Luo, Xin-long; Xiao, Hang; Lv, Jia-hui Continuation Newton methods with the residual trust-region time-stepping scheme for nonlinear equations. (English) Zbl 1480.65125 Numer. Algorithms 89, No. 1, 223-247 (2022). MSC: 65H20 65H10 65K05 65L05 65L20 PDFBibTeX XMLCite \textit{X.-l. Luo} et al., Numer. Algorithms 89, No. 1, 223--247 (2022; Zbl 1480.65125) 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
Hauenstein, Jonathan D.; Rodriguez, Jose Israel Multiprojective witness sets and a trace test. (English) Zbl 1448.65054 Adv. Geom. 20, No. 3, 297-318 (2020). Reviewer: Luca Chiantini (Siena) MSC: 65H20 14Q15 PDFBibTeX XMLCite \textit{J. D. Hauenstein} and \textit{J. I. Rodriguez}, Adv. Geom. 20, No. 3, 297--318 (2020; Zbl 1448.65054) Full Text: DOI arXiv
Duff, Timothy; Hill, Cvetelina; Jensen, Anders; Lee, Kisun; Leykin, Anton; Sommars, Jeff Solving polynomial systems via homotopy continuation and monodromy. (English) Zbl 1462.65055 IMA J. Numer. Anal. 39, No. 3, 1421-1446 (2019). MSC: 65H20 PDFBibTeX XMLCite \textit{T. Duff} et al., IMA J. Numer. Anal. 39, No. 3, 1421--1446 (2019; Zbl 1462.65055) Full Text: DOI arXiv
Leykin, Anton; Yu, Josephine Beyond polyhedral homotopies. (English) Zbl 1435.14053 J. Symb. Comput. 91, 173-180 (2019). MSC: 14Q15 14T15 65H20 65H14 PDFBibTeX XMLCite \textit{A. Leykin} and \textit{J. Yu}, J. Symb. Comput. 91, 173--180 (2019; Zbl 1435.14053) Full Text: DOI arXiv
Wang, Yu; Wu, Wenyuan; Xia, Bican Early ending in homotopy path-tracking for real roots. (English) Zbl 07704991 Fleuriot, Jacques (ed.) et al., Artificial intelligence and symbolic computation. 13th international conference, AISC 2018, Suzhou, China, September 16–19, 2018. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 11110, 181-194 (2018). MSC: 65H20 PDFBibTeX XMLCite \textit{Y. Wang} et al., Lect. Notes Comput. Sci. 11110, 181--194 (2018; Zbl 07704991) Full Text: DOI
Zhang, Xuping; Zhang, Jintao; Yu, Bo Symmetric homotopy method for discretized elliptic equations with cubic and quintic nonlinearities. (English) Zbl 1373.65086 J. Sci. Comput. 70, No. 3, 1316-1335 (2017). Reviewer: Vit Dolejsi (Praha) MSC: 65N35 65H20 35J61 35P10 PDFBibTeX XMLCite \textit{X. Zhang} et al., J. Sci. Comput. 70, No. 3, 1316--1335 (2017; Zbl 1373.65086) Full Text: DOI
Chen, Tianran; Mehta, Dhagash Parallel degree computation for binomial systems. (English) Zbl 1357.65063 J. Symb. Comput. 79, Part 3, 535-558 (2017). MSC: 65H20 13P15 65Y10 PDFBibTeX XMLCite \textit{T. Chen} and \textit{D. Mehta}, J. Symb. Comput. 79, Part 3, 535--558 (2017; Zbl 1357.65063) Full Text: DOI
Chen, Liping; Han, Lixing; Zhou, Liangmin Computing tensor eigenvalues via homotopy methods. (English) Zbl 1376.15017 SIAM J. Matrix Anal. Appl. 37, No. 1, 290-319 (2016). MSC: 15A69 15A18 65H10 65F15 65H20 65H17 PDFBibTeX XMLCite \textit{L. Chen} et al., SIAM J. Matrix Anal. Appl. 37, No. 1, 290--319 (2016; Zbl 1376.15017) Full Text: DOI arXiv
Bates, Daniel J.; Newell, Andrew J.; Niemerg, Matthew BertiniLab: a MATLAB interface for solving systems of polynomial equations. (English) Zbl 1333.65054 Numer. Algorithms 71, No. 1, 229-244 (2016). MSC: 65H10 65H04 65H20 PDFBibTeX XMLCite \textit{D. J. Bates} et al., Numer. Algorithms 71, No. 1, 229--244 (2016; Zbl 1333.65054) Full Text: DOI
Hauenstein, Jonathan D.; Liddell, Alan C. Certified predictor-corrector tracking for Newton homotopies. (English) Zbl 1329.65110 J. Symb. Comput. 74, 239-254 (2016). MSC: 65H20 65H10 65H04 PDFBibTeX XMLCite \textit{J. D. Hauenstein} and \textit{A. C. Liddell}, J. Symb. Comput. 74, 239--254 (2016; Zbl 1329.65110) Full Text: DOI
Chen, Tianran; Li, Tien-Yien Homotopy continuation method for solving systems of nonlinear and polynomial equations. (English) Zbl 1337.65044 Commun. Inf. Syst. 15, No. 2, 119-307 (2015). Reviewer: Sonia Pérez Díaz (Madrid) MSC: 65H20 65Y05 65H04 12Y05 PDFBibTeX XMLCite \textit{T. Chen} and \textit{T.-Y. Li}, Commun. Inf. Syst. 15, No. 2, 119--307 (2015; Zbl 1337.65044) Full Text: DOI
Feng, Yong; Wu, Wenyuan; Zhang, Jingzhong; Chen, Jingwei Exact bivariate polynomial factorization over \(\mathbb Q\) by approximation of roots. (English) Zbl 1328.65108 J. Syst. Sci. Complex. 28, No. 1, 243-260 (2015). MSC: 65H04 PDFBibTeX XMLCite \textit{Y. Feng} et al., J. Syst. Sci. Complex. 28, No. 1, 243--260 (2015; Zbl 1328.65108) Full Text: DOI
Bozóki, Sándor; Lee, Tsung-Lin; Rónyai, Lajos Seven mutually touching infinite cylinders. (English) Zbl 1310.65022 Comput. Geom. 48, No. 2, 87-93 (2015). MSC: 65D18 65H20 PDFBibTeX XMLCite \textit{S. Bozóki} et al., Comput. Geom. 48, No. 2, 87--93 (2015; Zbl 1310.65022) Full Text: DOI arXiv
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.; Davis, Brent; Eklund, David; Hanson, Eric; Peterson, Chris Perturbed homotopies for finding all isolated solutions of polynomial systems. (English) Zbl 1338.13046 Appl. Math. Comput. 247, 301-311 (2014). MSC: 13P15 65H10 65H20 PDFBibTeX XMLCite \textit{D. J. Bates} et al., Appl. Math. Comput. 247, 301--311 (2014; Zbl 1338.13046) Full Text: DOI
Luo, Zhongxuan; Feng, Erbao; Zhang, Jiejin A numerical realization of the conditions of Max Nöther’s residual intersection theorem. (English) Zbl 1324.65032 Appl. Math., Ser. B (Engl. Ed.) 29, No. 4, 481-502 (2014). MSC: 65D18 13D15 14Q05 65H20 65Y20 PDFBibTeX XMLCite \textit{Z. Luo} et al., Appl. Math., Ser. B (Engl. Ed.) 29, No. 4, 481--502 (2014; Zbl 1324.65032) Full Text: DOI
Chen, Tianran; Li, Tien-Yien Spherical projective path tracking for homotopy continuation methods. (English) Zbl 1308.65078 Commun. Inf. Syst. 12, No. 3, 195-220 (2012). MSC: 65H20 65H04 65H10 PDFBibTeX XMLCite \textit{T. Chen} and \textit{T.-Y. Li}, Commun. Inf. Syst. 12, No. 3, 195--220 (2012; Zbl 1308.65078) Full Text: DOI
Bates, Daniel J.; Sottile, Frank Khovanskii-Rolle continuation for real solutions. (English) Zbl 1231.14047 Found. Comput. Math. 11, No. 5, 563-587 (2011). MSC: 14P05 14Q99 65H10 65H20 PDFBibTeX XMLCite \textit{D. J. Bates} and \textit{F. Sottile}, Found. Comput. Math. 11, No. 5, 563--587 (2011; Zbl 1231.14047) Full Text: DOI arXiv
Beltrán, Carlos A continuation method to solve polynomial systems and its complexity. (English) Zbl 1216.65058 Numer. Math. 117, No. 1, 89-113 (2011). Reviewer: Przemyslaw Stpiczynski (Lublin) MSC: 65H10 65Y20 12Y05 PDFBibTeX XMLCite \textit{C. Beltrán}, Numer. Math. 117, No. 1, 89--113 (2011; Zbl 1216.65058) Full Text: DOI
Tari, Hafez; Su, Hai-Jun; Li, Tien-Yien A constrained homotopy technique for excluding unwanted solutions from polynomial equations arising in kinematics problems. (English) Zbl 1359.70037 Mech. Mach. Theory 45, No. 6, 898-910 (2010). MSC: 70B15 65H20 PDFBibTeX XMLCite \textit{H. Tari} et al., Mech. Mach. Theory 45, No. 6, 898--910 (2010; Zbl 1359.70037) Full Text: DOI
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
Leykin, Anton; Sottile, Frank Galois groups of Schubert problems via homotopy computation. (English) Zbl 1210.14064 Math. Comput. 78, No. 267, 1749-1765 (2009). Reviewer: Emilia Mezzetti (Trieste) MSC: 14N15 65H20 PDFBibTeX XMLCite \textit{A. Leykin} and \textit{F. Sottile}, Math. Comput. 78, No. 267, 1749--1765 (2009; Zbl 1210.14064) Full Text: DOI arXiv