Publications of Jan Verschelde

Elizabeth Gross, Sonja Petrović and Jan Verschelde.  Interfacing with PHCpack.  J. Softw. Algebra Geom., 5:20--25, 2013. MR3273856
Elizabeth Gross, Sonja Petrovic and Jan Verschelde.  Interfacing with phcpack.  The Journal of Software for Algebra and Geometry, 5:20-25, 2013.
Danko Adrovic and Jan Verschelde.  Polyhedral methods for space curves exploiting symmetry applied to the cyclic n-roots problem.  In Computer algebra in scientific computing, 15th international workshop, CASC 2013, Berlin, Germany, volume 8136 of Lecture Notes in Computer Science, pages 10-29.  Springer-Verlag, 2013.
Jan Verschelde and Genady Yoffe.  Orthogonalization on a general purpose graphics processing unit with double double and quad double arithmetic.  In Proceedings of the 2013 IEEE 27th international parallel and distributed processing symposium workshops (PDSEC 2013), pages 1373-1380.  IEEE, 2013.
Jan Verschelde.  Modernizing PHCpack through phcpy.  Accepted for publication in the EuroSciPy 2013 Proceedings.  2013.
Danko Adrovic and Jan Verschelde.  Computing Puiseux series for algebraic surfaces.  In ISSAC 2012---Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation, pages 20--27.  ACM, New York, 2012. MR3206282
Danko Adrovic and Jan Verschelde.  Computing Puiseux series for algebraic surfaces.  In Proceedings of the 27th international symposium on symbolic and algebraic computation (ISSAC 2012), pages 20-27.  ACM, 2012.
Jan Verschelde and Genady Yoffe.  Evaluating polynomials in several variables and their derivatives on a GPU computing processor.  In Proceedings of the 2012 IEEE 26th international parallel and distributed processing workshops (PDSEC 2012), pages 1391-1399.  IEEE, 2012.
Yun Guan and Jan Verschelde.  Sampling algebraic sets in local intrinsic coordinates.  Comput. Math. Appl., 62(10):3706--3721, 2011. MR2852093
Kathy Piret and Jan Verschelde.  Sweeping algebraic curves for singular solutions.  J. Comput. Appl. Math., 234(4):1228--1237, 2010. MR2609576
Frank Sottile, Ravi Vakil and Jan Verschelde.  Solving Schubert problems with Littlewood-Richardson homotopies.  In ISSAC 2010---Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation, pages 179--186.  ACM, New York, 2010. MR2920552
Jan Verschelde and Genady Yoffe.  Polynomial homotopies on multicore workstations.  In PASCO 2010, proceedings of the 2010 international workshop on parallel symbolic computation, pages 131-140.  ACM, 2010.
Jan Verschelde.  Polynomial Homotopy Continuation with PHCpack.  ACM Communications in Computer Algebra, 44(4):217-220, 2010.
Jan Verschelde.  Polyhedral methods in numerical algebraic geometry.  In Interactions of classical and numerical algebraic geometry, pages 243--263.  Amer. Math. Soc., Providence, RI, 2009. MR2555958
Anton Leykin and Jan Verschelde.  Decomposing solution sets of polynomial systems: a new parallel monodromy breakup algorithm.  The International Journal of Computational Science and Engineering, 4(2):94-101, 2009.
Anton Leykin, Jan Verschelde and Ailing Zhao.  Higher-order deflation for polynomial systems with isolated singular solutions.  In Algorithms in algebraic geometry, pages 79--97.  Springer, New York, 2008. MR2397938
Andrew J. Sommese, Jan Verschelde and Charles W. Wampler.  Solving polynomial systems equation by equation.  In Algorithms in algebraic geometry, pages 133--152.  Springer, New York, 2008. MR2397941
Yun Guan and Jan Verschelde.  PHClab: a MATLAB/Octave interface to PHCpack.  In Software for algebraic geometry, pages 15--32.  Springer, New York, 2008. MR2410714
Michael E. Stillman, Nobuki Takayama and Jan Verschelde, editors.  Software for algebraic geometry, volume 148 of The IMA Volumes in Mathematics and its Applications.  Springer, New York, 2008. Papers from the workshop held at the University of Minnesota, Minneapolis, MN, October 23--27, 2006.  MR2416197
Dario Andrea Bini, Victor Y. Pan and Jan Verschelde.  Preface [Symbolic-numerical computations].  Theoret. Comput. Sci., 409(2):155--157, 2008. MR2474332
Anton Leykin and Jan Verschelde.  Higher-order deflation for polynomial systems with isolated singular solutions.  In Algorithms in algebraic geometry, pages 79-97.  Springer-Verlag, 2008.
Yun Guan and Jan Verschelde.  Parallel implementation of a subsystem-by-subsystem solver.  In Proceedings of the 22th high performance computing symposium, quebec city, 9-11 june 2008, pages 117-123.  IEEE Computer Society, 2008.
Jan Verschelde and Stephen M. Watt, editors.  SNC'07.  Association for Computing Machinery (ACM), New York, 2007. MR2404064
Anton Leykin, Jan Verschelde and Ailing Zhao.  Evaluation of Jacobian matrices for Newton's method with deflation to approximate isolated singular solutions of polynomial systems.  In Symbolic-numeric computation, pages 269--278.  Birkhäuser, Basel, 2007. MR2428452
Anton Leykin, Jan Verschelde and Ailing Zhao.  Evaluation of Jacobian matrices for Newton's method with deflation to approximate isolated singular solutions of polynomial systems.  In Symbolic-numeric computation, edited by dongming wang and lihong zhi., pages 269--278.  Birkhäuser, 2007.
Jan Verschelde and Stephen Watt, editors.  Proceedings of the 2007 international workshop on symbolic-numeric computation.  ACM, 2007.
Anton Leykin, Jan Verschelde and Ailing Zhao.  Newton's method with deflation for isolated singularities of polynomial systems.  Theoret. Comput. Sci., 359(1-3):111--122, 2006. MR2251604
Anton Leykin, Jan Verschelde and Yan Zhuang.  Parallel homotopy algorithms to solve polynomial systems.  In Mathematical software---ICMS 2006, pages 225--234.  Springer, Berlin, 2006. MR2387173
Anton Leykin and Jan Verschelde.  Interfacing with the numerical homotopy algorithms in PHCpack.  In Mathematical software---ICMS 2006, pages 354--360.  Springer, Berlin, 2006. MR2387182
Anton Leykin, Jan Verschelde and Yan Zhuang.  Parallel homotopy algorithms to solve polynomial systems.  In Proceedings of icms 2006, lncs 4151, edited by andrew iglesias and nobuki takayama., pages 225--234.  Springer, 2006.
Jan Verschelde and Yan Zhuang.  Parallel implementation of the polyhedral homotopy method..  In Proceedings of the 2006 icpp workshops. 14-18 august 2006. columbus, ohio. hpsec 2006, pages 481--488.  IEEE Computer Society, 2006.
Andrew J. Sommese, Jan Verschelde and Charles W. Wampler.  An intrinsic homotopy for intersecting algebraic varieties.  J. Complexity, 21(4):593--608, 2005. MR2152724
Andrew J. Sommese, Jan Verschelde and Charles W. Wampler.  Introduction to numerical algebraic geometry.  In Solving polynomial equations, pages 301--335.  Springer, Berlin, 2005. MR2161992
Greg Reid, Jan Verschelde, Allan Wittkopf and Wenyuan Wu.  Symbolic-numeric completion of differential systems by homotopy continuation.  In ISSAC'05, pages 269--276 (electronic).  ACM, New York, 2005. MR2280557
Anton Leykin and Jan Verschelde.  Factoring solution sets of polynomial systems in parallel.  In Proceedings of the 7th workshop on high performance scientific and engineering computing (Hpsec-05), pages 173--180.  IEEE Computer Society, 2005.
Jan Verschelde.  Introduction to symbolic computation: a Maple/MATLAB course.  In Maple conference 2005. wilfried laurier university. july 17-21, 2005. waterloo ontario, canada., pages 500--509.  Maplesoft, 2005.
Andrew J. Sommese, Jan Verschelde and Charles W. Wampler.  Numerical factorization of multivariate complex polynomials.  Theoret. Comput. Sci., 315(2-3):651--669, 2004. MR2073069
Jan Verschelde and Yusong Wang.  Computing dynamic output feedback laws.  IEEE Trans. Automat. Control, 49(8):1393--1397, 2004. MR2078254
Andrew J. Sommese, Jan Verschelde and Charles W. Wampler.  Homotopies for intersecting solution components of polynomial systems.  SIAM J. Numer. Anal., 42(4):1552--1571 (electronic), 2004. MR2114290
Andrew J Sommese, Jan Verschelde and Charles W Wampler.  Advances in polynomial continuation for solving problems in kinematics..  ASME Journal of Mechanical Design, 126:262--268, 2004.
Jan Verschelde and Yusong Wang.  Computing feedback laws for linear systems with a parallel Pieri homotopy.  In Proceedings of the 2004 workshop on high performance scientific and engineering computing, pages 222--229.  IEEE Computer Society, 2004.
Anton Leykin and Jan Verschelde.  PHCmaple: a Maple interface to the numerical homotopy algori thms in PHCpack..  In Proceedings of the tenth international conference on application s of computer algebra (Aca\'2004), pages 139--147.  2004.
Andrew J. Sommese, Jan Verschelde and Charles W. Wampler.  Numerical irreducible decomposition using PHCpack.  In Algebra, geometry, and software systems, pages 109--129.  Springer, Berlin, 2003. MR2011756
Andrew J. Sommese, Jan Verschelde and Charles W. Wampler.  A method for tracking singular paths with application to the numerical irreducible decomposition.  In Algebraic geometry, pages 329--345.  de Gruyter, Berlin, 2002. MR1954072
Andrew J. Sommese, Jan Verschelde and Charles W. Wampler.  Symmetric functions applied to decomposing solution sets of polynomial systems.  SIAM J. Numer. Anal., 40(6):2026--2046 (electronic) (2003), 2002. MR1974173
Andrew J. Sommese, Jan Verschelde and Charles W. Wampler.  Numerical decomposition of the solution sets of polynomial systems into irreducible components.  SIAM J. Numer. Anal., 38(6):2022--2046 (electronic), 2001. MR1856241
A. J. Sommese, J. Verschelde and C. W. Wampler.  Using monodromy to decompose solution sets of polynomial systems into irreducible components.  In Applications of algebraic geometry to coding theory, physics and computation (Eilat, 2001), pages 297--315.  Kluwer Acad. Publ., Dordrecht, 2001. MR1866906
Andrew J. Sommese, Jan Verschelde and Charles W. Wampler.  Numerical irreducible decomposition using projections from points on the components.  In Symbolic computation: solving equations in algebra, geometry, and engineering (South Hadley, MA, 2000), pages 37--51.  Amer. Math. Soc., Providence, RI, 2001. MR1874270
Birkett Huber and Jan Verschelde.  Pieri homotopies for problems in enumerative geometry applied to pole placement in linear systems control.  SIAM J. Control Optim., 38(4):1265--1287 (electronic), 2000. MR1760069
Jan Verschelde.  Toric Newton method for polynomial homotopies.  J. Symbolic Comput., 29(4-5):777--793, 2000. MR1769666
Tangan Gao, T. Y. Li, Jan Verschelde and Mengnien Wu.  Balancing the lifting values to improve the numerical stability of polyhedral homotopy continuation methods.  Appl. Math. Comput., 114(2-3):233--247, 2000. MR1779225
Jan Verschelde.  Numerical evidence for a conjecture in real algebraic geometry.  Experiment. Math., 9(2):183--196, 2000. MR1780205
Andrew J. Sommese and Jan Verschelde.  Numerical homotopies to compute generic points on positive dimensional algebraic sets.  J. Complexity, 16(3):572--602, 2000. MR1787886
T. Michiels and J. Verschelde.  Enumerating regular mixed-cell configurations.  Discrete Comput. Geom., 21(4):569--579, 1999. MR1681890
Ioannis Z. Emiris and Jan Verschelde.  How to count efficiently all affine roots of a polynomial system.  Discrete Appl. Math., 93(1):21--32, 1999. MR1684911
Jan Verschelde.  Algorithm 795: PHCpack: a general-purpose solver for polynomial systems by homotopy continuation.  ACM Transactions on Mathematical Software, 25(2):251-276, 1999.
Birkett Huber and Jan Verschelde.  Polyhedral end games for polynomial continuation.  Numer. Algorithms, 18(1):91--108, 1998. MR1659862
J. Verschelde, K. Gatermann and R. Cools.  Mixed-volume computation by dynamic lifting applied to polynomial system solving.  Discrete Comput. Geom., 16(1):69--112, 1996. MR1397788
Jan Verschelde and Karin Gatermann.  Symmetric Newton polytopes for solving sparse polynomial systems.  Adv. in Appl. Math., 16(1):95--127, 1995. MR1317613
Jan Verschelde, Pierre Verlinden and Ronald Cools.  Homotopies exploiting Newton polytopes for solving sparse polynomial systems.  SIAM J. Numer. Anal., 31(3):915--930, 1994. MR1275120
Jan Verschelde and Ronald Cools.  Symmetric homotopy construction.  In Proceedings of the Fifth International Congress on Computational and Applied Mathematics (Leuven, 1992), volume 50 of, pages 575--592.  1994. MR1284290
Jan Verschelde and Ann Haegemans.  Homotopies for solving polynomial systems within a bounded domain.  Theoret. Comput. Sci., 133(1):165--185, 1994. MR1294431
Jan Verschelde and Ann Haegemans.  The $GBQ$-algorithm for constructing start systems of homotopies for polynomial systems.  SIAM J. Numer. Anal., 30(2):583--594, 1993. MR1211406
Jan Verschelde and Ronald Cools.  Symbolic homotopy construction.  Appl. Algebra Engrg. Comm. Comput., 4(3):169--183, 1993. MR1226323
Jan Verschelde and Ronald Cools.  Nonlinear reduction for solving deficient polynomial systems by continuation methods.  Numer. Math., 63(2):263--282, 1992. MR1182978
Jan Verschelde, Marc Beckers and Ann Haegemans.  A new start system for solving deficient polynomial systems using continuation.  Appl. Math. Comput., 44(3):225--239, 1991. MR1115067
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