Burr, M.; Sottile, F.; Walker, E. Numerical homotopies from Khovanskii bases. (English) Zbl 1519.14047 Math. Comput. 92, No. 343, 2333-2353 (2023). Reviewer: Gema Maria Diaz Toca (Murcia) MSC: 14M25 68W30 65H10 65H20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Hauenstein, Jon D.; Safey El Din, Mohab; Schost, Éric; Vu, Thi Xuan Solving determinantal systems using homotopy techniques. (English) Zbl 1461.13034 J. Symb. Comput. 104, 754-804 (2021). Reviewer: Amir Hashemi (Isfahan) MSC: 13P15 65H20 × Cite Format Result Cite Review PDF 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 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Rodriguez, Jose Israel Combinatorial excess intersection. (English) Zbl 1316.14111 J. Symb. Comput. 68, Part 2, 297-307 (2015). Reviewer: Carlos D’Andrea (Barcelona) MSC: 14Qxx 65H20 68W30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv HAL
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 × Cite Format Result Cite Review PDF Full Text: DOI
Dong, Bo; Yu, Bo; Yu, Yan A symmetric homotopy and hybrid polynomial system solving method for mixed trigonometric polynomial systems. (English) Zbl 1327.13102 Math. Comput. 83, No. 288, 1847-1868 (2014). MSC: 13P15 65H20 65H10 14Q99 68W30 × Cite Format Result Cite Review PDF Full Text: DOI
Beltrán, Carlos; Leykin, Anton Robust certified numerical homotopy tracking. (English) Zbl 1267.14075 Found. Comput. Math. 13, No. 2, 253-295 (2013). Reviewer: Hang Lau (Montréal) MSC: 14Q20 65H20 68W30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
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 × Cite Format Result Cite Review PDF Full Text: DOI
Verschelde, Jan Polynomial homotopy continuation with PHCpack. (English) Zbl 1308.68198 ACM Commun. Comput. Algebra 44, No. 4, 217-220 (2010). MSC: 68W30 65H20 × Cite Format Result Cite Review PDF 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 × Cite Format Result Cite Review PDF 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 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
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 × Cite Format Result Cite Review PDF
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 × Cite Format Result Cite Review PDF 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 × Cite Format Result Cite Review PDF 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 × Cite Format Result Cite Review PDF Full Text: DOI Link