- Nathan Bliss and Jan Verschelde:
**The Method of Gauss-Newton to Compute Power Series Solutions of Polynomial Homotopies.**The abstract and revised manuscript.*Linear Algebra and Its Applications*542:569-588, 2018. - Anders Jensen, Jeff Sommars, and Jan Verschelde:
**Computing Tropical Prevarieties in Parallel.**The abstract and revised manuscript. In PASCO 2017: Proceedings of the International Workshop on Parallel Symbolic Computation, Kaiserslautern, Germany, July 23-24, 2017, edited by Hans-Wolfgang Loidl, Michael Monagan, Jean-Charles Faugere. - Jeff Sommars and Jan Verschelde:
**Pruning Algorithms for Pretropisms of Newton Polytopes.**The abstract and manuscript. In the Proceedings of the 18th International Workshop on Computer Algebra in Scientific Computing (CASC 2016), edited by V.P. Gerdt, W. Koepf, W.M. Seiler, and E.V. Vorozhtsov, volume 9890 of Lecture Notes in Computer Science, pages 489-503, Springer-Verlag, 2016. - Nathan Bliss and Jan Verschelde:
**Computing All Space Curve Solutions of Polynomial Systems by Polyhedral Methods.**The abstract and manuscript. In the Proceedings of the 18th International Workshop on Computer Algebra in Scientific Computing (CASC 2016), edited by V.P. Gerdt, W. Koepf, W.M. Seiler, and E.V. Vorozhtsov, volume 9890 of Lecture Notes in Computer Science, pages 73-86, Springer-Verlag, 2016. - Jeff Sommars and Jan Verschelde:
**Computing Pretropisms for the Cyclic n-Roots Problem.**In EuroCG 2016, 32nd European Workshop on Computational Geometry, EuroCG 2016, Lugano, Switzerland, March 30--April 1, 2016, pages 235-238. The abstract and manuscript. - Jan Verschelde and Xiangcheng Yu:
**Polynomial Homotopy Continuation on GPUs.**The abstract and manuscript.*ACM Communications in Computer Algebra*, volume 49, issue 4, pages 130-133, 2015. - Nathan Bliss, Jeff Sommars, Jan Verschelde,
and Xiangcheng Yu:
**Solving Polynomial Systems in the Cloud with Polynomial Homotopy Continuation.**The abstract and manuscript. In the Proceedings of the 17th International Workshop on Computer Algebra in Scientific Computing (CASC 2015), edited by V.P. Gerdt, W. Koepf, W.M. Seiler, and E.V. Vorozhtsov, volume 9301 of Lecture Notes in Computer Science, pages 87-100, Springer-Verlag, 2015. - Jan Verschelde and Xiangcheng Yu:
**Tracking Many Solution Paths of a Polynomial Homotopy on a Graphics Processing Unit in Double Double and Quad Double Arithmetic.**The abstract and manuscript. In the Proceedings of the 17th IEEE International Conference on High Performance Computing and Communications (HPCC 2015), pages 371-376, IEEE Computer Society, 2015. - Jan Verschelde and Xiangcheng Yu:
**Accelerating Polynomial Homotopy Continuation on a Graphics Processing Unit with Double Double and Quad Double Arithmetic.**The abstract and manuscript. In PASCO 2015, Proceedings of the 7th International Workshop on Parallel Symbolic Computation, edited by Jean-Guillaume Dumas and Erich L. Kaltofen, pages 109-118, ACM 2015. - Jan Verschelde and Xiangcheng Yu:
**GPU acceleration of Newton's method for large systems of polynomial equations in double double and quad double arithmetic.**The abstract and revised manuscript. In the Proceedings of the 16th IEEE International Conference on High Performance Computing and Communication (HPCC 2014), pages 161-164, IEEE Computer Society, 2014. - Jan Verschelde:
**modernizing PHCpack through phcpy.**The abstract and manuscript. In Proceedings of the 6th European Conference on Python in Science (EuroSciPy 2013), edited by Pierre de Buyl and Nelle Varoquaux, pages 71-76, 2014. - Elizabeth
Gross, Sonja
Petrovic, and Jan Verschelde:
**Interfacing with PHCpack.**The revised abstract and revised manuscript; the Macaulay2 package PHCpack.m2 and its documentation PHCpackDoc.m2.*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.**The abstract and (revised) manuscript. In Computer Algebra in Scientific Computing, 15th International Workshop, CASC 2013, Berlin, Germany, edited by Vladimir P. Gerdt, Wolfram Koepf, Ernst W. Mayr, and Evgenii V. Vorozhtsov. Lecture Notes in Computer Science, Volume 8136, 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.**The abstract and revised manuscript. In the Proceedings of the 2013 IEEE 27th International Parallel and Distributed Processing Symposium Workshops (PDSEC 2013). 20-24 May 2013, Boston, Massachusetts. IEEE Computer Society, 2013, pages 1373-1380. - Danko Adrovic and Jan Verschelde:
**Computing Puiseux Series for Algebraic Surfaces.**The abstract and revised manuscript. In the Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation (ISSAC 2012), Grenoble, France, July 22-25, 2012. Edited by Joris van der Hoeven and Mark van Hoeij, pages 20-27, ACM 2012. - Jan Verschelde and
Genady Yoffe:
**Evaluating polynomials in several variables and their derivatives on a GPU computing processor.**The abstract and manuscript. In the Proceedings of the 2012 IEEE 26th International Parallel and Distributed Processing Symposium Workshops (PDSEC 2012). 21-25 May 2012, Shanghai China. IEEE Computer Society, 2012. Pages 1391-1399. - Yun Guan and Jan Verschelde:
**Sampling Algebraic Sets in Local Intrinsic Coordinates.**The abstract and manuscript.*Computers and Mathematics with Applications*62(10): 3706-2721, 2011. -
Danko Adrovic
and Jan Verschelde:
**Tropical Algebraic Geometry in Maple: A preprocessing algorithm for finding common factors to multivariate polynomials with approximate coefficients.**The abstract and revised manuscript.*Journal of Symbolic Computation*46(7):755-772, 2011. Special Issue in Honour of Keith Geddes on his 60th Birthday, edited by Mark W. Giesbrecht and Stephen M. Watt. - Jan Verschelde:
**Polynomial Homotopy Continuation with PHCpack.**The abstract and manuscript.*ACM Communications in Computer Algebra*44(4):217-220, 2010. - Frank
Sottile,
Ravi Vakil
and Jan Verschelde:
**Solving Schubert Problems with Littlewood-Richardson Homotopies.**The abstract and manuscript. In ISSAC 2010, Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation, edited by Stephen M. Watt, pages 179-186, ACM 2010. - Jan Verschelde and
Genady Yoffe:
**Polynomial Homotopies on Multicore Workstations.**The abstract and manuscript. In PASCO 2010, Proceedings of the 2010 International Workshop on Parallel Symbolic Computation, edited by Marc Moreno Maza and Jean-Louis Roch, pages 131-140, ACM 2010. - Kathy Piret and Jan Verschelde:
**Sweeping Algebraic Curves for Singular Solutions**. The abstract and revised manuscript,*Journal of Computational and Applied Mathematics*234(4): 1228-1237, 2010. - Jan Verschelde:
**Polyhedral Methods in Numerical Algebraic Geometry**. The abstract and (revised) manuscript. In*Interactions of Classical and Numerical Algebraic Geometry*, edited by Dan Bates, GianMario Besana, Sandra Di Rocco, and Charles Wampler, Contemporary Mathematics 496, pages 243-263, AMS 2009. -
Anton Leykin and Jan Verschelde:
**Decomposing Solution Sets of Polynomial Systems: A New Parallel Monodromy Breakup Algorithm.**The Abstract, revised manuscript in pdf format.*The International Journal of Computational Science and Engineering*4(2):94-101, 2009. - Yun Guan and Jan Verschelde:
**Parallel Implementation of a Subsystem-by-Subsystem Solver**. The abstract and manuscript. In the proceedings of the 22th High Performance Computing Symposium, Quebec City, 9-11 June 2008. Pages 117-123. IEEE Computer Society, 2008. - Yun Guan and Jan Verschelde:
**PHClab: A MATLAB/Octave interface to PHCpack**. The abstract, the poster, and paper . In IMA Volume 148: Software for Algebraic Geometry, edited by Michael E. Stillman, Nobuki Takayama, and Jan Verschelde. Pages 15-32, Springer-Verlag, 2008. -
Andrew J. Sommese,
Jan Verschelde, and
Charles W. Wampler:
**Solving Polynomial Systems Equation by Equation**. The Abstract, revised manuscript in pdf format. In IMA Volume 146: Algorithms in Algebraic Geometry, edited by Alicia Dickenstein, Frank-Olaf Schreyer, and Andrew J. Sommese. Pages 133-152, Springer-Verlag, 2008. -
Anton Leykin,
Jan Verschelde, and Ailing Zhao:
**Higher-Order Deflation for Polynomial Systems with Isolated Singular Solutions.**The Abstract and revised manuscript in pdf format. In IMA Volume 146: Algorithms in Algebraic Geometry, edited by Alicia Dickenstein, Frank-Olaf Schreyer, and Andrew J. Sommese. Pages 79-97, Springer-Verlag, 2008. -
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.**The Abstract, revised manuscript in gzipped ps, and in pdf format. In*Symbolic-Numeric Computation*, edited by Dongming Wang and Lihong Zhi. Pages 269-278. Trends in Mathematics. Birkhauser, 2007. -
Anton Leykin
and Jan Verschelde:
**Interfacing with the Numerical Homotopy Algorithms in PHCpack.**The Abstract, manuscript in gzipped ps, and in pdf format. Proceedings of ICMS 2006, LNCS 4151, edited by Andrew Iglesias and Nobuki Takayama. Pages 354-360, Springer-Verlag, 2006. -
Anton Leykin,
Jan Verschelde, and Yan Zhuang:
**Parallel Homotopy Algorithms to Solve Polynomial Systems.**The Abstract, revised manuscript in gzipped ps, and in pdf format. Proceedings of ICMS 2006, LNCS 4151, edited by Andrew Iglesias and Nobuki Takayama. Pages 225-234, Springer-Verlag, 2006. - Jan Verschelde and Yan Zhuang:
**Parallel Implementation of the Polyhedral Homotopy Method.**The Abstract, revised manuscript in gzipped ps, and in pdf format. Proceedings of the 2006 International Conference on Parallel Processing Workshops. 14-18 August 2006. Columbus, Ohio. High Performance Scientific and Engineering Computing. Edited by Timothy Mark Pinkston and Fusun Ozguner. Pages 481-488, IEEE Computer Society, 2006. poster presented at the IMA Software for Algebraic Geometry workshop, 23-27 October 2006. -
Anton Leykin,
Jan Verschelde, and Ailing Zhao:
**Newton's method with deflation for isolated singularities of polynomial systems.**The Abstract, revised manuscript in pdf format.*Theoretical Computer Science*359(1-3): 111-122, 2006. -
Greg Reid, Jan Verschelde,
Allan Wittkopf, and Wenyuan Wu:
**Symbolic-Numeric Completion of Differential Systems by Homotopy Continuation.**The Abstract, (revised) manuscript in gzipped ps, and in pdf format. Proceedings of the 2005 International Symposium on Symbolic and Algebraic Computation (ISSAC'05), July 24-27 2005, Beijing, China. Edited by Manuel Kauers, pages 269-276, ACM 2005. -
Jan Verschelde:
**Introduction to Symbolic Computation: a Maple/MATLAB Course**. The Abstract and manuscript in gzipped ps and in pdf format. Maple Conference 2005. Wilfrid Laurier University. July 17-21, 2005. Waterloo Ontario, Canada. Book of Proceedings. Edited by Ilias Kotsireas. Pages 500-509, Maplesoft, 2005. -
Andrew J. Sommese,
Jan Verschelde, and
Charles W. Wampler:
**An intrinsic homotopy for intersecting algebraic varieties**. The Abstract and manuscript (revised) in gzipped ps and in pdf format.*Journal of Complexity*21(4): 593-608, 2005. -
Anton Leykin
and Jan Verschelde:
**Factoring Solution Sets of Polynomial Systems in Parallel.**The Abstract, manuscript in gzipped ps, and in pdf format. Proceedings of the 2005 International Conference on Parallel Processing Workshops. 14-17 June 2005. Oslo, Norway. High Performance Scientific and Engineering Computing. Edited by Tor Skeie and Chu-Sing Yang. Pages 173-180, IEEE Computer Society, 2005. -
Andrew J. Sommese,
Jan Verschelde, and
Charles W. Wampler:
**Introduction to Numerical Algebraic Geometry.**The Abstract and manuscript in pdf format. In A. Dickenstein and I.Z. Emiris (Eds.),*Solving Polynomial Equations: Foundations, Algorithms, and Applications.*Volume 14 of*Algorithms and Computation in Mathematics*, Springer-Verlag, pages 339-392, 2005. -
Andrew J. Sommese, Jan Verschelde, and
Charles W. Wampler:
**Homotopies for intersecting solution components of polynomial systems.**The Abstract and manuscript in pdf format.*SIAM J. Numerical Anal.*42(4):1552-1571, 2004. - Jan Verschelde and Yusong Wang:
**Computing Dynamic Output Feedback Laws.**The Abstract and the revised manuscript in pdf format. Data consists of input and output.*IEEE Transactions on Automatic Control*49(8):1393-1397, 2004. - Jan Verschelde and Yusong Wang:
**Computing Feedback Laws for Linear Systems with a Parallel Pieri Homotopy**. The Abstract and manuscript in pdf format. Proceedings of the 2004 International Conference on Parallel Processing Workshops. 15-18 August 2004. Montreal, Quebec, Canada. High Performance Scientific and Engineering Computing. Edited by Yuanyuan Yang. Pages 222-229, IEEE Computer Society, 2004. -
Anton Leykin
and Jan Verschelde:
*PHCmaple*: A Maple Interface to the Numerical Homotopy Algorithms in PHCpack.*Proceedings of the Tenth International Conference on Applications of Computer Algebra*(ACA'2004), edited by Quoc-Nam Tran, pages 139-147, 2004. -
Andrew J. Sommese, Jan Verschelde, and
Charles W. Wampler:
**Advances in Polynomial Continuation for Solving Problems in Kinematics.**The Abstract and gzipped postscript file,*ASME Journal of Mechanical Design*126(2):262-268, 2004. This is the revised version of what earlier appeared as Paper DETC2002/MECH-34254, Proc. ASME Design Engineering Technical Conf. (CDROM), Montreal, Quebec, Sept. 29-Oct. 2, 2002. -
Andrew J. Sommese, Jan Verschelde, and
Charles W. Wampler:
**Numerical Factorization of Multivariate Complex Polynomials.**The Abstract and revised gzipped postscript file, manuscript in pdf format.*Theoretical Computer Science*315(2-3): 651-669, 2004. Special Issue on Algebraic and Numerical Algorithms edited by I.Z. Emiris, B. Mourrain, and V.Y. Pan. -
Andrew J. Sommese, Jan Verschelde, and
Charles W. Wampler:
**Numerical Irreducible Decomposition using PHCpack.**The Abstract and gzipped postscript file, manuscript in pdf format. In*Algebra, Geometry and Software Systems*, edited by M. Joswig and N. Takayama, pages 109-130, Springer-Verlag 2003. -
Andrew J. Sommese,
Jan Verschelde, and
Charles W. Wampler:
**Symmetric Functions Applied to Decomposing Solution Sets of Polynomial Systems.**The Abstract and revised gzipped postscript file , manuscript in pdf format.*SIAM J. Numer. Anal.*40(6):2026-2046, 2002. -
Andrew J. Sommese, Jan Verschelde, and
Charles W. Wampler:
**A Method for Tracking Singular Paths with Application to the Numerical Irreducible Decomposition.**The Abstract and revised gzipped postscript file, manuscript in pdf format. In "Algebraic Geometry, a Volume in Memory of Paolo Francia" (ed. by M.C. Beltrametti, F. Catanese, C. Ciliberto, A. Lanteri, C. Pedrini), pages 329-345, W. de Gruyter, 2002. - Jan Verschelde and Yusong Wang:
**Numerical Homotopy Algorithms for Satellite Trajectory Control by Pole Placement.**The Abstract and Revised gzipped postscript file, manuscript in pdf format. Proceedings of MTNS 2002, Mathematical Theory of Networks and Systems (CDROM), Notre Dame, August 12-16, 2002. -
Greg Reid,
Chris Smith, and Jan Verschelde:
**Geometric Completion of Differential Systems using Numeric-Symbolic Continuation.**The Abstract and revised gzipped postscript file, and manuscript in pdf format.*SIGSAM Bulletin*36(2):1-17, 2002. -
Andrew J. Sommese, Jan Verschelde, and
Charles W. Wampler:
**Numerical Irreducible Decomposition using Projections from Points on the Components.**The Abstract and gzipped postscript file. In*Symbolic Computation: Solving Equations in Algebra, Geometry, and Engineering*, edited by E.L. Green, S. Hosten, R. Laubenbacher, and V.A. Powers.*Contemporary Mathematics*, volume 286, pages 37-51, AMS 2001. -
Andrew J. Sommese, Jan Verschelde, and
Charles W. Wampler:
**Using Monodromy to Decompose Solution Sets of Polynomial Systems into Irreducible Components.**The Abstract , the gzipped postscript file, and pdf file. In*Application of Algebraic Geometry to Coding Theory, Physics, and Computation*, edited by C. Ciliberto, F. Hirzebruch, R. Miranda, and M. Teicher. Proceedings of a NATO Conference, February 25 - March 1, 2001, Eilat, Israel. Pages 297-315, Kluwer Academic Publishers. -
Andrew J. Sommese, Jan Verschelde, and
Charles W. Wampler:
**Numerical Decomposition of the Solution Sets of Polynomial Systems into Irreducible Components.**The Abstract and gzipped postscript file of revised version.*SIAM J. Numer. Anal.*38(6):2022-2046, 2001. -
Andrew J. Sommese and Jan Verschelde:
**Numerical Homotopies to compute Generic Points on Positive Dimensional Algebraic Sets.**The Abstract and gzipped postscript file, Revised version.*Journal of Complexity*16(3):572-602, 2000. - Tangan Gao,
T.Y. Li ,
Jan Verschelde, and Mengnien Wu:
**Balancing the lifting values to improve the numerical stability of polyhedral homotopy continuation methods.**Abstract and (gzipped .ps file, revised version)*Appl. Math. Comput.*114: 233-247, 2000. - Jan Verschelde:
**Numerical Evidence for a Conjecture in Real Algebraic Geometry.**Abstract and (gzipped .ps file, revised version)*Experimental Mathematics*9(2): 183-196, 2000. - Jan Verschelde:
**Toric Newton Method for Polynomial Homotopies**The Abstract and (gzipped .ps file: revised version).*J. Symb. Comput.*29(4 and 5): 777-793, 2000. - Birkett Huber and Jan Verschelde:
**Pieri Homotopies for Problems in Enumerative Geometry applied to Pole Placement in Linear Systems Control.**The Abstract and gzipped postscript file, revised version.*SIAM J. Control Optim.*38(4): 1265-1287, 2000. - 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. Abstract and paper; see also html version of the paper. -
Ioannis Z. Emiris and Jan Verschelde:
**How to count efficiently all affine roots of a polynomial system**.*Discrete Applied Mathematics*93(1): 21-32, 1999. Abstract and (gzipped .ps file: revised version). - Tom Michiels and Jan Verschelde:
**Enumerating Regular Mixed-Cell Configurations**. Report TW 258, Dept. of Computer Science, K.U.Leuven, 1997. Abstract and (gzipped .ps file)*Discrete Comput. Geom.*21(4): 569-579, 1999. (gzipped .ps file: revised and shortened version). - Birkett Huber and Jan Verschelde:
**Polyhedral End Games for Polynomial Continuation**.*Numerical Algorithms*18(1): 91-108, 1998. Abstract and (gzipped .ps file: revised version) - Jan Verschelde and Ronald Cools:
**Polynomial Homotopy Continuation, A Portable Ada Software Package**.*The Ada-Belgium Newsletter*, 4:59-83, 1996. Proceedings of the 1996 Ada-Belgium Seminar, 22 November 1996, Eurocontrol, Brussels, Belgium. Abstract and (.html file) - Jan Verschelde, Karin Gatermann, and Ronald Cools:
**Mixed-Volume Computation by Dynamic Lifting applied to Polynomial System Solving.***Discrete Comput. Geom.*16(1): 69-112, 1996. Abstract - Jan Verschelde and Karin Gatermann:
**Symmetric Newton Polytopes for Solving Sparse Polynomial Systems.***Adv. Appl. Math.*16(1): 95-127, 1995. Abstract - Jan Verschelde:
**PHC and MVC: two programs for solving polynomial systems by homotopy continuation**.*Proceedings of the POSSO Workshop on Software*pages 165-176. Edited by J.-C. Faugere, J. Marchand, R. Rioboo, Paris 1-4 March 1995. Abstract - Jan Verschelde and Ann Haegemans:
**Homotopies for Solving Polynomial Systems within a Bounded Domain.***Theoretical Comp. Sci. A.*133(3): 165-185, 1994. Abstract and manuscript in pdf format. - 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. Abstract - Jan Verschelde and Ronald Cools:
**Symmetric Homotopy Construction.***J. Comput. Appl. Math.*50:572-592, 1994. Abstract - Jan Verschelde and Ronald Cools:
**Symbolic Homotopy Construction.***Applicable Algebra in Engineering, Communication and Computing*4(3):169-183, 1993. Abstract and manuscript in pdf format. - Jan Verschelde and Ronald Cools:
**An Ada Workbench for Homotopy Continuation for Solving Polynomial Systems.***The Ada-Belgium Newsletter*2(1):23-40, 1993. Abstract - 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. Abstract - Jan Verschelde and Ronald Cools:
**Nonlinear Reduction for Solving Deficient Polynomial Systems by Continuation Methods.***Numer. Math.*63(2):263-282, 1992. Abstract - 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. Abstract