McCoy, Timothy M.; Peterson, Chris; Sommese, Andrew J. Numerical irreducible decomposition over a number field. (English) Zbl 1408.14194 J. Algebra Appl. 17, No. 10, Article ID 1850195, 12 p. (2018). Reviewer: Sonia Pérez Díaz (Madrid) MSC: 14Q99 65H20 65H10 68W30 26C10 PDFBibTeX XMLCite \textit{T. M. McCoy} et al., J. Algebra Appl. 17, No. 10, Article ID 1850195, 12 p. (2018; Zbl 1408.14194) Full Text: DOI
Bates, Daniel J.; Brake, Dani A.; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W. Homotopies for connected components of algebraic sets with application to computing critical sets. (English) Zbl 1497.14121 Blömer, Johannes (ed.) et al., Mathematical aspects of computer and information sciences. 7th international conference, MACIS 2017, Vienna, Austria, November 15–17, 2017. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 10693, 107-120 (2017). MSC: 14Q30 14F45 PDFBibTeX XMLCite \textit{D. J. Bates} et al., Lect. Notes Comput. Sci. 10693, 107--120 (2017; Zbl 1497.14121) Full Text: DOI
Brake, Daniel A.; Bates, Daniel J.; Hao, Wenrui; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W. Algorithm 976: Bertini_real: numerical decomposition of real algebraic curves and surfaces. (English) Zbl 1484.14109 ACM Trans. Math. Softw. 44, No. 1, Article No. 10, 30 p. (2017). MSC: 14Q20 68W30 03C10 PDFBibTeX XMLCite \textit{D. A. Brake} et al., ACM Trans. Math. Softw. 44, No. 1, Article No. 10, 30 p. (2017; Zbl 1484.14109) Full Text: DOI
Hauenstein, Jonathan D. (ed.); Sommese, Andrew J. (ed.) Foreword. What is numerical algebraic geometry? (English) Zbl 1360.00098 J. Symb. Comput. 79, Part 3, 499-507 (2017). MSC: 00B15 14-06 65-06 14Q99 65H10 68W30 PDFBibTeX XMLCite \textit{J. D. Hauenstein} (ed.) and \textit{A. J. Sommese} (ed.), J. Symb. Comput. 79, Part 3, 499--507 (2017; Zbl 1360.00098) Full Text: DOI
Bates, Daniel J.; Decker, Wolfram; Hauenstein, Jonathan D.; Peterson, Chris; Pfister, Gerhard; Schreyer, Frank-Olaf; Sommese, Andrew J.; Wampler, Charles W. Comparison of probabilistic algorithms for analyzing the components of an affine algebraic variety. (English) Zbl 1410.65205 Appl. Math. Comput. 231, 619-633 (2014). MSC: 65H20 14Q15 68W30 PDFBibTeX XMLCite \textit{D. J. Bates} et al., Appl. Math. Comput. 231, 619--633 (2014; Zbl 1410.65205) Full Text: DOI
Bates, Daniel J.; Brake, Daniel A.; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W. On computing a cell decomposition of a real surface containing infinitely many singularities. (English) Zbl 1437.14061 Hong, Hoon (ed.) et al., Mathematical software – ICMS 2014. 4th international congress, Seoul, South Korea, August 5–9, 2014. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 8592, 246-252 (2014). MSC: 14Q65 14Q30 14-04 PDFBibTeX XMLCite \textit{D. J. Bates} et al., Lect. Notes Comput. Sci. 8592, 246--252 (2014; Zbl 1437.14061) Full Text: DOI
Brake, Daniel A.; Bates, Daniel J.; Hao, Wenrui; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W. Bertini_real: software for one- and two-dimensional real algebraic sets. (English) Zbl 1437.14005 Hong, Hoon (ed.) et al., Mathematical software – ICMS 2014. 4th international congress, Seoul, South Korea, August 5–9, 2014. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 8592, 175-182 (2014). MSC: 14-04 14P05 14Q65 68W30 PDFBibTeX XMLCite \textit{D. A. Brake} et al., Lect. Notes Comput. Sci. 8592, 175--182 (2014; Zbl 1437.14005) Full Text: DOI
Hao, Wenrui; Hauenstein, Jonathan D.; Hu, Bei; Sommese, Andrew J. A bootstrapping approach for computing multiple solutions of differential equations. (English) Zbl 1294.65085 J. Comput. Appl. Math. 258, 181-190 (2014). MSC: 65L80 34A09 65L10 14Q99 PDFBibTeX XMLCite \textit{W. Hao} et al., J. Comput. Appl. Math. 258, 181--190 (2014; Zbl 1294.65085) Full Text: DOI
Hao, Wenrui; Hauenstein, Jonathan D.; Shu, Chi-Wang; Sommese, Andrew J.; Xu, Zhiliang; Zhang, Yong-Tao A homotopy method based on WENO schemes for solving steady state problems of hyperbolic conservation laws. (English) Zbl 1349.65558 J. Comput. Phys. 250, 332-346 (2013). MSC: 65N06 35L65 35Q35 PDFBibTeX XMLCite \textit{W. Hao} et al., J. Comput. Phys. 250, 332--346 (2013; Zbl 1349.65558) Full Text: DOI
Bates, Daniel J.; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W. Numerically solving polynomial systems with Bertini. (English) Zbl 1295.65057 Software - Environments - Tools 25. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM) (ISBN 978-1-611972-69-6/pbk). xx, 352 p. (2013). Reviewer: Guillermo Matera (Buenos Aires) MSC: 65-02 12Y05 14Q15 65H04 65H10 65H20 65Y15 68W30 PDFBibTeX XMLCite \textit{D. J. Bates} et al., Numerically solving polynomial systems with Bertini. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM) (2013; Zbl 1295.65057)
Hao, Wenrui; Hu, Bei; Sommese, Andrew J. Cell cycle control and bifurcation for a free boundary problem modeling tissue growth. (English) Zbl 1271.92012 J. Sci. Comput. 56, No. 2, 350-365 (2013). MSC: 92C37 35R35 35Q92 92-08 PDFBibTeX XMLCite \textit{W. Hao} et al., J. Sci. Comput. 56, No. 2, 350--365 (2013; Zbl 1271.92012) Full Text: DOI
Besana, Gian Mario; Di Rocco, Sandra; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W. Cell decomposition of almost smooth real algebraic surfaces. (English) Zbl 1271.65031 Numer. Algorithms 63, No. 4, 645-678 (2013). MSC: 65D17 14Q10 65H20 PDFBibTeX XMLCite \textit{G. M. Besana} et al., Numer. Algorithms 63, No. 4, 645--678 (2013; Zbl 1271.65031) Full Text: DOI
Bates, Daniel J.; Hauenstein, Jonathan D.; McCoy, Timothy M.; Peterson, Chris; Sommese, Andrew J. Recovering exact results from inexact numerical data in algebraic geometry. (English) Zbl 1284.14084 Exp. Math. 22, No. 1, 38-50 (2013). Reviewer: Carlos D’Andrea (Barcelona) MSC: 14Q99 65H10 68W30 13P99 PDFBibTeX XMLCite \textit{D. J. Bates} et al., Exp. Math. 22, No. 1, 38--50 (2013; Zbl 1284.14084) Full Text: DOI
Hao, Wenrui; Hauenstein, Jonathan D.; Hu, Bei; McCoy, Timothy; Sommese, Andrew J. Computing steady-state solutions for a free boundary problem modeling tumor growth by Stokes equation. (English) Zbl 1303.92044 J. Comput. Appl. Math. 237, 326-334 (2013). MSC: 92C50 PDFBibTeX XMLCite \textit{W. Hao} et al., J. Comput. Appl. Math. 237, 326--334 (2013; Zbl 1303.92044) Full Text: DOI
Hao, Wenrui; Hauenstein, Jonathan D.; Hu, Bei; Liu, Yuan; Sommese, Andrew J.; Zhang, Yong-Tao Continuation along bifurcation branches for a tumor model with a necrotic core. (English) Zbl 1328.92032 J. Sci. Comput. 53, No. 2, 395-413 (2012). MSC: 92C50 65H20 65M06 PDFBibTeX XMLCite \textit{W. Hao} et al., J. Sci. Comput. 53, No. 2, 395--413 (2012; Zbl 1328.92032) Full Text: DOI
Bates, Daniel J.; Hauenstein, Jonathan D.; Sommese, Andrew J. A parallel endgame. (English) Zbl 1238.14007 Gurvits, Leonid (ed.) et al., Randomization, relaxation, and complexity in polynomial equation solving. Banff International Research Station workshop on randomization, relaxation, and complexity, Banff, Ontario, Canada, February 28–March 5, 2010. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-5228-6/pbk). Contemporary Mathematics 556, 25-35 (2011). Reviewer: Gabriela Cristescu (Arad) MSC: 14D05 14Q99 65H10 65H20 65E05 65Y05 PDFBibTeX XMLCite \textit{D. J. Bates} et al., Contemp. Math. 556, 25--35 (2011; Zbl 1238.14007)
Bates, Daniel J.; Hauenstein, Jonathan D.; Sommese, Andrew J. Efficient path tracking methods. (English) Zbl 1230.65059 Numer. Algorithms 58, No. 4, 451-459 (2011). MSC: 65H20 14Q15 65L06 65H04 PDFBibTeX XMLCite \textit{D. J. Bates} et al., Numer. Algorithms 58, No. 4, 451--459 (2011; Zbl 1230.65059) Full Text: DOI
Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W. Regenerative cascade homotopies for solving polynomial systems. (English) Zbl 1231.65190 Appl. Math. Comput. 218, No. 4, 1240-1246 (2011). MSC: 65M99 PDFBibTeX XMLCite \textit{J. D. Hauenstein} et al., Appl. Math. Comput. 218, No. 4, 1240--1246 (2011; Zbl 1231.65190) Full Text: DOI
Hao, Wenrui; Hauenstein, Jonathan D.; Hu, Bei; Liu, Yuan; Sommese, Andrew J.; Zhang, Yong-Tao Multiple stable steady states of a reaction-diffusion model on zebrafish dorsal-ventral patterning. (English) Zbl 1218.65043 Discrete Contin. Dyn. Syst., Ser. S 4, No. 6, 1413-1428 (2011). MSC: 65H04 65H20 65M06 65N06 92B05 PDFBibTeX XMLCite \textit{W. Hao} et al., Discrete Contin. Dyn. Syst., Ser. S 4, No. 6, 1413--1428 (2011; Zbl 1218.65043) Full Text: DOI
Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W. Regeneration homotopies for solving systems of polynomials. (English) Zbl 1221.65121 Math. Comput. 80, No. 273, 345-377 (2011). Reviewer: Alyson Reeves (Bowie) MSC: 65H10 65H20 13P05 68W30 65H04 14Q15 30C15 PDFBibTeX XMLCite \textit{J. D. Hauenstein} et al., Math. Comput. 80, No. 273, 345--377 (2011; Zbl 1221.65121) Full Text: DOI
Di Rocco, Sandra; Eklund, David; Peterson, Chris; Sommese, Andrew J. Chern numbers of smooth varieties via homotopy continuation and intersection theory. (English) Zbl 1200.14014 J. Symb. Comput. 46, No. 1, 23-33 (2011). MSC: 14C15 14C17 14M07 PDFBibTeX XMLCite \textit{S. Di Rocco} et al., J. Symb. Comput. 46, No. 1, 23--33 (2011; Zbl 1200.14014) Full Text: DOI arXiv
Di Rocco, Sandra; Eklund, David; Sommese, Andrew J.; Wampler, Charles W. Algebraic \(\mathbb C^*\)-actions and the inverse kinematics of a general 6R manipulator. (English) Zbl 1208.65028 Appl. Math. Comput. 216, No. 9, 2512-2524 (2010). Reviewer: Jason Hanson (Redmond) MSC: 65D18 PDFBibTeX XMLCite \textit{S. Di Rocco} et al., Appl. Math. Comput. 216, No. 9, 2512--2524 (2010; Zbl 1208.65028) Full Text: DOI
Bates, Daniel J.; Hauenstein, Jonathan D.; Peterson, Chris; Sommese, Andrew J. A numerical local dimension test for points on the solution set of a system of polynomial equations. (English) Zbl 1211.14066 SIAM J. Numer. Anal. 47, No. 5, 3608-3623 (2009). Reviewer: Josef Schicho (Linz) MSC: 14Q99 65H10 68W30 PDFBibTeX XMLCite \textit{D. J. Bates} et al., SIAM J. Numer. Anal. 47, No. 5, 3608--3623 (2009; Zbl 1211.14066) Full Text: DOI
Bates, Daniel J.; Hauenstein, Jonathan D.; Peterson, Chris; Sommese, Andrew J. Numerical decomposition of the rank-deficiency set of a matrix of multivariate polynomials. (English) Zbl 1191.14071 Robbiano, Lorenzo (ed.) et al., Approximate commutative algebra. Berlin: Springer (ISBN 978-3-211-99313-2/pbk; 978-3-211-99314-9/e-book). Texts and Monographs in Symbolic Computation, 55-77 (2009). MSC: 14Q15 14M15 13Pxx 15A54 65H10 PDFBibTeX XMLCite \textit{D. J. Bates} et al., in: Approximate commutative algebra. Berlin: Springer. 55--77 (2009; Zbl 1191.14071) Full Text: DOI
Hauenstein, Jonathan D.; Migliore, Juan C.; Peterson, Chris; Sommese, Andrew J. Numerical computation of the dimensions of the cohomology of twists of ideal sheaves. (English) Zbl 1185.14041 Bates, Daniel J. (ed.) et al., Interactions of classical and numerical algebraic geometry. A conference in honor of Andrew Sommese, Notre Dame, IN, USA, May 22–24, 2008. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4746-6/pbk). Contemporary Mathematics 496, 235-242 (2009). Reviewer: Gerhard Pfister (Kaiserslautern) MSC: 14M06 65H10 65E05 PDFBibTeX XMLCite \textit{J. D. Hauenstein} et al., Contemp. Math. 496, 235--242 (2009; Zbl 1185.14041)
Bates, Daniel J.; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W. II Stepsize control for path tracking. (English) Zbl 1181.65071 Bates, Daniel J. (ed.) et al., Interactions of classical and numerical algebraic geometry. A conference in honor of Andrew Sommese, Notre Dame, IN, USA, May 22–24, 2008. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4746-6/pbk). Contemporary Mathematics 496, 21-31 (2009). MSC: 65H10 65H20 PDFBibTeX XMLCite \textit{D. J. Bates} et al., Contemp. Math. 496, 21--31 (2009; Zbl 1181.65071)
Bates, Daniel J.; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler II, Charles W. Adaptive multiprecision path tracking. (English) Zbl 1162.65026 SIAM J. Numer. Anal. 46, No. 2, 722-746 (2008). MSC: 65H10 65H20 30C15 12Y05 14Q15 PDFBibTeX XMLCite \textit{D. J. Bates} et al., SIAM J. Numer. Anal. 46, No. 2, 722--746 (2008; Zbl 1162.65026) Full Text: DOI arXiv
Sommese, Andrew J.; Wampler, Charles W. Exceptional sets and fiber products. (English) Zbl 1151.14041 Found. Comput. Math. 8, No. 2, 171-196 (2008). Reviewer: Gerhard Pfister (Kaiserslautern) MSC: 14Q99 65H10 68W30 PDFBibTeX XMLCite \textit{A. J. Sommese} and \textit{C. W. Wampler}, Found. Comput. Math. 8, No. 2, 171--196 (2008; Zbl 1151.14041) Full Text: DOI
Bates, Daniel J.; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W. II Software for numerical algebraic geometry: a paradigm and progress towards its implementation. (English) Zbl 1143.65344 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, 1-14 (2008). MSC: 65H20 65H10 14Q15 12Y05 30C15 PDFBibTeX XMLCite \textit{D. J. Bates} et al., IMA Vol. Math. Appl. 148, 1--14 (2008; Zbl 1143.65344)
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
Bates, Daniel J.; Peterson, Chris; Sommese, Andrew J. Application of a numerical version of Terracini’s lemma for secants and joins. (English) Zbl 1137.65035 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, 1-14 (2008). MSC: 65H10 65H20 68W30 14Q15 PDFBibTeX XMLCite \textit{D. J. Bates} et al., IMA Vol. Math. Appl. 146, 1--14 (2008; Zbl 1137.65035)
Lu, Ye; Bates, Daniel J.; Sommese, Andrew J.; Wampler, Charles W. Finding all real points of a complex curve. (English) Zbl 1136.65050 Corso, Alberto (ed.) et al., Algebra, geometry and their interactions. International conference on Midwest algebra, geometry and their interactions, MAGIC’ 05, Notre Dame, IN, USA, October 7–11, 2005. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4094-8/pbk). Contemporary Mathematics 448, 183-205 (2007). MSC: 65H10 65H20 14Q15 70B15 PDFBibTeX XMLCite \textit{Y. Lu} et al., Contemp. Math. 448, 183--205 (2007; Zbl 1136.65050)
Bates, Dan; Peterson, Chris; Sommese, Andrew J. A numerical-symbolic algorithm for computing the multiplicity of a component of an algebraic set. (English) Zbl 1100.65046 J. Complexity 22, No. 4, 475-489 (2006). MSC: 65H10 65H20 68W30 30C15 PDFBibTeX XMLCite \textit{D. Bates} et al., J. Complexity 22, No. 4, 475--489 (2006; Zbl 1100.65046) Full Text: DOI
Allgower, E. L.; Bates, D. J.; Sommese, A. J.; Wampler, C. W. Solution of polynomial systems derived from differential equations. (English) Zbl 1086.65075 Computing 76, No. 1-2, 1-10 (2006). MSC: 65L10 65H20 34B15 65L12 PDFBibTeX XMLCite \textit{E. L. Allgower} et al., Computing 76, No. 1--2, 1--10 (2006; Zbl 1086.65075) Full Text: DOI arXiv
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
Sommese, Andrew J.; Wampler, Charles W. II The numerical solution of systems of polynomials. Arising in engineering and science. (English) Zbl 1091.65049 River Edge, NJ: World Scientific (ISBN 981-256-184-6/hbk; 978-981-256-772-7/ebook). xxii, 401 p. (2005). Reviewer: Zhen Mei (Toronto) MSC: 65H10 12Y05 26C10 30C15 14Q15 13P10 65H20 65-02 PDFBibTeX XMLCite \textit{A. J. Sommese} and \textit{C. W. Wampler II}, The numerical solution of systems of polynomials. Arising in engineering and science. River Edge, NJ: World Scientific (2005; Zbl 1091.65049) Full Text: DOI Link
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)
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
Allgower, Eugene L.; Sommese, Andrew J. Piecewise linear approximation of smooth compact fibers. (English) Zbl 1028.65054 J. Complexity 18, No. 2, 547-556 (2002). Reviewer: Zhen Mei (Toronto) MSC: 65H20 58C06 PDFBibTeX XMLCite \textit{E. L. Allgower} and \textit{A. J. Sommese}, J. Complexity 18, No. 2, 547--556 (2002; Zbl 1028.65054) Full Text: DOI Link
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
Wise, Steven M.; Sommese, Andrew J.; Watson, Layne T. Algorithm 801: POLSYS_PLP. A partitioned linear product homotopy code for solving polynomial systems of equations. (English) Zbl 1137.65353 ACM Trans. Math. Softw. 26, No. 1, 176-200 (2000). MSC: 65H20 65H10 65Y15 68W30 PDFBibTeX XMLCite \textit{S. M. Wise} et al., ACM Trans. Math. Softw. 26, No. 1, 176--200 (2000; Zbl 1137.65353) 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
Morgan, Alexander P.; Sommese, Andrew J.; Wampler, Charles W. A product-decomposition bound for Bézout numbers. (English) Zbl 0854.65038 SIAM J. Numer. Anal. 32, No. 4, 1308-1325 (1995). Reviewer: V.A.Kostova (Russe) MSC: 65H10 12Y05 65H20 26C10 70B10 PDFBibTeX XMLCite \textit{A. P. Morgan} et al., SIAM J. Numer. Anal. 32, No. 4, 1308--1325 (1995; Zbl 0854.65038) Full Text: DOI
Morgan, Alexander P.; Sommese, Andrew J. Errata: Computing all solutions to polynomial systems using homotopy continuation. (English) Zbl 0777.65032 Appl. Math. Comput. 51, No. 2-3, 209 (1992). MSC: 65H10 65H20 30C15 PDFBibTeX XMLCite \textit{A. P. Morgan} and \textit{A. J. Sommese}, Appl. Math. Comput. 51, No. 2--3, 209 (1992; Zbl 0777.65032) Full Text: DOI
Morgan, Alexander P.; Sommese, Andrew J. Errata: Coefficient-parameter polynomial continuation. (English) Zbl 0755.65050 Appl. Math. Comput. 51, No. 2-3, 207 (1992). MSC: 65H10 65H20 PDFBibTeX XMLCite \textit{A. P. Morgan} and \textit{A. J. Sommese}, Appl. Math. Comput. 51, No. 2--3, 207 (1992; Zbl 0755.65050) Full Text: DOI
Morgan, Alexander P.; Sommese, Andrew J.; Wampler, Charles W. A power series method for computing singular solutions to nonlinear analytic systems. (English) Zbl 0756.65079 Numer. Math. 63, No. 3, 391-409 (1992). Reviewer: A.P.Morgan MSC: 65H10 65E05 65H20 PDFBibTeX XMLCite \textit{A. P. Morgan} et al., Numer. Math. 63, No. 3, 391--409 (1992; Zbl 0756.65079) Full Text: DOI EuDML
Morgan, Alexander P.; Sommese, Andrew J.; Wampler, Charles W. Computing singular solutions to nonlinear analytic systems. (English) Zbl 0721.65027 Numer. Math. 58, No. 7, 669-684 (1991). Reviewer: H.Matthies (Hamburg) MSC: 65H10 65H20 PDFBibTeX XMLCite \textit{A. P. Morgan} et al., Numer. Math. 58, No. 7, 669--684 (1991; Zbl 0721.65027) Full Text: DOI EuDML
Morgan, Alexander P.; Sommese, Andrew J. Generically nonsingular polynomial continuation. (English) Zbl 0699.65036 Computational solution of nonlinear systems of equations, Proc. SIAM-AMS Summer Semin., Ft. Collins/CO (USA) 1988, Lect. Appl. Math. 26, 467-493 (1990). Reviewer: E.Allgower MSC: 65H10 PDFBibTeX XML
Morgan, Alexander P.; Sommese, Andrew J.; Watson, Layne T. Finding all isolated solutions to polynomial systems using HOMPACK. (English) Zbl 0900.65151 ACM Trans. Math. Softw. 15, No. 2, 93-122 (1989). MSC: 65H10 12Y05 30C15 65H20 PDFBibTeX XMLCite \textit{A. P. Morgan} et al., ACM Trans. Math. Softw. 15, No. 2, 93--122 (1989; Zbl 0900.65151) Full Text: DOI Link Link
Morgan, Alexander; Sommese, Andrew Computing all solutions to polynomial systems using homotopy continuation. (English) Zbl 0635.65058 Appl. Math. Comput. 24, 115-138 (1987). Reviewer: C.Schmidt-Lainé MSC: 65H10 30C15 PDFBibTeX XMLCite \textit{A. Morgan} and \textit{A. Sommese}, Appl. Math. Comput. 24, 115--138 (1987; Zbl 0635.65058) Full Text: DOI
Morgan, Alexander; Sommese, Andrew A homotopy for solving general polynomial systems that respects m- homogeneous structures. (English) Zbl 0635.65057 Appl. Math. Comput. 24, 101-113 (1987). Reviewer: C.Schmidt-Lainé MSC: 65H10 30C15 PDFBibTeX XMLCite \textit{A. Morgan} and \textit{A. Sommese}, Appl. Math. Comput. 24, 101--113 (1987; Zbl 0635.65057) Full Text: DOI
Sommese, Andrew John; van de Ven, A. Homotopy groups of pullbacks of varieties. (English) Zbl 0564.14010 Nagoya Math. J. 102, 79-90 (1986). MSC: 14F35 57T20 14M17 14D05 32M10 PDFBibTeX XMLCite \textit{A. J. Sommese} and \textit{A. van de Ven}, Nagoya Math. J. 102, 79--90 (1986; Zbl 0564.14010) Full Text: DOI
Sommese, Andrew John A convexity theorem. (English) Zbl 0515.32006 Singularities, Summer Inst., Arcata/Calif. 1981, Proc. Symp. Pure Math. 40, Part 2, 497-505 (1983). MSC: 32F10 32L15 55Q52 14K20 PDFBibTeX XML
Sommese, Andrew John Complex subspaces of homogeneous complex manifolds. II. Homotopy results. (English) Zbl 0497.32026 Nagoya Math. J. 86, 101-129 (1982). MSC: 32M10 14M17 55Q52 32F10 14M15 32J25 32C25 PDFBibTeX XMLCite \textit{A. J. Sommese}, Nagoya Math. J. 86, 101--129 (1982; Zbl 0497.32026) Full Text: DOI
Sommese, Andrew J. Complex subspaces of homogeneous complex manifolds. II. (English) Zbl 0454.32019 Nagoya Math. J. (to appear). MSC: 32M10 32F10 14M17 14M15 32J25 55Q52 PDFBibTeX XML
Sommese, Andrew John Theorems of Barth-Lefschetz type for complex subspaces of homogeneous complex manifolds. (English) Zbl 0354.32035 Proc. Natl. Acad. Sci. USA 74, 1332-1333 (1977). MSC: 32M10 14M15 14M10 14F35 PDFBibTeX XMLCite \textit{A. J. Sommese}, Proc. Natl. Acad. Sci. USA 74, 1332--1333 (1977; Zbl 0354.32035) Full Text: DOI