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
Batselier, Kim; Dreesen, Philippe; de Moor, Bart The geometry of multivariate polynomial division and elimination. (English) Zbl 1269.65026 SIAM J. Matrix Anal. Appl. 34, No. 1, 102-125 (2013). MSC: 65D99 13P05 13P10 65F15 65F30 PDFBibTeX XMLCite \textit{K. Batselier} et al., SIAM J. Matrix Anal. Appl. 34, No. 1, 102--125 (2013; Zbl 1269.65026) Full Text: DOI Link
Hauenstein, Jonathan D. Numerically computing real points on algebraic sets. (English) Zbl 1269.65048 Acta Appl. Math. 125, No. 1, 105-119 (2013). Reviewer: Hang Lau (Montréal) MSC: 65H10 13P05 65H20 14Q15 PDFBibTeX XMLCite \textit{J. D. Hauenstein}, Acta Appl. Math. 125, No. 1, 105--119 (2013; Zbl 1269.65048) Full Text: DOI arXiv
Fünfzig, Christoph; Michelucci, Dominique; Foufou, Sebti Polytope-based computation of polynomial ranges. (English) Zbl 1244.65071 Comput. Aided Geom. Des. 29, No. 1, 18-29 (2012). MSC: 65H10 65H04 65G30 12D10 12Y05 13P15 90C05 PDFBibTeX XMLCite \textit{C. Fünfzig} et al., Comput. Aided Geom. Des. 29, No. 1, 18--29 (2012; Zbl 1244.65071) Full Text: DOI
Huang, Yanli; Wang, Dongming Computing intersection and self-intersection loci of parametrized surfaces using regular systems and Gröbner bases. (English) Zbl 1247.65022 Comput. Aided Geom. Des. 28, No. 9, 566-581 (2011). Reviewer: Costică Moroşanu (Iaşi) MSC: 65D18 13P10 PDFBibTeX XMLCite \textit{Y. Huang} and \textit{D. Wang}, Comput. Aided Geom. Des. 28, No. 9, 566--581 (2011; Zbl 1247.65022) Full Text: DOI
Zeng, Zhonggang The numerical greatest common divisor of univariate polynomials. (English) Zbl 1236.65051 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, 187-217 (2011). MSC: 65H04 11A05 11Y40 12D05 13P05 PDFBibTeX XMLCite \textit{Z. Zeng}, Contemp. Math. 556, 187--217 (2011; Zbl 1236.65051) Full Text: arXiv
Choulakian, Vartan Some numerical results on the rank of generic three-way arrays over \(\mathbb{R}\). (English) Zbl 1206.65143 SIAM J. Matrix Anal. Appl. 31, No. 4, 1541-1551 (2010). Reviewer: R. Militaru (Craiova) MSC: 65F30 15A69 13P10 PDFBibTeX XMLCite \textit{V. Choulakian}, SIAM J. Matrix Anal. Appl. 31, No. 4, 1541--1551 (2010; Zbl 1206.65143) Full Text: DOI arXiv
Janovská, Drahoslava; Opfer, Gerhard Quadratic one sided quaternionic polynomials. (English) Zbl 1182.65076 Simos, Theodore E. (ed.) et al., Numerical analysis and applied mathematics. International conference on numerical analysis and applied mathematics 2009, Rethymno, Crete, Greece, September 18–22, 2009. Vol. 1. Melville, NY: American Institute of Physics (AIP) (ISBN 978-0-7354-0705-3/hbk; 978-0-7354-0709-1/set). AIP Conference Proceedings 1168, 1, 367-370 (2009). MSC: 65H04 12Y05 13P05 30C15 PDFBibTeX XMLCite \textit{D. Janovská} and \textit{G. Opfer}, AIP Conf. Proc. 1168, 367--370 (2009; Zbl 1182.65076) Full Text: DOI
Zeng, Zhonggang The closedness subspace method for computing the multiplicity structure of a polynomial system. (English) Zbl 1181.65074 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, 347-362 (2009). MSC: 65H10 68W25 68W30 14Q99 74G35 13P10 PDFBibTeX XMLCite \textit{Z. Zeng}, Contemp. Math. 496, 347--362 (2009; Zbl 1181.65074)
Xu, Jingfei The multivariate spline ideal Gröbner bases on the simple partition. (Chinese. English summary) Zbl 1199.65041 J. Liaoning Norm. Univ., Nat. Sci. 31, No. 3, 270-274 (2008). MSC: 65D07 13P10 41A15 41A63 65H10 65H04 PDFBibTeX XMLCite \textit{J. Xu}, J. Liaoning Norm. Univ., Nat. Sci. 31, No. 3, 270--274 (2008; Zbl 1199.65041)
Viazminsky, C. P. Necessary and sufficient conditions for a function to be separable. (English) Zbl 1157.65014 Appl. Math. Comput. 204, No. 2, 658-670 (2008). MSC: 65D15 12Y05 13P05 PDFBibTeX XMLCite \textit{C. P. Viazminsky}, Appl. Math. Comput. 204, No. 2, 658--670 (2008; Zbl 1157.65014) Full Text: DOI
Akritas, Alkiviadis G.; Strzeboński, Adam W.; Vigklas, Panagiotis S. On the various bisection methods derived from Vincent’s theorem. (English) Zbl 1152.65055 Serdica J. Comput. 2, No. 1, 89-104 (2008). MSC: 65H05 65E05 12Y05 26C10 30C15 13P05 PDFBibTeX XMLCite \textit{A. G. Akritas} et al., Serdica J. Comput. 2, No. 1, 89--104 (2008; Zbl 1152.65055) Full Text: EuDML
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
Milev, Lozko Numerical computation of the Markov factors for the systems of polynomials with the Hermite and Laguerre weights. (English) Zbl 1137.65328 Boyanov, Todor (ed.) et al., Numerical methods and applications. 6th international conference, NMA 2006, Borovets, Bulgaria, August 20–24, 2006. Revised papers. Berlin: Springer (ISBN 978-3-540-70940-4/pbk). Lecture Notes in Computer Science 4310, 386-393 (2007). MSC: 65D20 13P05 PDFBibTeX XMLCite \textit{L. Milev}, Lect. Notes Comput. Sci. 4310, 386--393 (2007; Zbl 1137.65328) Full Text: DOI
Karcanias, N.; Fatouros, S.; Mitrouli, M.; Halikias, G. H. Approximate greatest common divisor of many polynomials, generalised resultants, and strength of approximation. (English) Zbl 1134.65334 Comput. Math. Appl. 51, No. 12, 1817-1830 (2006). MSC: 65D20 12Y05 13P05 PDFBibTeX XMLCite \textit{N. Karcanias} et al., Comput. Math. Appl. 51, No. 12, 1817--1830 (2006; Zbl 1134.65334) Full Text: DOI
Chen, Falai Applications of interval arithmetic in solving polynomial equations by Wu’s elimination method. (English) Zbl 1117.65326 Sci. China, Ser. A 48, No. 9, 1260-1273 (2005). MSC: 65H10 65G30 13P10 12Y05 PDFBibTeX XMLCite \textit{F. Chen}, Sci. China, Ser. A 48, No. 9, 1260--1273 (2005; Zbl 1117.65326)
Jiang, Zhaolin; Liu, Sanyang An algorithm for finding the minimal polynomial of a scaled circulant factor matrix. (English) Zbl 1053.65031 Math. Appl. 17, No. 1, 61-66 (2004). Reviewer: Prem Narain (Faridabad) MSC: 65F30 65F05 13P10 15A21 65F15 PDFBibTeX XMLCite \textit{Z. Jiang} and \textit{S. Liu}, Math. Appl. 17, No. 1, 61--66 (2004; Zbl 1053.65031)
Hoffman, J. William; Madden, James J.; Zhang, Hong Pseudozeros of multivariate polynomials. (English) Zbl 1017.65047 Math. Comput. 72, No. 242, 975-1002 (2003). Reviewer: Matthew He (Ft.Lauderdale) MSC: 65H05 14P10 13P05 12Y05 26C10 30C15 PDFBibTeX XMLCite \textit{J. W. Hoffman} et al., Math. Comput. 72, No. 242, 975--1002 (2003; Zbl 1017.65047) Full Text: DOI
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)
Bykov, V. I.; Kytmanov, A. M.; Osetrova, T. A. Computer algebra of polynomials: A modified method of eliminating unknowns. (English. Russian original) Zbl 0894.65021 Dokl. Math. 54, No. 2, 718-720 (1996); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 350, No. 4, 443-445 (1996). MSC: 65H10 12Y05 30C15 13P10 68W30 PDFBibTeX XMLCite \textit{V. I. Bykov} et al., Dokl. Math. 54, No. 2, 718--720 (1996; Zbl 0894.65021); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 350, No. 4, 443--445 (1996)
Bovbel’, E. I.; Rubanov, N. S. Fast number-theoretic transforms in direct products of finite fields. (Russian. English summary) Zbl 0822.65131 Dokl. Akad. Nauk Belarusi 38, No. 2, 27-30 (1994). Reviewer: G.Plonka (Rostock) MSC: 65T50 11Y40 13B05 13B25 PDFBibTeX XMLCite \textit{E. I. Bovbel'} and \textit{N. S. Rubanov}, Dokl. Akad. Nauk Belarusi 38, No. 2, 27--30 (1994; Zbl 0822.65131)