2008.

  53. Ye Lu, Daniel J. Bates, Andrew J. Sommese, and Charles W. Wampler,
    Finding all Real Points of a Complex Curve, (pdf)
    In Proceedings of the Midwest Algebra, Geometry and Its Interactions Conference, Contemporary Mathematics, AMS, 448:183--205, 2007.

  54. C.W. Wampler, B.T. Larson, and A.G. Erdman,
    A New Mobility Formula for Spatial Mechanisms, (pdf)
    paper DETC2007-35574, Proc. ASME Design Engineering Technical Conf., Las Vegas, Sept.~4--7, 2007.

  55. Eugene L. Allgower, Daniel J. Bates, Andrew J. Sommese, and Charles W. Wampler,
    Solution of Polynomial Systems Derived from Differential Equations, (dvi) (ps) (pdf)
    Computing, 76:1-2:1-10 (2006).

  56. C.W. Wampler,
    On a rigid body subject to point-plane constraints, (pdf)
    ASME J. of Mechanical Design, 128(1):151--158, Jan. 2006.

  57. Andrew J. Sommese, Jan Verschelde, and Charles W. Wampler,
    An Intrinsic Homotopy for Intersecting Algebraic Varieties, (dvi) (ps) (pdf) (abstract)
    Journal of Complexity 21:593-608 (2005).

  58. Andrew J. Sommese, Jan Verschelde, and Charles W. Wampler,
    Introduction to Numerical Algebraic Geometry, (ps) (pdf) (abstract)
    Chapter~8, Solving Polynomial Equations: Foundations, Algorithms, and Applications, Algorithms and Computation in Mathematics 14, A.Dickenstein, I.Z.Emiris (Eds.), Springer, 2005, pp. 339--392.

  59. Andrew J. Sommese, Jan Verschelde, and Charles W. Wampler,
    Homotopies for Intersecting Solution Components of Polynomial Systems, (dvi) (ps) (pdf) (abstract)
    SIAM Journal on Numerical Analysis, 42:4:1552-1571 (2004).

  60. Andrew J. Sommese, Jan Verschelde, and Charles W. Wampler,
    Numerical Factorization of Multivariate Complex Polynomials, (dvi) (ps) (pdf) (abstract)
    Theoretical Computer Science, 315:2-3:651-669 (2004).

  61. Andrew J. Sommese, Jan Verschelde, and Charles W. Wampler,
    Advances in Polynomial Continuation for Solving Problems in Kinematics, (pdf) (abstract)
    Paper DETC2002/MECH-34254, Proc. ASME Design Engineering Technical Conf. (CDROM), Montreal, Quebec, Sept. 29-Oct. 2, 2002. Revised version in ASME Journal of Mechanical Design 126:2:262-268 (2004).

  62. H.-J. Su, C.W. Wampler, and J.M. McCarthy,
    Geometric design of cylindric PRS serial chains, (pdf)
    Proc. ASME Design Engineering Technical Conf., Chicago, September 2 6, 2003. Revised version in ASME J. Mechanical Design, 126:2:269-277 (2004).

  63. C.W. Wampler,
    Singular foci of planar linkages, (pdf)
    Mechanism Machine Theory, 39:11:1123-1138 (2004).

  64. C.W. Wampler,
    The geometry of singular foci of planar linkages, (pdf)
    Mechanism Machine Theory, 39:11:1139-1153 (2004).

  65. C.W. Wampler,
    Displacement analysis of spherical mechanisms having three or fewer loops, (pdf)
    ASME J. Mechanical Design, 126:1:93-100 (2004). Earlier version Paper DETC2002/MECH-34326, Proc. ASME Design Engineering Technical Conf. (CDROM), Montreal, Quebec, Sept. 29-Oct. 2, 2002.

  66. Andrew J. Sommese, Jan Verschelde, and Charles W. Wampler,
    Numerical Irreducible Decomposition using PHCpack, (dvi) (ps) (pdf) (abstract)
    in Mathematics and Visualization, edited by M. Joswig and N. Takayama, Springer-Verlag (2003), 109-130.

  67. Andrew J. Sommese, Jan Verschelde, and Charles W. Wampler,
    Method for Tracking Singular Paths with Application to the Numerical Irreducible Decomposition, (dvi) (ps) (pdf) (abstract)
    in Algebraic Geometry, a Volume in Memory of Paolo Francia, ed. by M.C. Beltrametti, F. Catanese, C. Ciliberto, A. Lanteri, and C. Pedrini; De Gruyter (2002), 329-345.

  68. Andrew J. Sommese, Jan Verschelde, and Charles W. Wampler,
    Symmetric Functions Applied to Decomposing Polynomial Systems, (dvi) (ps) (pdf) (abstract)
    SIAM Journal on Numerical Analysis 40:6:2026-2046 (2002).

  69. Andrew J. Sommese, Jan Verschelde, and Charles W. Wampler,
    Using Monodromy to Decompose Solution Sets of Polynomial Systems into Irreducible Components, (dvi) (ps) (pdf) (abstract)
    in Proceedings of the 2001 NATO Advance Research Conference, Eilat, Israel, on Applications of Algebraic Geometry to Coding Theory, Physics, and Computation, edited by C. Ciliberto, F. Hirzebruch, R. Miranda, and M. Teicher, (2001) 297-315.

  70. Andrew J. Sommese, Jan Verschelde, and Charles W. Wampler,
    Numerical Irreducible Decomposition using Projections from Points on Components, (dvi) (ps) (pdf) (abstract)
    in Symbolic Computation: Solving Equations in Algebra, Geometry, and Engineering, ed. by Green, Hosten, Laubenbacher, and Power, Contemporary Mathematics 206 (2001), pages 37-51.

  71. Andrew J. Sommese, Jan Verschelde, and Charles W. Wampler,
    Numerical Decomposition of the Solution Sets of Polynomial Systems into Irreducible Components, (pdf)
    SIAM Journal on Numerical Analysis, 38:6:2022-2046 (2001).

  72. C.W. Wampler,
    Solving the kinematics of planar mechanisms by Dixon determinant and a complex-plane formulation, (pdf)
    in Proc. ASME Design Engr. Tech. Conf. (CDROM), Sept. 10--13, 2000, Baltimore, MD. Revised version in ASME J. Mechanical Design, 123:3:382--387 (2001).

  73. C.W. Wampler,
    Solving the kinematics of planar mechanisms, (pdf)
    Proc. ASME Design Engr. Tech. Conf. (CDROM), Sept. 13--16, 1998, Atlanta, Ga. Revised version in ASME J. Mechanical Design, 121:3:387-391 (1999).

  74. C.W. Wampler,
    Forward displacement analysis of general six-in-parallel SPS (Stewart) platform manipulators using soma coordinates, (pdf)
    Mechanism and Machine Theory, 31:3:331-337 (1996).

  75. J.M. Hollerbach, and C.W. Wampler,
    The calibration index and a taxonomy for robot kinematic calibration methods, (ps) (pdf)
    Int. J. of Robotics Research, 15:6:573-591 (1996).

  76. J.M. Hollerbach, and C.W. Wampler,
    The calibration index and the role of input noise in robot calibration, (ps)
    Robotics Research: The Seventh International Symposium, G. Giralt and G Hirzinger, eds., Springer-Verlag, London, 1996, pp. 558-568.

  77. C.W. Wampler,
    Isotropic coordinates, circularity, and Bezout numbers: Planar kinematics from a new perspective, (pdf)
    Proc. ASME Design Engr. Tech. Conf. (CDROM), Aug. 18-22, 1996, Irvine, CA.

  78. Andrew J. Sommese and Charles W. Wampler,
    Numerical Algebraic Geometry, (dvi) (ps) (pdf)
    in The Mathematics of Numerical Analysis: Real Number Algorithms, Park City, Utah, Summer 1995, ed. by J. Renegar, M. Shub, and S. Smale, Lectures in Applied Math. 32 (1996), 749-763.

  79. Alexander P. Morgan, Andrew J. Sommese and Charles W. Wampler,
    A Product-Decomposition Bound for Bezout Numbers, (jstor link)
    SIAM Journal on Numerical Analysis 32:4:1308-1325 (1995).

  80. C.W. Wampler, J.M. Hollerbach, and T. Arai,
    An implicit loop method for kinematic calibration and its application to closed-chain mechanisms, (pdf)
    IEEE Trans. Robotics and Automation, 11:5:710-724 (1995).

  81. A.P. Morgan, A.J. Sommese, and C.W. Wampler,
    A power series method for computing singular solutions to nonlinear analytic systems, (pdf)
    Numerische Mathematik, 63:391-409, 1992.

  82. C.W. Wampler, A.P. Morgan, and A.J. Sommese
    Complete solution of the nine-point path synthesis problem for four-bar linkages, (pdf)
    J. Mechanical Design, 114:153--159, 1992.
    Commentary in J. Mechanical Design, Vol. 119, 1997:

  83. C.W. Wampler and A.P. Morgan,
    Solving the 6R inverse position problem using a generic-case solution methodology, (pdf)
    Mechanism and Machine Theory, 26:1:91-106, 1991.

  84. A.P. Morgan, A.J. Sommese, and C.W. Wampler,
    Computing singular solutions to nonlinear analytic systems, (pdf)
    Numerische Mathematik, 58:669-684, 1991.