Duff, T.; Telen, S.; Walker, E.; Yahl, T. Polyhedral homotopies in Cox coordinates. (English) Zbl 07793928 J. Algebra Appl. 23, No. 4, Article ID 2450073, 35 p. (2024). MSC: 13P15 14M25 68W30 PDFBibTeX XMLCite \textit{T. Duff} et al., J. Algebra Appl. 23, No. 4, Article ID 2450073, 35 p. (2024; Zbl 07793928) Full Text: DOI arXiv
Duff, Timothy; Leykin, Anton; Rodriguez, Jose Israel \(u\)-generation: solving systems of polynomials equation-by-equation. (English) Zbl 07792401 Numer. Algorithms 95, No. 2, 813-838 (2024). Reviewer: Nikolay Kyurkchiev (Plovdiv) MSC: 65H20 65H10 14Q65 68W30 PDFBibTeX XMLCite \textit{T. Duff} et al., Numer. Algorithms 95, No. 2, 813--838 (2024; Zbl 07792401) Full Text: DOI arXiv
Ergür, Alperen A.; de Wolff, Timo A polyhedral homotopy algorithm for real zeros. (English) Zbl 1520.14109 Arnold Math. J. 9, No. 3, 305-338 (2023). Reviewer: Vladimir P. Kostov (Nice) MSC: 14P05 14P25 68R05 52B11 65D99 65Y20 PDFBibTeX XMLCite \textit{A. A. Ergür} and \textit{T. de Wolff}, Arnold Math. J. 9, No. 3, 305--338 (2023; Zbl 1520.14109) Full Text: DOI arXiv
Lee, Kisun; Tang, Xindong On the polyhedral homotopy method for solving generalized Nash equilibrium problems of polynomials. (English) Zbl 1519.91013 J. Sci. Comput. 95, No. 1, Paper No. 13, 26 p. (2023); correction ibid. 95, No. 3, Paper No. 83, 2 p. (2023). MSC: 91A11 65H14 90C23 PDFBibTeX XMLCite \textit{K. Lee} and \textit{X. Tang}, J. Sci. Comput. 95, No. 1, Paper No. 13, 26 p. (2023; Zbl 1519.91013) Full Text: DOI arXiv
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 PDFBibTeX XMLCite \textit{M. Burr} et al., Math. Comput. 92, No. 343, 2333--2353 (2023; Zbl 1519.14047) Full Text: DOI arXiv
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
Breiding, P.; Sottile, F.; Woodcock, J. Euclidean distance degree and mixed volume. (English) Zbl 1505.14124 Found. Comput. Math. 22, No. 6, 1743-1765 (2022). Reviewer: Timothy Duff (Seattle) MSC: 14Qxx 13P25 14M25 90C26 PDFBibTeX XMLCite \textit{P. Breiding} et al., Found. Comput. Math. 22, No. 6, 1743--1765 (2022; Zbl 1505.14124) Full Text: DOI arXiv
Frohmader, Andrew; Heaton, Alexander Epsilon local rigidity and numerical algebraic geometry. (English) Zbl 1485.70001 J. Algebra Appl. 21, No. 1, Article ID 2250009, 21 p. (2022). MSC: 70B15 65D17 14Q99 PDFBibTeX XMLCite \textit{A. Frohmader} and \textit{A. Heaton}, J. Algebra Appl. 21, No. 1, Article ID 2250009, 21 p. (2022; Zbl 1485.70001) Full Text: DOI arXiv
Brysiewicz, Taylor; Rodriguez, Jose Israel; Sottile, Frank; Yahl, Thomas Decomposable sparse polynomial systems. (English) Zbl 1483.14087 J. Softw. Algebra Geom. 11, 53-59 (2021). MSC: 14M25 65H10 65H20 PDFBibTeX XMLCite \textit{T. Brysiewicz} et al., J. Softw. Algebra Geom. 11, 53--59 (2021; Zbl 1483.14087) Full Text: DOI arXiv
Wei, Xiaoqi; Wei, Guo-Wei Homotopy continuation for the spectra of persistent Laplacians. (English) Zbl 1494.55011 Found. Data Sci. 3, No. 4, 677-700 (2021). Reviewer: Bastian Rieck (Bern) MSC: 55N31 55U10 65H14 PDFBibTeX XMLCite \textit{X. Wei} and \textit{G.-W. Wei}, Found. Data Sci. 3, No. 4, 677--700 (2021; Zbl 1494.55011) Full Text: DOI
Timme, Sascha Mixed precision path tracking for polynomial homotopy continuation. (English) Zbl 1487.65057 Adv. Comput. Math. 47, No. 5, Paper No. 75, 23 p. (2021). MSC: 65H20 65H10 PDFBibTeX XMLCite \textit{S. Timme}, Adv. Comput. Math. 47, No. 5, Paper No. 75, 23 p. (2021; Zbl 1487.65057) Full Text: DOI arXiv
Brysiewicz, Taylor; Rodriguez, Jose Israel; Sottile, Frank; Yahl, Thomas Solving decomposable sparse systems. (English) Zbl 1473.65059 Numer. Algorithms 88, No. 1, 453-474 (2021). MSC: 65H10 65H20 PDFBibTeX XMLCite \textit{T. Brysiewicz} et al., Numer. Algorithms 88, No. 1, 453--474 (2021; Zbl 1473.65059) 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 PDFBibTeX XMLCite \textit{J. D. Hauenstein} et al., J. Symb. Comput. 104, 754--804 (2021; Zbl 1461.13034) Full Text: DOI arXiv
Zhang, Xuping; Zhang, Jintao; Yu, Bo Finding multiple solutions to elliptic systems with polynomial nonlinearity. (English) Zbl 07771428 Numer. Methods Partial Differ. Equations 36, No. 5, 1074-1097 (2020). MSC: 65-XX 35-XX PDFBibTeX XMLCite \textit{X. Zhang} et al., Numer. Methods Partial Differ. Equations 36, No. 5, 1074--1097 (2020; Zbl 07771428) Full Text: DOI
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
Hao, Wenrui; Zheng, Chunyue An adaptive homotopy method for computing bifurcations of nonlinear parametric systems. (English) Zbl 1437.37111 J. Sci. Comput. 82, No. 3, Paper No. 53, 19 p. (2020). MSC: 37M20 PDFBibTeX XMLCite \textit{W. Hao} and \textit{C. Zheng}, J. Sci. Comput. 82, No. 3, Paper No. 53, 19 p. (2020; Zbl 1437.37111) Full Text: DOI arXiv
Bozorgmanesh, Hassan; Hajarian, Masoud Solving tensor E-eigenvalue problem faster. (English) Zbl 1427.15009 Appl. Math. Lett. 100, Article ID 106020, 9 p. (2020). MSC: 15A18 15A69 65F15 PDFBibTeX XMLCite \textit{H. Bozorgmanesh} and \textit{M. Hajarian}, Appl. Math. Lett. 100, Article ID 106020, 9 p. (2020; Zbl 1427.15009) Full Text: DOI
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
Chen, Justin; Kileel, Joe Numerical implicitization: a Macaulay2 package. (English) Zbl 1430.14112 J. Softw. Algebra Geom. 9, 55-63 (2019). Reviewer: Sonia Pérez Díaz (Madrid) MSC: 14Q65 14-04 65H14 PDFBibTeX XMLCite \textit{J. Chen} and \textit{J. Kileel}, J. Softw. Algebra Geom. 9, No. 1, 55--63 (2019; Zbl 1430.14112) Full Text: DOI arXiv
Chen, Tianran Unmixing the mixed volume computation. (English) Zbl 1417.52021 Discrete Comput. Geom. 62, No. 1, 55-86 (2019). MSC: 52B55 65H10 65H20 52A39 PDFBibTeX XMLCite \textit{T. Chen}, Discrete Comput. Geom. 62, No. 1, 55--86 (2019; Zbl 1417.52021) 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
Bliss, Nathan; Duff, Timothy; Leykin, Anton; Sommars, Jeff Monodromy solver. Sequential and parallel. (English) Zbl 1467.65055 Arreche, Carlos (ed.), Proceedings of the 43rd international symposium on symbolic and algebraic computation, ISSAC 2018, New York, NY, USA, July 16–19, 2018. New York, NY: Association for Computing Machinery (ACM). 87-94 (2018). MSC: 65H20 14Q20 68W20 PDFBibTeX XMLCite \textit{N. Bliss} et al., in: Proceedings of the 43rd international symposium on symbolic and algebraic computation, ISSAC 2018, New York, NY, USA, July 16--19, 2018. New York, NY: Association for Computing Machinery (ACM). 87--94 (2018; Zbl 1467.65055) 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
Breiding, Paul; Timme, Sascha HomotopyContinuation.jl: a package for homotopy continuation in Julia. (English) Zbl 1396.14003 Davenport, James H. (ed.) et al., Mathematical software – ICMS 2018. 6th international conference, South Bend, IN, USA, July 24–27, 2018. Proceedings. Cham: Springer (ISBN 978-3-319-96417-1/pbk; 978-3-319-96418-8/ebook). Lecture Notes in Computer Science 10931, 458-465 (2018). MSC: 14-04 14Qxx 65H10 13P10 PDFBibTeX XMLCite \textit{P. Breiding} and \textit{S. Timme}, Lect. Notes Comput. Sci. 10931, 458--465 (2018; Zbl 1396.14003) Full Text: DOI arXiv
Leykin, Anton Homotopy continuation in Macaulay2. (English) Zbl 1395.13028 Davenport, James H. (ed.) et al., Mathematical software – ICMS 2018. 6th international conference, South Bend, IN, USA, July 24–27, 2018. Proceedings. Cham: Springer (ISBN 978-3-319-96417-1/pbk; 978-3-319-96418-8/ebook). Lecture Notes in Computer Science 10931, 328-334 (2018). MSC: 13P10 14Qxx 65H10 PDFBibTeX XMLCite \textit{A. Leykin}, Lect. Notes Comput. Sci. 10931, 328--334 (2018; Zbl 1395.13028) Full Text: DOI
Mahmoud, Abdrhaman; Yu, Bo; Zhang, Xuping Eigenfunction expansion method for multiple solutions of fourth-order ordinary differential equations with cubic polynomial nonlinearity. (English) Zbl 1402.65073 ETNA, Electron. Trans. Numer. Anal. 48, 81-96 (2018). Reviewer: Serhiy Yanchuk (Berlin) MSC: 65L10 34L10 34B15 PDFBibTeX XMLCite \textit{A. Mahmoud} et al., ETNA, Electron. Trans. Numer. Anal. 48, 81--96 (2018; Zbl 1402.65073) Full Text: DOI Link
Wang, Yu; Wu, Wenyuan; Xia, Bican A special homotopy continuation method for a class of polynomial systems. (English) Zbl 1455.65079 Gerdt, Vladimir P. (ed.) et al., Computer algebra in scientific computing. 19th international workshop, CASC 2017, Beijing, China, September 18–22, 2017. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 10490, 362-376 (2017). MSC: 65H10 65H20 PDFBibTeX XMLCite \textit{Y. Wang} et al., Lect. Notes Comput. Sci. 10490, 362--376 (2017; Zbl 1455.65079) Full Text: DOI arXiv
Malajovich, Gregorio Computing mixed volume and all mixed cells in quermassintegral time. (English) Zbl 1383.65050 Found. Comput. Math. 17, No. 5, 1293-1334 (2017). Reviewer: Sonia Pérez Díaz (Madrid) MSC: 65H10 52A39 14M25 14N10 52B55 65H20 65D18 PDFBibTeX XMLCite \textit{G. Malajovich}, Found. Comput. Math. 17, No. 5, 1293--1334 (2017; Zbl 1383.65050) Full Text: DOI arXiv
Bernardi, Alessandra; Daleo, Noah S.; Hauenstein, Jonathan D.; Mourrain, Bernard Tensor decomposition and homotopy continuation. (English) Zbl 1377.65057 Differ. Geom. Appl. 55, 78-105 (2017). MSC: 65H10 14Q15 15A69 13P05 PDFBibTeX XMLCite \textit{A. Bernardi} et al., Differ. Geom. Appl. 55, 78--105 (2017; Zbl 1377.65057) Full Text: DOI arXiv
Batenkov, Dmitry Accurate solution of near-colliding Prony systems via decimation and homotopy continuation. (English) Zbl 1375.65071 Theor. Comput. Sci. 681, 27-40 (2017). MSC: 65H10 65H20 PDFBibTeX XMLCite \textit{D. Batenkov}, Theor. Comput. Sci. 681, 27--40 (2017; Zbl 1375.65071) Full Text: DOI arXiv
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; Lee, Tsung-Lin; Li, Tien-Yien Mixed cell computation in HOM4ps. (English) Zbl 1365.13047 J. Symb. Comput. 79, Part 3, 516-534 (2017). Reviewer: Thomas Kahle (Magdeburg) MSC: 13P15 68W10 52B55 65Y05 65Y20 05C85 14Q99 PDFBibTeX XMLCite \textit{T. Chen} et al., J. Symb. Comput. 79, Part 3, 516--534 (2017; Zbl 1365.13047) Full Text: DOI
Bates, Daniel J.; Newell, Andrew J.; Niemerg, Matthew E. Decoupling highly structured polynomial systems. (English) Zbl 1360.13064 J. Symb. Comput. 79, Part 3, 508-515 (2017). Reviewer: Sonia Pérez Díaz (Madrid) MSC: 13P15 13-04 14Qxx 68W30 65H10 78-04 PDFBibTeX XMLCite \textit{D. J. Bates} et al., J. Symb. Comput. 79, Part 3, 508--515 (2017; Zbl 1360.13064) 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
Leykin, Anton Polynomial homotopy continuation in Macaulay2. (English) Zbl 1365.68499 ACM Commun. Comput. Algebra 50, No. 3, 113-116 (2016). MSC: 68W30 14-04 14F35 PDFBibTeX XMLCite \textit{A. Leykin}, ACM Commun. Comput. Algebra 50, No. 3, 113--116 (2016; Zbl 1365.68499) Full Text: DOI
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
Jensen, Anders; Leykin, Anton; Yu, Josephine Computing tropical curves via homotopy continuation. (English) Zbl 1350.14045 Exp. Math. 25, No. 1, 83-93 (2016). Reviewer: Nikita Kalinin (Col. San Pedro Zacatenco) MSC: 14T05 14Q05 57M25 65H20 PDFBibTeX XMLCite \textit{A. Jensen} et al., Exp. Math. 25, No. 1, 83--93 (2016; Zbl 1350.14045) Full Text: DOI arXiv
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
Jiao, Libin; Dong, Bo; Zhang, Jintao; Yu, Bo Polynomial homotopy method for the sparse interpolation problem. I: Equally spaced sampling. (English) Zbl 1382.65033 SIAM J. Numer. Anal. 54, No. 1, 462-480 (2016). MSC: 65D05 65J22 65H20 PDFBibTeX XMLCite \textit{L. Jiao} et al., SIAM J. Numer. Anal. 54, No. 1, 462--480 (2016; Zbl 1382.65033) Full Text: DOI
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
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
Bates, Daniel J.; Davis, Brent R.; Kirby, Michael; Marks, Justin; Peterson, Chris The max-length-vector line of best fit to a set of vector subspaces and an optimization problem over a set of hyperellipsoids. (English) Zbl 1363.65100 Numer. Linear Algebra Appl. 22, No. 3, 453-464 (2015). MSC: 65K05 65F15 14Q99 90C90 65D10 65H20 PDFBibTeX XMLCite \textit{D. J. Bates} et al., Numer. Linear Algebra Appl. 22, No. 3, 453--464 (2015; Zbl 1363.65100) 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
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 PDFBibTeX XMLCite \textit{J. I. Rodriguez}, J. Symb. Comput. 68, Part 2, 297--307 (2015; Zbl 1316.14111) 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
Bates, Daniel J.; Niemerg, Matthew Using monodromy to avoid high precision in homotopy continuation. (English) Zbl 1302.65137 Math. Comput. Sci. 8, No. 2, 253-262 (2014). MSC: 65H20 13P15 PDFBibTeX XMLCite \textit{D. J. Bates} and \textit{M. Niemerg}, Math. Comput. Sci. 8, No. 2, 253--262 (2014; Zbl 1302.65137) Full Text: DOI
Chen, Tianran; Lee, Tsung-Lin; Li, Tien-Yien Hom4PS-3: a parallel numerical solver for systems of polynomial equations based on polyhedral homotopy continuation methods. (English) Zbl 1434.65065 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, 183-190 (2014). MSC: 65H04 65Y05 PDFBibTeX XMLCite \textit{T. Chen} et al., Lect. Notes Comput. Sci. 8592, 183--190 (2014; Zbl 1434.65065) 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 PDFBibTeX XMLCite \textit{B. Dong} et al., Math. Comput. 83, No. 288, 1847--1868 (2014; Zbl 1327.13102) 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
Vazquez-Leal, H.; Marin-Hernandez, A.; Khan, Y.; Yıldırım, A.; Filobello-Nino, U.; Castaneda-Sheissa, R.; Jimenez-Fernandez, V. M. Exploring collision-free path planning by using homotopy continuation methods. (English) Zbl 1366.70011 Appl. Math. Comput. 219, No. 14, 7514-7532 (2013). MSC: 70E60 PDFBibTeX XMLCite \textit{H. Vazquez-Leal} et al., Appl. Math. Comput. 219, No. 14, 7514--7532 (2013; Zbl 1366.70011) 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
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 PDFBibTeX XMLCite \textit{C. Beltrán} and \textit{A. Leykin}, Found. Comput. Math. 13, No. 2, 253--295 (2013; Zbl 1267.14075) Full Text: DOI arXiv
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
Beltrán, Carlos; Leykin, Anton Certified numerical homotopy tracking. (English) Zbl 1238.14048 Exp. Math. 21, No. 1, 69-83 (2012). MSC: 14Q20 65H10 65H20 PDFBibTeX XMLCite \textit{C. Beltrán} and \textit{A. Leykin}, Exp. Math. 21, No. 1, 69--83 (2012; Zbl 1238.14048) Full Text: DOI arXiv
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
Luo, Zhongxuan; Hu, Wenyu; Feng, Erbao Computing curve intersection by homotopy methods. (English) Zbl 1252.65048 J. Comput. Appl. Math. 236, No. 5, 892-905 (2011). MSC: 65D18 65H20 PDFBibTeX XMLCite \textit{Z. Luo} et al., J. Comput. Appl. Math. 236, No. 5, 892--905 (2011; Zbl 1252.65048) Full Text: DOI
Rüffer, Björn S.; Wirth, Fabian R. Stability verification for monotone systems using homotopy algorithms. (English) Zbl 1229.93115 Numer. Algorithms 58, No. 4, 529-543 (2011). MSC: 93C55 47H07 65H20 93B28 PDFBibTeX XMLCite \textit{B. S. Rüffer} and \textit{F. R. Wirth}, Numer. Algorithms 58, No. 4, 529--543 (2011; Zbl 1229.93115) 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 PDFBibTeX XMLCite \textit{J. D. Hauenstein} et al., Math. Comput. 80, No. 273, 345--377 (2011; Zbl 1221.65121) Full Text: DOI
Beltrán, Carlos; Pardo, Luis Miguel Fast linear homotopy to find approximate zeros of polynomial systems. (English) Zbl 1232.65075 Found. Comput. Math. 11, No. 1, 95-129 (2011). Reviewer: Przemyslaw Stpiczynski (Lublin) MSC: 65H10 65H04 65H20 12Y05 13P15 65Y20 PDFBibTeX XMLCite \textit{C. Beltrán} and \textit{L. M. Pardo}, Found. Comput. Math. 11, No. 1, 95--129 (2011; Zbl 1232.65075) 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
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
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
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
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
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
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
Lee, Tsung-Lin; Santoprete, Manuele Central configurations of the five-body problem with equal masses. (English) Zbl 1204.70013 Celest. Mech. Dyn. Astron. 104, No. 4, 369-381 (2009). MSC: 70F10 70F15 PDFBibTeX XMLCite \textit{T.-L. Lee} and \textit{M. Santoprete}, Celest. Mech. Dyn. Astron. 104, No. 4, 369--381 (2009; Zbl 1204.70013) Full Text: DOI arXiv
Sun, Yang; Tao, Yu-Hui; Bai, Feng-Shan Incomplete Gröbner basis as a preconditioner for polynomial systems. (English) Zbl 1165.65026 J. Comput. Appl. Math. 226, No. 1, 2-9 (2009). Reviewer: Alyson Reeves (Bowie) MSC: 65H10 65H20 13P10 26C10 PDFBibTeX XMLCite \textit{Y. Sun} et al., J. Comput. Appl. Math. 226, No. 1, 2--9 (2009; Zbl 1165.65026) Full Text: DOI
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
Lee, T. L.; Li, T. Y.; Tsai, C. H. HOM4PS-2.0: a software package for solving polynomial systems by the polyhedral homotopy continuation method. (English) Zbl 1167.65366 Computing 83, No. 2-3, 109-133 (2008). MSC: 65H20 PDFBibTeX XMLCite \textit{T. L. Lee} et al., Computing 83, No. 2--3, 109--133 (2008; Zbl 1167.65366) Full Text: DOI
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)
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
Kuo, Y. C.; Li, T. Y. Determining dimension of the solution component that contains a computed zero of a polynomial system. (English) Zbl 1133.65028 J. Math. Anal. Appl. 338, No. 2, 840-851 (2008). MSC: 65H10 65H20 12Y05 30C15 13P05 PDFBibTeX XMLCite \textit{Y. C. Kuo} and \textit{T. Y. Li}, J. Math. Anal. Appl. 338, No. 2, 840--851 (2008; Zbl 1133.65028) Full Text: DOI
Moreno Maza, Marc; Reid, Greg J.; Scott, Robin; Wu, Wenyuan On approximate linearized triangular decompositions. (English) Zbl 1121.13032 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, 279-298 (2007). Reviewer: Alyson Reeves (Bowie) MSC: 13P10 65L07 PDFBibTeX XMLCite \textit{M. Moreno Maza} 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. 279--298 (2007; Zbl 1121.13032)
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)
Mizutani, Tomohiko; Takeda, Akiko; Kojima, Masakazu Dynamic enumeration of all mixed cells. (English) Zbl 1113.65055 Discrete Comput. Geom. 37, No. 3, 351-367 (2007). MSC: 65H10 65H20 12Y05 30C15 26C10 PDFBibTeX XMLCite \textit{T. Mizutani} et al., Discrete Comput. Geom. 37, No. 3, 351--367 (2007; Zbl 1113.65055) Full Text: DOI
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
Su, Hai-Jun; Mccarthy, J. Michael; Sosonkina, Masha; Watson, Layne T. Algorithm 857: POLSYS\(_-\)GLP – a parallel general linear product homotopy code for solving polynomial systems of equations. (English) Zbl 1230.65058 ACM Trans. Math. Softw. 32, No. 4, 561-579 (2006). MSC: 65H10 65H20 65Y05 PDFBibTeX XMLCite \textit{H.-J. Su} et al., ACM Trans. Math. Softw. 32, No. 4, 561--579 (2006; Zbl 1230.65058) Full Text: DOI
Buot, Max-Louis G.; Richards, Donald St. P. Counting and locating the solutions of polynomial systems of maximum likelihood equations. I. (English) Zbl 1120.62014 J. Symb. Comput. 41, No. 2, 234-244 (2006). MSC: 62F10 65H99 PDFBibTeX XMLCite \textit{M.-L. G. Buot} and \textit{D. St. P. Richards}, J. Symb. Comput. 41, No. 2, 234--244 (2006; Zbl 1120.62014) Full Text: DOI
Gunji, T.; Kim, S.; Fujisawa, K.; Kojima, M. PHoMpara-parallel implementation of the polyhedral homotopy continuation method for polynomial systems. (English) Zbl 1122.65048 Computing 77, No. 4, 387-411 (2006). MSC: 65H10 65H20 12Y05 26C10 30C15 PDFBibTeX XMLCite \textit{T. Gunji} et al., Computing 77, No. 4, 387--411 (2006; Zbl 1122.65048) 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
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.; 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
Kim, S.; Kojima, M. Numerical stability of path tracing in polyhedral homotopy continuation methods. (English) Zbl 1061.65042 Computing 73, No. 4, 329-348 (2004). MSC: 65H10 65H20 12Y05 26C10 30C15 PDFBibTeX XMLCite \textit{S. Kim} and \textit{M. Kojima}, Computing 73, No. 4, 329--348 (2004; Zbl 1061.65042) Full Text: DOI
Syam, Muhammed I. Finding all real zeros of polynomial systems using multi-resultant. (English) Zbl 1053.65039 J. Comput. Appl. Math. 167, No. 2, 417-428 (2004). MSC: 65H10 65H20 26C10 PDFBibTeX XMLCite \textit{M. I. Syam}, J. Comput. Appl. Math. 167, No. 2, 417--428 (2004; Zbl 1053.65039) 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
Datta, Ruchira S. Using computer algebra to find Nash equilibria. (English) Zbl 1072.68659 Sendra, J. Rafael (ed.), ISSAC 2003. Proceedings of the 2003 international symposium on symbolic and algebraic computation, Philadelphia, PA, USA, August 3–6, 2003. New York, NY: ACM Press (ISBN 1-58113-641-2/pbk). 74-79 (2003). MSC: 68W30 91A99 PDFBibTeX XMLCite \textit{R. S. Datta}, in: Proceedings of the 2003 international symposium on symbolic and algebraic computation, ISSAC 2003, Philadelphia, PA, USA, August 3--6, 2003. New York, NY: ACM Press. 74--79 (2003; Zbl 1072.68659)
Hazaveh, K.; Jeffrey, D. J.; Reid, G. J.; Watt, S. M.; Wittkopf, A. D. An exploration of homotopy solving in Maple. (English) Zbl 1047.65033 Li, Ziming (ed.) et al., Computer mathematics. Proceedings of the sixth Asian symposium (ASCM 2003), Beijing, China, April 17–19, 2003. River Edge, NJ: World Scientific (ISBN 981-238-220-8/hbk). Lect. Notes Ser. Comput. 10, 145-162 (2003). MSC: 65H10 65L05 68W30 34A34 12Y05 26C10 30C15 PDFBibTeX XMLCite \textit{K. Hazaveh} et al., Lect. Notes Ser. Comput. 10, 145--162 (2003; Zbl 1047.65033)
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)
Takeda, Akiko; Kojima, Masakazu; Fujisawa, Katsuki Enumeration of all solutions of a combinatorial linear inequality system arising from the polyhedral homotopy continuation method. (English) Zbl 1031.65074 J. Oper. Res. Soc. Japan 45, No. 1, 64-82 (2002). Reviewer: Hans Benker (Merseburg) MSC: 65K05 65H20 90C27 90C05 90C57 PDFBibTeX XMLCite \textit{A. Takeda} et al., J. Oper. Res. Soc. Japan 45, No. 1, 64--82 (2002; Zbl 1031.65074) 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)