Verschelde, Jan; Viswanathan, Kylash Locating the closest singularity in a polynomial homotopy. (English) Zbl 1507.14084 Boulier, François (ed.) et al., Computer algebra in scientific computing. 24th international workshop, CASC 2022, Gebze, Turkey, August 22–26, 2022. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 13366, 333-352 (2022). MSC: 14Q65 68W30 PDFBibTeX XMLCite \textit{J. Verschelde} and \textit{K. Viswanathan}, Lect. Notes Comput. Sci. 13366, 333--352 (2022; Zbl 1507.14084) Full Text: DOI arXiv
Leykin, Anton; Del Campo, Abraham Martín; Sottile, Frank; Vakil, Ravi; Verschelde, Jan Numerical Schubert calculus via the Littlewood-Richardson homotopy algorithm. (English) Zbl 1468.14093 Math. Comput. 90, No. 329, 1407-1433 (2021). Reviewer: Sonia Pérez Díaz (Madrid) MSC: 14N15 65H10 14Q65 PDFBibTeX XMLCite \textit{A. Leykin} et al., Math. Comput. 90, No. 329, 1407--1433 (2021; Zbl 1468.14093) Full Text: DOI arXiv
Telen, Simon; Van Barel, Marc; Verschelde, Jan Robust numerical tracking of one path of a polynomial homotopy on parallel shared memory computers. (English) Zbl 07635852 Boulier, François (ed.) et al., Computer algebra in scientific computing. 22nd international workshop, CASC 2020, Linz, Austria, September 14–18, 2020. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 12291, 563-582 (2020). MSC: 68W30 PDFBibTeX XMLCite \textit{S. Telen} et al., Lect. Notes Comput. Sci. 12291, 563--582 (2020; Zbl 07635852) Full Text: DOI arXiv
Telen, Simon; Van Barel, Marc; Verschelde, Jan A robust numerical path tracking algorithm for polynomial homotopy continuation. (English) Zbl 1457.65023 SIAM J. Sci. Comput. 42, No. 6, A3610-A3637 (2020). MSC: 65H20 65H04 65H10 41A21 PDFBibTeX XMLCite \textit{S. Telen} et al., SIAM J. Sci. Comput. 42, No. 6, A3610--A3637 (2020; Zbl 1457.65023) Full Text: DOI arXiv
Bliss, Nathan; Verschelde, Jan The method of Gauss-Newton to compute power series solutions of polynomial homotopies. (English) Zbl 1418.65068 Linear Algebra Appl. 542, 569-588 (2018). MSC: 65H10 PDFBibTeX XMLCite \textit{N. Bliss} and \textit{J. Verschelde}, Linear Algebra Appl. 542, 569--588 (2018; Zbl 1418.65068) Full Text: DOI arXiv
Verschelde, Jan A blackbox polynomial system solver on parallel shared memory computers. (English) Zbl 1453.65469 Gerdt, Vladimir P. (ed.) et al., Computer algebra in scientific computing. 20th international workshop, CASC 2018, Lille, France, September 17–21, 2018. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 11077, 361-375 (2018). MSC: 65Y10 13P05 26C99 68W30 PDFBibTeX XMLCite \textit{J. Verschelde}, Lect. Notes Comput. Sci. 11077, 361--375 (2018; Zbl 1453.65469) Full Text: DOI arXiv
Bliss, Nathan; Verschelde, Jan Computing all space curve solutions of polynomial systems by polyhedral methods. (English) Zbl 1453.13084 Gerdt, Vladimir P. (ed.) et al., Computer algebra in scientific computing. 18th international workshop, CASC 2016, Bucharest, Romania, September 19–23, 2016. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 9890, 73-86 (2016). MSC: 13P15 14M25 14T15 65H10 65H20 68W30 PDFBibTeX XMLCite \textit{N. Bliss} and \textit{J. Verschelde}, Lect. Notes Comput. Sci. 9890, 73--86 (2016; Zbl 1453.13084) Full Text: DOI arXiv
Verschelde, Jan; Yu, Xiangcheng Polynomial homotopy continuation on GPUs. (English) Zbl 1365.65149 ACM Commun. Comput. Algebra 49, No. 4, 130-133 (2015). MSC: 65H20 65Y10 65Y15 PDFBibTeX XMLCite \textit{J. Verschelde} and \textit{X. Yu}, ACM Commun. Comput. Algebra 49, No. 4, 130--133 (2015; Zbl 1365.65149) Full Text: DOI
Bliss, Nathan; Sommars, Jeff; Verschelde, Jan; Yu, Xiangcheng Solving polynomial systems in the cloud with polynomial homotopy continuation. (English) Zbl 1439.13078 Gerdt, Vladimir P. (ed.) et al., Computer algebra in scientific computing. 17th international workshop, CASC 2015, Aachen, Germany, September 14–18, 2015. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 9301, 87-100 (2015). MSC: 13P15 13-04 65H14 14Q65 68W30 65H10 PDFBibTeX XMLCite \textit{N. Bliss} et al., Lect. Notes Comput. Sci. 9301, 87--100 (2015; Zbl 1439.13078) Full Text: DOI arXiv
Verschelde, Jan Polynomial homotopy continuation with PHCpack. (English) Zbl 1308.68198 ACM Commun. Comput. Algebra 44, No. 4, 217-220 (2010). MSC: 68W30 65H20 PDFBibTeX XMLCite \textit{J. Verschelde}, ACM Commun. Comput. Algebra 44, No. 4, 217--220 (2010; Zbl 1308.68198) Full Text: DOI
Piret, Kathy; Verschelde, Jan Sweeping algebraic curves for singular solutions. (English) Zbl 1189.65101 J. Comput. Appl. Math. 234, No. 4, 1228-1237 (2010). MSC: 65H10 65H20 12Y05 26C10 30C15 PDFBibTeX XMLCite \textit{K. Piret} and \textit{J. Verschelde}, J. Comput. Appl. Math. 234, No. 4, 1228--1237 (2010; Zbl 1189.65101) Full Text: DOI arXiv
Guan, Yun; Verschelde, Jan PHClab: a MATLAB/Octave interface to PHCpack. (English) Zbl 1148.68578 Stillman, Michael E. (ed.) et al., Software for algebraic geometry. Papers of a workshop, Minneapolis, MN, USA, October 23–27, 2006. New York, NY: Springer (ISBN 978-0-387-78132-7/hbk). The IMA Volumes in Mathematics and its Applications 148, 15-32 (2008). MSC: 68W30 PDFBibTeX XMLCite \textit{Y. Guan} and \textit{J. Verschelde}, IMA Vol. Math. Appl. 148, 15--32 (2008; Zbl 1148.68578)
Sommese, Andrew J.; Verschelde, Jan; Wampler, Charles W. Solving polynomial systems equation by equation. (English) Zbl 1136.65052 Dickenstein, Alicia (ed.) et al., Algorithms in algebraic geometry. Based on the workshop, Minneapolis, MN, USA, September 18–22, 2006. New York, NY: Springer (ISBN 978-0-387-75154-2/hbk). The IMA Volumes in Mathematics and its Applications 146, 133-152 (2008). MSC: 65H10 65H20 13P05 14Q15 12Y05 30C15 PDFBibTeX XMLCite \textit{A. J. Sommese} et al., IMA Vol. Math. Appl. 146, 133--152 (2008; Zbl 1136.65052) Full Text: arXiv
Leykin, Anton; Verschelde, Jan; Zhao, Ailing Evaluation of Jacobian matrices for Newton’s method with deflation to approximate isolated singular solutions of polynomial systems. (English) Zbl 1117.65074 Wang, Dongming (ed.) et al., Symbolic-numeric computation. Invited and contributed presentations given at the international workshop (SNC 2005), Xi’an, China, July 19–21 (2005). Basel: Birkhäuser (ISBN 978-3-7643-7983-4/hbk). Trends in Mathematics, 269-278 (2007). MSC: 65H10 12Y05 26C10 68W30 14Q15 PDFBibTeX XMLCite \textit{A. Leykin} et al., in: Symbolic-numeric computation. Invited and contributed presentations given at the international workshop (SNC 2005), Xi'an, China, July 19--21 (2005). Basel: Birkhäuser. 269--278 (2007; Zbl 1117.65074)
Leykin, Anton; Verschelde, Jan Interfacing with the numerical homotopy algorithms in PHCpack. (English) Zbl 1230.65061 Iglesias, Andrés (ed.) et al., Mathematical software – ICMS 2006. Second international congress on mathematical software, Castro Urdiales, Spain, September 1–3, 2006. Proceedings. Berlin: Springer (ISBN 978-3-540-38084-9/pbk). Lecture Notes in Computer Science 4151, 354-360 (2006). MSC: 65H20 12Y05 65Y15 PDFBibTeX XMLCite \textit{A. Leykin} and \textit{J. Verschelde}, Lect. Notes Comput. Sci. 4151, 354--360 (2006; Zbl 1230.65061) Full Text: DOI
Leykin, Anton; Verschelde, Jan; Zhuang, Yan Parallel homotopy algorithms to solve polynomial systems. (English) Zbl 1230.65062 Iglesias, Andrés (ed.) et al., Mathematical software – ICMS 2006. Second international congress on mathematical software, Castro Urdiales, Spain, September 1–3, 2006. Proceedings. Berlin: Springer (ISBN 978-3-540-38084-9/pbk). Lecture Notes in Computer Science 4151, 225-234 (2006). MSC: 65H20 14Q99 65H10 65Y05 65Y15 PDFBibTeX XMLCite \textit{A. Leykin} et al., Lect. Notes Comput. Sci. 4151, 225--234 (2006; Zbl 1230.65062) Full Text: DOI
Leykin, Anton; Verschelde, Jan; Zhao, Ailing Newton’s method with deflation for isolated singularities of polynomial systems. (English) Zbl 1106.65046 Theor. Comput. Sci. 359, No. 1-3, 111-122 (2006). Reviewer: Sonia Pérez Díaz (Madrid) MSC: 65H10 68W30 12Y05 26C10 30C15 65H20 PDFBibTeX XMLCite \textit{A. Leykin} et al., Theor. Comput. Sci. 359, No. 1--3, 111--122 (2006; Zbl 1106.65046) Full Text: DOI arXiv
Reid, Greg; Verschelde, Jan; Wittkopf, Allan; Wu, Wenyuan Symbolic-numeric completion of differential systems by homotopy continuation. (English) Zbl 1361.13013 Kauers, Manuel (ed.), Proceedings of the 2005 international symposium on symbolic and algebraic computation, ISSAC’05, Beijing, China, July 24–27, 2005. New York, NY: ACM Press (ISBN 1-59593-095-7). 269-276 (2005). MSC: 13N15 13P99 68W30 PDFBibTeX XMLCite \textit{G. Reid} et al., in: Proceedings of the 2005 international symposium on symbolic and algebraic computation, ISSAC'05, Beijing, China, July 24--27, 2005. New York, NY: ACM Press. 269--276 (2005; Zbl 1361.13013) Full Text: DOI
Sommese, Andrew J.; Verschelde, Jan; Wampler, Charles W. An intrinsic homotopy for intersecting algebraic varieties. (English) Zbl 1108.13309 J. Complexity 21, No. 4, 593-608 (2005). MSC: 13P05 14Q99 65H10 65H20 68W30 PDFBibTeX XMLCite \textit{A. J. Sommese} et al., J. Complexity 21, No. 4, 593--608 (2005; Zbl 1108.13309) Full Text: DOI arXiv
Verschelde, Jan Numerical algebraic geometry and symbolic computation. (English) Zbl 1134.65349 Gutierrez, Jaime (ed.), ISSAC 2004. Proceedings of the 2004 international symposium on symbolic and algebraic computation, Santander, Spain, July 4–7, 2004. New York, NY: ACM Press (ISBN 1-58113-827-X/pbk). 3 (2004). MSC: 65H20 14Q99 PDFBibTeX XMLCite \textit{J. Verschelde}, in: Proceedings of the 2004 international symposium on symbolic and algebraic computation, ISSAC 2004, Santander, Spain, July 4--7, 2004. New York, NY: ACM Press. 3 (2004; Zbl 1134.65349) Full Text: DOI
Sommese, Andrew J.; Verschelde, Jan; Wampler, Charles W. Homotopies for intersecting solution components of polynomial systems. (English) Zbl 1108.13308 SIAM J. Numer. Anal. 42, No. 4, 1552-1571 (2004). MSC: 13P05 14Q99 65H10 68W30 PDFBibTeX XMLCite \textit{A. J. Sommese} et al., SIAM J. Numer. Anal. 42, No. 4, 1552--1571 (2004; Zbl 1108.13308) Full Text: DOI
Sommese, Andrew J.; Verschelde, Jan; Wampler, Charles W. Numerical factorization of multivariate complex polynomials. (English) Zbl 1147.13302 Theor. Comput. Sci. 315, No. 2-3, 651-669 (2004). MSC: 13P05 14Q99 65H10 68W30 PDFBibTeX XMLCite \textit{A. J. Sommese} et al., Theor. Comput. Sci. 315, No. 2--3, 651--669 (2004; Zbl 1147.13302) Full Text: DOI
Sommese, Andrew J.; Verschelde, Jan; Wampler, Charles W. Numerical irreducible decomposition. (English) Zbl 1027.65066 Joswig, Michael (ed.) et al., Algebra, geometry, and software systems. Berlin: Springer. 109-129 (2003). Reviewer: Corina Mohorianu (Iaşi) MSC: 65H10 65Y15 12Y05 13P05 14Q15 68N30 68W30 PDFBibTeX XMLCite \textit{A. J. Sommese} et al., in: Algebra, geometry, and software systems. Berlin: Springer. 109--129 (2003; Zbl 1027.65066)
Reid, Greg; Smith, Chris; Verschelde, Jan Geometric completion of differential systems using numeric symbolic continuation. (English) Zbl 1054.65090 SIGSAM Bull. 36, No. 2, 1-17 (2002). MSC: 65L80 34A09 65H20 68W30 PDFBibTeX XMLCite \textit{G. Reid} et al., SIGSAM Bull. 36, No. 2, 1--17 (2002; Zbl 1054.65090) Full Text: DOI
Sommese, Andrew J.; Verschelde, Jan; Wampler, Charles W. A method for tracking singular paths with application to the numerical irreducible decomposition. (English) Zbl 1014.65035 Beltrametti, Mauro C. (ed.) et al., Algebraic geometry. A volume in memory of Paolo Francia. Berlin: de Gruyter. 329-345 (2002). MSC: 65H10 12Y05 30C15 14Q15 26C10 65H20 68W30 PDFBibTeX XMLCite \textit{A. J. Sommese} et al., in: Algebraic geometry. A volume in memory of Paolo Francia. Berlin: de Gruyter. 329--345 (2002; Zbl 1014.65035)
Sommese, Andrew J.; Verschelde, Jan; Wampler, Charles W. Symmetric functions applied to decomposing solution sets of polynomial systems. (English) Zbl 1034.65034 SIAM J. Numer. Anal. 40, No. 6, 2026-2046 (2002). MSC: 65H10 13P05 12Y05 68W30 26C10 30C15 65H20 PDFBibTeX XMLCite \textit{A. J. Sommese} et al., SIAM J. Numer. Anal. 40, No. 6, 2026--2046 (2002; Zbl 1034.65034) Full Text: DOI
Sommese, A. J.; Verschelde, J.; Wampler, C. W. Using monodromy to decompose solution sets of polynomial systems into irreducible components. (English) Zbl 0990.65051 Ciliberto, Ciro (ed.) et al., Applications of algebraic geometry to coding theory, physics and computation. Proceedings of the NATO advanced research workshop, Eilat, Israel, February 25-March 1, 2001. Dordrecht: Kluwer Academic Publishers. NATO Sci. Ser. II, Math. Phys. Chem. 36, 297-315 (2001). MSC: 65H10 13P05 14Q99 68W30 PDFBibTeX XMLCite \textit{A. J. Sommese} et al., NATO Sci. Ser. II, Math. Phys. Chem. 36, 297--315 (2001; Zbl 0990.65051)
Sommese, Andrew J.; Verschelde, Jan; Wampler, Charles W. Numerical decomposition of the solution sets of polynomial systems into irreducible components. (English) Zbl 1002.65060 SIAM J. Numer. Anal. 38, No. 6, 2022-2046 (2001). Reviewer: René Lamour (Berlin) MSC: 65H10 65H20 68W30 12Y05 26C10 30C15 PDFBibTeX XMLCite \textit{A. J. Sommese} et al., SIAM J. Numer. Anal. 38, No. 6, 2022--2046 (2001; Zbl 1002.65060) Full Text: DOI
Verschelde, Jan Numerical evidence for a conjecture in real algebraic geometry. (English) Zbl 1054.14080 Exp. Math. 9, No. 2, 183-196 (2000). MSC: 14Q15 65H10 14P05 14M15 PDFBibTeX XMLCite \textit{J. Verschelde}, Exp. Math. 9, No. 2, 183--196 (2000; Zbl 1054.14080) Full Text: DOI Euclid EuDML
Gao, Tangan; Li, T. Y.; Verschelde, Jan; Wu, Mengnien Balancing the lifting values to improve the numerical stability of polyhedral homotopy continuation methods. (English) Zbl 1023.65048 Appl. Math. Comput. 114, No. 2-3, 233-247 (2000). MSC: 65H10 12Y05 26C10 30C15 62H20 PDFBibTeX XMLCite \textit{T. Gao} et al., Appl. Math. Comput. 114, No. 2--3, 233--247 (2000; Zbl 1023.65048) Full Text: DOI
Sommese, Andrew J.; Verschelde, Jan Numerical homotopies to compute generic points on positive dimensional algebraic sets. (English) Zbl 0982.65070 J. Complexity 16, No. 3, 572-602 (2000). Reviewer: Robert F.Lax (Baton Rouge) MSC: 65H10 14Q99 65H20 12Y05 30C15 PDFBibTeX XMLCite \textit{A. J. Sommese} and \textit{J. Verschelde}, J. Complexity 16, No. 3, 572--602 (2000; Zbl 0982.65070) Full Text: DOI arXiv
Huber, Birkett; Verschelde, Jan Pieri homotopies for problems in enumerative geometry applied to pole placement in linear systems control. (English) Zbl 0955.14038 SIAM J. Control Optimization 38, No. 4, 1265-1287 (2000). MSC: 14N10 93B55 65H10 68W30 93B27 14M15 PDFBibTeX XMLCite \textit{B. Huber} and \textit{J. Verschelde}, SIAM J. Control Optim. 38, No. 4, 1265--1287 (2000; Zbl 0955.14038) Full Text: DOI
Verschelde, Jan Toric Newton method for polynomial homotopies. (English) Zbl 0992.65048 J. Symb. Comput. 29, No. 4-5, 777-793 (2000). MSC: 65H10 12Y05 26C10 30C15 65H20 PDFBibTeX XMLCite \textit{J. Verschelde}, J. Symb. Comput. 29, No. 4--5, 777--793 (2000; Zbl 0992.65048) Full Text: DOI Link
Verschelde, Jan Algorithm 795: PHCpack: A general-purpose solver for polynomial systems by homotopy continuation. (English) Zbl 0961.65047 ACM Trans. Math. Softw. 25, No. 2, 251-276 (1999). MSC: 65H10 12Y05 26C10 30C15 65Y15 65Y20 PDFBibTeX XMLCite \textit{J. Verschelde}, ACM Trans. Math. Softw. 25, No. 2, 251--276 (1999; Zbl 0961.65047) Full Text: DOI
Huber, Birkett; Verschelde, Jan Polyhedral end games for polynomial continuation. (English) Zbl 0933.65057 Numer. Algorithms 18, No. 1, 91-108 (1998). Reviewer: E.L.Allgower (Fort Collins) MSC: 65H20 65H10 52A39 PDFBibTeX XMLCite \textit{B. Huber} and \textit{J. Verschelde}, Numer. Algorithms 18, No. 1, 91--108 (1998; Zbl 0933.65057) Full Text: DOI
Verschelde, J.; Gatermann, K.; Cools, R. Mixed-volume computation by dynamic lifting applied to polynomial system solving. (English) Zbl 0854.68111 Discrete Comput. Geom. 16, No. 1, 69-112 (1996). MSC: 68U05 PDFBibTeX XMLCite \textit{J. Verschelde} et al., Discrete Comput. Geom. 16, No. 1, 69--112 (1996; Zbl 0854.68111) Full Text: DOI
Verschelde, Jan; Gatermann, Karin Symmetric Newton polytopes for solving sparse polynomial systems. (English) Zbl 0832.65048 Adv. Appl. Math. 16, No. 1, 95-127 (1995). Reviewer: I.Coroian (Baia Mare) MSC: 65H10 65H20 12Y05 26C10 55P15 PDFBibTeX XMLCite \textit{J. Verschelde} and \textit{K. Gatermann}, Adv. Appl. Math. 16, No. 1, 95--127 (1995; Zbl 0832.65048) Full Text: DOI
Verschelde, Jan; Haegemans, Ann Homotopies for solving polynomial systems within a bounded domain. (English) Zbl 0811.65041 Theor. Comput. Sci. 133, No. 1, 165-185 (1994). Reviewer: E.L.Allgower (Fort Collins) MSC: 65H10 65H20 26C10 30C15 12Y05 PDFBibTeX XMLCite \textit{J. Verschelde} and \textit{A. Haegemans}, Theor. Comput. Sci. 133, No. 1, 165--185 (1994; Zbl 0811.65041) Full Text: DOI
Verschelde, Jan; Cools, Ronald Symmetric homotopy construction. (English) Zbl 0806.65055 J. Comput. Appl. Math. 50, No. 1-3, 575-592 (1994). Reviewer: E.L.Allgower (Fort Collins) MSC: 65H20 65H10 30C15 PDFBibTeX XMLCite \textit{J. Verschelde} and \textit{R. Cools}, J. Comput. Appl. Math. 50, No. 1--3, 575--592 (1994; Zbl 0806.65055) Full Text: DOI
Verschelde, Jan; Verlinden, Pierre; Cools, Ronald Homotopies exploiting Newton polytopes for solving sparse polynomial systems. (English) Zbl 0809.65048 SIAM J. Numer. Anal. 31, No. 3, 915-930 (1994). Reviewer: V.Berinde (Baia Mare) MSC: 65H10 65H20 PDFBibTeX XMLCite \textit{J. Verschelde} et al., SIAM J. Numer. Anal. 31, No. 3, 915--930 (1994; Zbl 0809.65048) Full Text: DOI
Verschelde, Jan; Cools, Ronald Symbolic homotopy construction. (English) Zbl 0804.65058 Appl. Algebra Eng. Commun. Comput. 4, No. 3, 169-183 (1993). Reviewer: E.L.Allgower (Fort Collins) MSC: 65H20 65H10 26C10 12Y05 PDFBibTeX XMLCite \textit{J. Verschelde} and \textit{R. Cools}, Appl. Algebra Eng. Commun. Comput. 4, No. 3, 169--183 (1993; Zbl 0804.65058) Full Text: DOI
Verschelde, Jan; Haegemans, Ann The GBQ-algorithm for constructing start systems of homotopies for polynomial systems. (English) Zbl 0806.65054 SIAM J. Numer. Anal. 30, No. 2, 583-594 (1993). Reviewer: Deng Naiyang (Beijing) MSC: 65H20 65H10 PDFBibTeX XMLCite \textit{J. Verschelde} and \textit{A. Haegemans}, SIAM J. Numer. Anal. 30, No. 2, 583--594 (1993; Zbl 0806.65054) Full Text: DOI
Verschelde, Jan; Cools, Ronald Nonlinear reduction for solving deficient polynomial systems by continuation methods. (English) Zbl 0756.65080 Numer. Math. 63, No. 2, 263-282 (1992). Reviewer: J.Verschelde MSC: 65H10 65H20 68W30 PDFBibTeX XMLCite \textit{J. Verschelde} and \textit{R. Cools}, Numer. Math. 63, No. 2, 263--282 (1992; Zbl 0756.65080) Full Text: DOI EuDML
Verschelde, Jan; Beckers, Marc; Haegemans, Ann A new start system for solving deficient polynomial systems using continuation. (English) Zbl 0743.65051 Appl. Math. Comput. 44, No. 3, 225-239 (1991). Reviewer: T.Y.Li MSC: 65H20 65H10 26C10 PDFBibTeX XMLCite \textit{J. Verschelde} et al., Appl. Math. Comput. 44, No. 3, 225--239 (1991; Zbl 0743.65051) Full Text: DOI