Edit Profile (opens in new tab) Hauenstein, Jonathan D. Co-Author Distance Author ID: hauenstein.jonathan-d Published as: Hauenstein, Jonathan D.; Hauenstein, Jonathan External Links: MGP · ORCID · Wikidata Documents Indexed: 90 Publications since 2008, including 1 Book 2 Contributions as Editor · 1 Further Contribution Co-Authors: 78 Co-Authors with 87 Joint Publications 2,593 Co-Co-Authors all top 5 Co-Authors 4 single-authored 33 Sommese, Andrew John 17 Wampler, Charles W. II 15 Bates, Daniel J. 9 Hao, Wenrui 7 Peterson, Chris 6 Brake, Daniel A. 6 Hu, Bei 6 Mehta, Dhagash 6 Sottile, Frank 6 Szántó, Ágnes 5 Daleo, Noah S. 5 Liddell, Alan C. jun. 5 Regan, Margaret H. 4 Rodriguez, Jose Israel 4 Sherman, Samantha N. 4 Zhang, Yongtao 3 Brake, Danielle A. 3 He, Yang-Hui Evariste 3 Ikenmeyer, Christian 3 Landsberg, Joseph Montague 3 Liu, Yuan 3 Mourrain, Bernard 3 Tang, Tingting 2 Griffin, Zachary A. 2 Harris, Katherine M. 2 Mccoy, Timothy M. 2 Oeding, Luke 2 Ottaviani, Giorgio Maria 2 Schreyer, Frank-Olaf 2 Sturmfels, Bernd 1 Ayyildiz Akoglu, Tulay 1 Bernal, Edgar A. 1 Bernardi, Alessandra 1 Besana, Gian Mario 1 Blekherman, Grigoriy 1 Brake, Dani A. 1 Chiantini, Luca 1 Collins, Joseph B. 1 Coss, Owen 1 Cox, David A. 1 D’Andrea, Carlos 1 Decker, Wolfram 1 Di Rocco, Sandra 1 Dickenstein, Alicia M. 1 Dörfler, Florian 1 Dufresne, Emilie 1 Gesmundo, Fulvio 1 Harrington, Heather A. 1 Haywood, Ian 1 Hein, Nickolas 1 Helmer, Martin 1 Hong, Hoon 1 Huang, Rijun 1 Kevrekidis, Panayotis G. 1 Kotsireas, Ilias S. 1 Kulkarni, Avinash 1 Lerario, Antonio 1 Levandovskyy, Viktor 1 Leykin, Anton 1 Lundberg, Erik 1 Mahdi, Adam 1 Manivel, Laurent 1 Matusevich, Laura Felicia 1 McPherson, Sanesha 1 Migliore, Juan Carlos 1 Molzahn, Daniel K. 1 Nezhad, Ali Mohammad 1 Niemerg, Matthew E. 1 Ottem, John Christian 1 Pan, Victor Yakovlevich 1 Pessoa, Claudio 1 Pfister, Gerhard 1 Ranestad, Kristian 1 Schenck, Hal 1 Sertöz, Emre Can 1 Shu, Chi-Wang 1 Sidman, Jessica 1 Stillman, Michael Eugene 1 Szendrői, Balázs 1 Terlaky, Tamás 1 Tripoli, Paolo 1 Vinzant, Cynthia 1 Xu, Zhiliang 1 Zhang, Yang 1 Zhang, Yi all top 5 Serials 10 Journal of Symbolic Computation 9 Applied Mathematics and Computation 4 Experimental Mathematics 4 Foundations of Computational Mathematics 3 Numerical Algorithms 3 Journal of High Energy Physics 3 Advances in Geometry 3 SIAM Journal on Applied Algebra and Geometry 2 Mathematics of Computation 2 ACM Transactions on Mathematical Software 2 Journal of Computational and Applied Mathematics 2 SIAM Journal on Numerical Analysis 2 Vietnam Journal of Mathematics 1 Journal of Computational Physics 1 Bulletin of the London Mathematical Society 1 Compositio Mathematica 1 Journal of Pure and Applied Algebra 1 Journal für die Reine und Angewandte Mathematik 1 Mathematics of Operations Research 1 Advances in Applied Mathematics 1 Acta Applicandae Mathematicae 1 Applied Numerical Mathematics 1 Journal of Scientific Computing 1 Differential Geometry and its Applications 1 Notices of the American Mathematical Society 1 Chaos 1 Mechanism and Machine Theory 1 Nonlinear Analysis. Real World Applications 1 Portugaliae Mathematica. Nova Série 1 Software - Environments - Tools 1 Mathematics in Computer Science 1 Discrete and Continuous Dynamical Systems. Series S 1 ACM Communications in Computer Algebra 1 Journal of Algebraic Statistics 1 CBMS Regional Conference Series in Mathematics 1 Results in Applied Mathematics all top 5 Fields 64 Algebraic geometry (14-XX) 56 Numerical analysis (65-XX) 35 Computer science (68-XX) 22 Commutative algebra (13-XX) 7 Field theory and polynomials (12-XX) 7 Linear and multilinear algebra; matrix theory (15-XX) 6 Biology and other natural sciences (92-XX) 4 Functions of a complex variable (30-XX) 4 Partial differential equations (35-XX) 4 Quantum theory (81-XX) 4 Operations research, mathematical programming (90-XX) 3 Ordinary differential equations (34-XX) 2 General and overarching topics; collections (00-XX) 2 Mechanics of particles and systems (70-XX) 1 Mathematical logic and foundations (03-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Convex and discrete geometry (52-XX) 1 Statistics (62-XX) 1 Fluid mechanics (76-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Relativity and gravitational theory (83-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 80 Publications have been cited 1,011 times in 439 Documents Cited by ▼ Year ▼ Numerically solving polynomial systems with Bertini. Zbl 1295.65057Bates, Daniel J.; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W. 116 2013 Software for numerical algebraic geometry: a paradigm and progress towards its implementation. Zbl 1143.65344Bates, Daniel J.; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W. II 66 2008 Algorithm 921: alphaCertified: certifying solutions to polynomial systems. Zbl 1365.65148Hauenstein, Jonathan D.; Sottile, Frank 51 2012 Adaptive multiprecision path tracking. Zbl 1162.65026Bates, Daniel J.; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler II, Charles W. 41 2008 Regeneration homotopies for solving systems of polynomials. Zbl 1221.65121Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W. 39 2011 Bifurcation for a free boundary problem modeling the growth of a tumor with a necrotic core. Zbl 1238.35193Hao, Wenrui; Hauenstein, Jonathan D.; Hu, Bei; Liu, Yuan; Sommese, Andrew J.; Zhang, Yong-Tao 38 2012 Isosingular sets and deflation. Zbl 1276.65029Hauenstein, Jonathan D.; Wampler, Charles W. 30 2013 Witness sets of projections. Zbl 1203.14072Hauenstein, Jonathan D.; Sommese, Andrew J. 30 2010 Continuation along bifurcation branches for a tumor model with a necrotic core. Zbl 1328.92032Hao, Wenrui; Hauenstein, Jonathan D.; Hu, Bei; Liu, Yuan; Sommese, Andrew J.; Zhang, Yong-Tao 25 2012 A numerical local dimension test for points on the solution set of a system of polynomial equations. Zbl 1211.14066Bates, Daniel J.; Hauenstein, Jonathan D.; Peterson, Chris; Sommese, Andrew J. 25 2009 Homotopy techniques for tensor decomposition and perfect identifiability. Zbl 1440.15019Hauenstein, Jonathan D.; Oeding, Luke; Ottaviani, Giorgio; Sommese, Andrew J. 24 2019 A homotopy method based on WENO schemes for solving steady state problems of hyperbolic conservation laws. Zbl 1349.65558Hao, Wenrui; Hauenstein, Jonathan D.; Shu, Chi-Wang; Sommese, Andrew J.; Xu, Zhiliang; Zhang, Yong-Tao 24 2013 Algebraic geometrization of the Kuramoto model: equilibria and stability analysis. Zbl 1374.34115Mehta, Dhagash; Daleo, Noah S.; Dörfler, Florian; Hauenstein, Jonathan D. 24 2015 Algebraic boundaries of Hilbert’s SOS cones. Zbl 1273.13043Blekherman, Grigoriy; Hauenstein, Jonathan; Ottem, John Christian; Ranestad, Kristian; Sturmfels, Bernd 23 2012 A bootstrapping approach for computing multiple solutions of differential equations. Zbl 1294.65085Hao, Wenrui; Hauenstein, Jonathan D.; Hu, Bei; Sommese, Andrew J. 22 2014 A three-dimensional steady-state tumor system. Zbl 1238.92019Hao, Wenrui; Hauenstein, Jonathan D.; Hu, Bei; Sommese, Andrew J. 21 2011 Numerically computing real points on algebraic sets. Zbl 1269.65048Hauenstein, Jonathan D. 21 2013 Efficient path tracking methods. Zbl 1230.65059Bates, Daniel J.; Hauenstein, Jonathan D.; Sommese, Andrew J. 20 2011 Stepsize control for path tracking. Zbl 1181.65071Bates, Daniel J.; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W. II 20 2009 Computing steady-state solutions for a free boundary problem modeling tumor growth by Stokes equation. Zbl 1303.92044Hao, Wenrui; Hauenstein, Jonathan D.; Hu, Bei; McCoy, Timothy; Sommese, Andrew J. 20 2013 Regenerative cascade homotopies for solving polynomial systems. Zbl 1231.65190Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W. 17 2011 Maximum likelihood for matrices with rank constraints. Zbl 1345.62043Hauenstein, Jonathan; Rodriguez, Jose Israel; Sturmfels, Bernd 16 2014 Membership tests for images of algebraic sets by linear projections. Zbl 1285.14066Hauenstein, Jonathan D.; Sommese, Andrew J. 16 2013 Bertini_real: software for one- and two-dimensional real algebraic sets. Zbl 1437.14005Brake, Daniel A.; Bates, Daniel J.; Hao, Wenrui; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W. 13 2014 Equations for lower bounds on border rank. Zbl 1361.68098Hauenstein, Jonathan D.; Ikenmeyer, Christian; Landsberg, J. M. 12 2013 Recovering exact results from inexact numerical data in algebraic geometry. Zbl 1284.14084Bates, Daniel J.; Hauenstein, Jonathan D.; McCoy, Timothy M.; Peterson, Chris; Sommese, Andrew J. 12 2013 Numerical elimination and moduli space of vacua. Zbl 1342.83004Hauenstein, Jonathan; He, Yang-Hui; Mehta, Dhagash 11 2013 Cell decomposition of almost smooth real algebraic surfaces. Zbl 1271.65031Besana, Gian Mario; Di Rocco, Sandra; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W. 11 2013 An a posteriori certification algorithm for Newton homotopies. Zbl 1325.65074Hauenstein, Jonathan D.; Haywood, Ian; Liddell, Alan C. jun. 10 2014 Tensor decomposition and homotopy continuation. Zbl 1377.65057Bernardi, Alessandra; Daleo, Noah S.; Hauenstein, Jonathan D.; Mourrain, Bernard 10 2017 Unification and extension of intersection algorithms in numerical algebraic geometry. Zbl 1411.65075Hauenstein, Jonathan D.; Wampler, Charles W. 9 2017 Certifying isolated singular points and their multiplicity structure. Zbl 1345.68286Hauenstein, Jonathan D.; Mourrain, Bernard; Szanto, Agnes 9 2015 Certified predictor-corrector tracking for Newton homotopies. Zbl 1329.65110Hauenstein, Jonathan D.; Liddell, Alan C. 9 2016 Experiments on the zeros of harmonic polynomials using certified counting. Zbl 1365.30002Hauenstein, J. D.; Lerario, A.; Lundberg, E.; Mehta, D. 8 2015 On deflation and multiplicity structure. Zbl 1387.13063Hauenstein, Jonathan D.; Mourrain, Bernard; Szanto, Agnes 8 2017 Numerical computation of Galois groups. Zbl 1442.14186Hauenstein, Jonathan D.; Rodriguez, Jose Israel; Sottile, Frank 8 2018 Mechanism mobility and a local dimension test. Zbl 1273.70004Wampler, Charles W.; Hauenstein, Jonathan D.; Sommese, Andrew J. 8 2011 Certifying solutions to overdetermined and singular polynomial systems over \(\mathbb{Q}\). Zbl 1415.65121Ayyildiz Akoglu, Tulay; Hauenstein, Jonathan D.; Szanto, Agnes 7 2018 Numerically deciding the arithmetically Cohen-Macaulayness of a projective scheme. Zbl 1329.14108Daleo, Noah S.; Hauenstein, Jonathan D. 7 2016 Locating and counting equilibria of the Kuramoto model with rank-one coupling. Zbl 1428.65003Coss, Owen; Hauenstein, Jonathan D.; Hong, Hoon; Molzahn, Daniel K. 7 2018 Numerical decomposition of the rank-deficiency set of a matrix of multivariate polynomials. Zbl 1191.14071Bates, Daniel J.; Hauenstein, Jonathan D.; Peterson, Chris; Sommese, Andrew J. 6 2009 Comparison of probabilistic algorithms for analyzing the components of an affine algebraic variety. Zbl 1410.65205Bates, Daniel J.; Decker, Wolfram; Hauenstein, Jonathan D.; Peterson, Chris; Pfister, Gerhard; Schreyer, Frank-Olaf; Sommese, Andrew J.; Wampler, Charles W. 6 2014 Real solutions to systems of polynomial equations and parameter continuation. Zbl 1309.65056Griffin, Zachary A.; Hauenstein, Jonathan D. 6 2015 Numerical computation of the Hilbert function and regularity of a zero dimensional scheme. Zbl 1315.13032Griffin, Zachary A.; Hauenstein, Jonathan D.; Peterson, Chris; Sommese, Andrew J. 6 2014 Multiprojective witness sets and a trace test. Zbl 1448.65054Hauenstein, Jonathan D.; Rodriguez, Jose Israel 6 2020 Numerical algebraic geometry: a new perspective on gauge and string theories. Zbl 1397.81271Mehta, Dhagash; He, Yang-Hui; Hauenstein, Jonathan D. 6 2012 Polynomials and the exponent of matrix multiplication. Zbl 1404.15020Chiantini, Luca; Hauenstein, Jonathan D.; Ikenmeyer, Christian; Landsberg, Joseph M.; Ottaviani, Giorgio 6 2018 Newton polytopes and witness sets. Zbl 1304.14077Hauenstein, Jonathan D.; Sottile, Frank 6 2014 Algorithm 976: Bertini_real: numerical decomposition of real algebraic curves and surfaces. Zbl 1484.14109Brake, Daniel A.; Bates, Daniel J.; Hao, Wenrui; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W. 6 2017 Global structure of curves from generalized unitarity cut of three-loop diagrams. Zbl 1388.81392Hauenstein, Jonathan D.; Huang, Rijun; Mehta, Dhagash; Zhang, Yang 5 2015 Foreword. What is numerical algebraic geometry? Zbl 1360.00098 5 2017 Multiple stable steady states of a reaction-diffusion model on zebrafish dorsal-ventral patterning. Zbl 1218.65043Hao, Wenrui; Hauenstein, Jonathan D.; Hu, Bei; Liu, Yuan; Sommese, Andrew J.; Zhang, Yong-Tao 5 2011 Numerically testing generically reduced projective schemes for the arithmetic Gorenstein property. Zbl 1460.14106Daleo, Noah S.; Hauenstein, Jonathan D. 4 2016 Complexity of linear circuits and geometry. Zbl 1345.68157Gesmundo, Fulvio; Hauenstein, Jonathan D.; Ikenmeyer, Christian; Landsberg, J. M. 4 2016 A hybrid symbolic-numerical approach to the center-focus problem. Zbl 1372.14053Mahdi, Adam; Pessoa, Claudio; Hauenstein, Jonathan D. 4 2017 Validating the completeness of the real solution set of a system of polynomial equations. Zbl 1362.13027Brake, Daniel A.; Hauenstein, Jonathan D.; Liddell, Alan C. 4 2016 A parallel endgame. Zbl 1238.14007Bates, Daniel J.; Hauenstein, Jonathan D.; Sommese, Andrew J. 4 2011 A primal-dual formulation for certifiable computations in Schubert calculus. Zbl 1360.14126Hauenstein, Jonathan D.; Hein, Nickolas; Sottile, Frank 4 2016 Numerically intersecting algebraic varieties via witness sets. Zbl 1295.14054Hauenstein, Jonathan D.; Wampler, Charles W. 4 2013 Decomposing solution sets of polynomial systems using derivatives. Zbl 1434.14022Brake, Daniel A.; Hauenstein, Jonathan D.; Liddell, Alan C. jun. 3 2016 Certifying solutions to square systems of polynomial-exponential equations. Zbl 1357.14071Hauenstein, Jonathan D.; Levandovskyy, Viktor 3 2017 Adaptive strategies for solving parameterized systems using homotopy continuation. Zbl 1427.65086Hauenstein, Jonathan D.; Regan, Margaret H. 3 2018 Computations and equations for Segre-Grassmann hypersurfaces. Zbl 1350.14034Daleo, Noah S.; Hauenstein, Jonathan D.; Oeding, Luke 3 2016 Applications of polynomial systems. With contributions by Carlos D’Andrea, Alicia Dickenstein, Jonathan Hauenstein, Hal Schenck, and Jessica Sidman. Zbl 1469.13001Cox, David A. 2 2020 Real monodromy action. Zbl 1433.65094Hauenstein, Jonathan D.; Regan, Margaret H. 2 2020 Exceptional Stewart-Gough platforms, Segre embeddings, and the special Euclidean group. Zbl 1455.65076Hauenstein, Jonathan D.; Sherman, Samantha N.; Wampler, Charles W. 2 2018 A numerical toolkit for multiprojective varieties. Zbl 1451.65065Hauenstein, Jonathan D.; Leykin, Anton; Rodriguez, Jose Israel; Sottile, Frank 2 2021 On computing a cell decomposition of a real surface containing infinitely many singularities. Zbl 1437.14061Bates, Daniel J.; Brake, Daniel A.; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W. 2 2014 Smooth points on semi-algebraic sets. Zbl 1499.14098Harris, Katherine; Hauenstein, Jonathan D.; Szanto, Agnes 2 2020 Numerical computation of the dimensions of the cohomology of twists of ideal sheaves. Zbl 1185.14041Hauenstein, Jonathan D.; Migliore, Juan C.; Peterson, Chris; Sommese, Andrew J. 2 2009 Numerical local irreducible decomposition. Zbl 1460.14131Brake, Daniel A.; Hauenstein, Jonathan D.; Sommese, Andrew J. 1 2016 A note on global Newton iteration over Archimedean and non-Archimedean fields. Zbl 1416.68221Hauenstein, Jonathan D.; Pan, Victor Y.; Szanto, Agnes 1 2014 Homotopies for connected components of algebraic sets with application to computing critical sets. Zbl 1497.14121Bates, Daniel J.; Brake, Dani A.; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W. 1 2017 Machine learning the real discriminant locus. Zbl 1504.14104Bernal, Edgar A.; Hauenstein, Jonathan D.; Mehta, Dhagash; Regan, Margaret H.; Tang, Tingting 1 2023 Evaluating and differentiating a polynomial using a pseudo-witness set. Zbl 1503.65111Hauenstein, Jonathan D.; Regan, Margaret H. 1 2020 On the equations defining some Hilbert schemes. Zbl 1485.14111Hauenstein, Jonathan D.; Manivel, Laurent; Szendrői, Balázs 1 2022 Binomiality testing and computing sparse polynomials via witness sets. Zbl 1498.14152Hauenstein, Jonathan D.; Matusevich, Laura; Peterson, Chris; Sherman, Samantha N. 1 2022 A counter example to an ideal membership test. Zbl 1410.68411Hauenstein, Jonathan D. 1 2010 Singular value decomposition of complexes. Zbl 1428.14091Brake, Danielle A.; Hauenstein, Jonathan D.; Schreyer, Frank-Olaf; Sommese, Andrew J.; Stillman, Michael E. 1 2019 Certifying reality of projections. Zbl 1396.14053Hauenstein, Jonathan D.; Kulkarni, Avinash; Sertöz, Emre C.; Sherman, Samantha N. 1 2018 Machine learning the real discriminant locus. Zbl 1504.14104Bernal, Edgar A.; Hauenstein, Jonathan D.; Mehta, Dhagash; Regan, Margaret H.; Tang, Tingting 1 2023 On the equations defining some Hilbert schemes. Zbl 1485.14111Hauenstein, Jonathan D.; Manivel, Laurent; Szendrői, Balázs 1 2022 Binomiality testing and computing sparse polynomials via witness sets. Zbl 1498.14152Hauenstein, Jonathan D.; Matusevich, Laura; Peterson, Chris; Sherman, Samantha N. 1 2022 A numerical toolkit for multiprojective varieties. Zbl 1451.65065Hauenstein, Jonathan D.; Leykin, Anton; Rodriguez, Jose Israel; Sottile, Frank 2 2021 Multiprojective witness sets and a trace test. Zbl 1448.65054Hauenstein, Jonathan D.; Rodriguez, Jose Israel 6 2020 Applications of polynomial systems. With contributions by Carlos D’Andrea, Alicia Dickenstein, Jonathan Hauenstein, Hal Schenck, and Jessica Sidman. Zbl 1469.13001Cox, David A. 2 2020 Real monodromy action. Zbl 1433.65094Hauenstein, Jonathan D.; Regan, Margaret H. 2 2020 Smooth points on semi-algebraic sets. Zbl 1499.14098Harris, Katherine; Hauenstein, Jonathan D.; Szanto, Agnes 2 2020 Evaluating and differentiating a polynomial using a pseudo-witness set. Zbl 1503.65111Hauenstein, Jonathan D.; Regan, Margaret H. 1 2020 Homotopy techniques for tensor decomposition and perfect identifiability. Zbl 1440.15019Hauenstein, Jonathan D.; Oeding, Luke; Ottaviani, Giorgio; Sommese, Andrew J. 24 2019 Singular value decomposition of complexes. Zbl 1428.14091Brake, Danielle A.; Hauenstein, Jonathan D.; Schreyer, Frank-Olaf; Sommese, Andrew J.; Stillman, Michael E. 1 2019 Numerical computation of Galois groups. Zbl 1442.14186Hauenstein, Jonathan D.; Rodriguez, Jose Israel; Sottile, Frank 8 2018 Certifying solutions to overdetermined and singular polynomial systems over \(\mathbb{Q}\). Zbl 1415.65121Ayyildiz Akoglu, Tulay; Hauenstein, Jonathan D.; Szanto, Agnes 7 2018 Locating and counting equilibria of the Kuramoto model with rank-one coupling. Zbl 1428.65003Coss, Owen; Hauenstein, Jonathan D.; Hong, Hoon; Molzahn, Daniel K. 7 2018 Polynomials and the exponent of matrix multiplication. Zbl 1404.15020Chiantini, Luca; Hauenstein, Jonathan D.; Ikenmeyer, Christian; Landsberg, Joseph M.; Ottaviani, Giorgio 6 2018 Adaptive strategies for solving parameterized systems using homotopy continuation. Zbl 1427.65086Hauenstein, Jonathan D.; Regan, Margaret H. 3 2018 Exceptional Stewart-Gough platforms, Segre embeddings, and the special Euclidean group. Zbl 1455.65076Hauenstein, Jonathan D.; Sherman, Samantha N.; Wampler, Charles W. 2 2018 Certifying reality of projections. Zbl 1396.14053Hauenstein, Jonathan D.; Kulkarni, Avinash; Sertöz, Emre C.; Sherman, Samantha N. 1 2018 Tensor decomposition and homotopy continuation. Zbl 1377.65057Bernardi, Alessandra; Daleo, Noah S.; Hauenstein, Jonathan D.; Mourrain, Bernard 10 2017 Unification and extension of intersection algorithms in numerical algebraic geometry. Zbl 1411.65075Hauenstein, Jonathan D.; Wampler, Charles W. 9 2017 On deflation and multiplicity structure. Zbl 1387.13063Hauenstein, Jonathan D.; Mourrain, Bernard; Szanto, Agnes 8 2017 Algorithm 976: Bertini_real: numerical decomposition of real algebraic curves and surfaces. Zbl 1484.14109Brake, Daniel A.; Bates, Daniel J.; Hao, Wenrui; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W. 6 2017 Foreword. What is numerical algebraic geometry? Zbl 1360.00098 5 2017 A hybrid symbolic-numerical approach to the center-focus problem. Zbl 1372.14053Mahdi, Adam; Pessoa, Claudio; Hauenstein, Jonathan D. 4 2017 Certifying solutions to square systems of polynomial-exponential equations. Zbl 1357.14071Hauenstein, Jonathan D.; Levandovskyy, Viktor 3 2017 Homotopies for connected components of algebraic sets with application to computing critical sets. Zbl 1497.14121Bates, Daniel J.; Brake, Dani A.; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W. 1 2017 Certified predictor-corrector tracking for Newton homotopies. Zbl 1329.65110Hauenstein, Jonathan D.; Liddell, Alan C. 9 2016 Numerically deciding the arithmetically Cohen-Macaulayness of a projective scheme. Zbl 1329.14108Daleo, Noah S.; Hauenstein, Jonathan D. 7 2016 Numerically testing generically reduced projective schemes for the arithmetic Gorenstein property. Zbl 1460.14106Daleo, Noah S.; Hauenstein, Jonathan D. 4 2016 Complexity of linear circuits and geometry. Zbl 1345.68157Gesmundo, Fulvio; Hauenstein, Jonathan D.; Ikenmeyer, Christian; Landsberg, J. M. 4 2016 Validating the completeness of the real solution set of a system of polynomial equations. Zbl 1362.13027Brake, Daniel A.; Hauenstein, Jonathan D.; Liddell, Alan C. 4 2016 A primal-dual formulation for certifiable computations in Schubert calculus. Zbl 1360.14126Hauenstein, Jonathan D.; Hein, Nickolas; Sottile, Frank 4 2016 Decomposing solution sets of polynomial systems using derivatives. Zbl 1434.14022Brake, Daniel A.; Hauenstein, Jonathan D.; Liddell, Alan C. jun. 3 2016 Computations and equations for Segre-Grassmann hypersurfaces. Zbl 1350.14034Daleo, Noah S.; Hauenstein, Jonathan D.; Oeding, Luke 3 2016 Numerical local irreducible decomposition. Zbl 1460.14131Brake, Daniel A.; Hauenstein, Jonathan D.; Sommese, Andrew J. 1 2016 Algebraic geometrization of the Kuramoto model: equilibria and stability analysis. Zbl 1374.34115Mehta, Dhagash; Daleo, Noah S.; Dörfler, Florian; Hauenstein, Jonathan D. 24 2015 Certifying isolated singular points and their multiplicity structure. Zbl 1345.68286Hauenstein, Jonathan D.; Mourrain, Bernard; Szanto, Agnes 9 2015 Experiments on the zeros of harmonic polynomials using certified counting. Zbl 1365.30002Hauenstein, J. D.; Lerario, A.; Lundberg, E.; Mehta, D. 8 2015 Real solutions to systems of polynomial equations and parameter continuation. Zbl 1309.65056Griffin, Zachary A.; Hauenstein, Jonathan D. 6 2015 Global structure of curves from generalized unitarity cut of three-loop diagrams. Zbl 1388.81392Hauenstein, Jonathan D.; Huang, Rijun; Mehta, Dhagash; Zhang, Yang 5 2015 A bootstrapping approach for computing multiple solutions of differential equations. Zbl 1294.65085Hao, Wenrui; Hauenstein, Jonathan D.; Hu, Bei; Sommese, Andrew J. 22 2014 Maximum likelihood for matrices with rank constraints. Zbl 1345.62043Hauenstein, Jonathan; Rodriguez, Jose Israel; Sturmfels, Bernd 16 2014 Bertini_real: software for one- and two-dimensional real algebraic sets. Zbl 1437.14005Brake, Daniel A.; Bates, Daniel J.; Hao, Wenrui; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W. 13 2014 An a posteriori certification algorithm for Newton homotopies. Zbl 1325.65074Hauenstein, Jonathan D.; Haywood, Ian; Liddell, Alan C. jun. 10 2014 Comparison of probabilistic algorithms for analyzing the components of an affine algebraic variety. Zbl 1410.65205Bates, Daniel J.; Decker, Wolfram; Hauenstein, Jonathan D.; Peterson, Chris; Pfister, Gerhard; Schreyer, Frank-Olaf; Sommese, Andrew J.; Wampler, Charles W. 6 2014 Numerical computation of the Hilbert function and regularity of a zero dimensional scheme. Zbl 1315.13032Griffin, Zachary A.; Hauenstein, Jonathan D.; Peterson, Chris; Sommese, Andrew J. 6 2014 Newton polytopes and witness sets. Zbl 1304.14077Hauenstein, Jonathan D.; Sottile, Frank 6 2014 On computing a cell decomposition of a real surface containing infinitely many singularities. Zbl 1437.14061Bates, Daniel J.; Brake, Daniel A.; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W. 2 2014 A note on global Newton iteration over Archimedean and non-Archimedean fields. Zbl 1416.68221Hauenstein, Jonathan D.; Pan, Victor Y.; Szanto, Agnes 1 2014 Numerically solving polynomial systems with Bertini. Zbl 1295.65057Bates, Daniel J.; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W. 116 2013 Isosingular sets and deflation. Zbl 1276.65029Hauenstein, Jonathan D.; Wampler, Charles W. 30 2013 A homotopy method based on WENO schemes for solving steady state problems of hyperbolic conservation laws. Zbl 1349.65558Hao, Wenrui; Hauenstein, Jonathan D.; Shu, Chi-Wang; Sommese, Andrew J.; Xu, Zhiliang; Zhang, Yong-Tao 24 2013 Numerically computing real points on algebraic sets. Zbl 1269.65048Hauenstein, Jonathan D. 21 2013 Computing steady-state solutions for a free boundary problem modeling tumor growth by Stokes equation. Zbl 1303.92044Hao, Wenrui; Hauenstein, Jonathan D.; Hu, Bei; McCoy, Timothy; Sommese, Andrew J. 20 2013 Membership tests for images of algebraic sets by linear projections. Zbl 1285.14066Hauenstein, Jonathan D.; Sommese, Andrew J. 16 2013 Equations for lower bounds on border rank. Zbl 1361.68098Hauenstein, Jonathan D.; Ikenmeyer, Christian; Landsberg, J. M. 12 2013 Recovering exact results from inexact numerical data in algebraic geometry. Zbl 1284.14084Bates, Daniel J.; Hauenstein, Jonathan D.; McCoy, Timothy M.; Peterson, Chris; Sommese, Andrew J. 12 2013 Numerical elimination and moduli space of vacua. Zbl 1342.83004Hauenstein, Jonathan; He, Yang-Hui; Mehta, Dhagash 11 2013 Cell decomposition of almost smooth real algebraic surfaces. Zbl 1271.65031Besana, Gian Mario; Di Rocco, Sandra; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W. 11 2013 Numerically intersecting algebraic varieties via witness sets. Zbl 1295.14054Hauenstein, Jonathan D.; Wampler, Charles W. 4 2013 Algorithm 921: alphaCertified: certifying solutions to polynomial systems. Zbl 1365.65148Hauenstein, Jonathan D.; Sottile, Frank 51 2012 Bifurcation for a free boundary problem modeling the growth of a tumor with a necrotic core. Zbl 1238.35193Hao, Wenrui; Hauenstein, Jonathan D.; Hu, Bei; Liu, Yuan; Sommese, Andrew J.; Zhang, Yong-Tao 38 2012 Continuation along bifurcation branches for a tumor model with a necrotic core. Zbl 1328.92032Hao, Wenrui; Hauenstein, Jonathan D.; Hu, Bei; Liu, Yuan; Sommese, Andrew J.; Zhang, Yong-Tao 25 2012 Algebraic boundaries of Hilbert’s SOS cones. Zbl 1273.13043Blekherman, Grigoriy; Hauenstein, Jonathan; Ottem, John Christian; Ranestad, Kristian; Sturmfels, Bernd 23 2012 Numerical algebraic geometry: a new perspective on gauge and string theories. Zbl 1397.81271Mehta, Dhagash; He, Yang-Hui; Hauenstein, Jonathan D. 6 2012 Regeneration homotopies for solving systems of polynomials. Zbl 1221.65121Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W. 39 2011 A three-dimensional steady-state tumor system. Zbl 1238.92019Hao, Wenrui; Hauenstein, Jonathan D.; Hu, Bei; Sommese, Andrew J. 21 2011 Efficient path tracking methods. Zbl 1230.65059Bates, Daniel J.; Hauenstein, Jonathan D.; Sommese, Andrew J. 20 2011 Regenerative cascade homotopies for solving polynomial systems. Zbl 1231.65190Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W. 17 2011 Mechanism mobility and a local dimension test. Zbl 1273.70004Wampler, Charles W.; Hauenstein, Jonathan D.; Sommese, Andrew J. 8 2011 Multiple stable steady states of a reaction-diffusion model on zebrafish dorsal-ventral patterning. Zbl 1218.65043Hao, Wenrui; Hauenstein, Jonathan D.; Hu, Bei; Liu, Yuan; Sommese, Andrew J.; Zhang, Yong-Tao 5 2011 A parallel endgame. Zbl 1238.14007Bates, Daniel J.; Hauenstein, Jonathan D.; Sommese, Andrew J. 4 2011 Witness sets of projections. Zbl 1203.14072Hauenstein, Jonathan D.; Sommese, Andrew J. 30 2010 A counter example to an ideal membership test. Zbl 1410.68411Hauenstein, Jonathan D. 1 2010 A numerical local dimension test for points on the solution set of a system of polynomial equations. Zbl 1211.14066Bates, Daniel J.; Hauenstein, Jonathan D.; Peterson, Chris; Sommese, Andrew J. 25 2009 Stepsize control for path tracking. Zbl 1181.65071Bates, Daniel J.; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W. II 20 2009 Numerical decomposition of the rank-deficiency set of a matrix of multivariate polynomials. Zbl 1191.14071Bates, Daniel J.; Hauenstein, Jonathan D.; Peterson, Chris; Sommese, Andrew J. 6 2009 Numerical computation of the dimensions of the cohomology of twists of ideal sheaves. Zbl 1185.14041Hauenstein, Jonathan D.; Migliore, Juan C.; Peterson, Chris; Sommese, Andrew J. 2 2009 Software for numerical algebraic geometry: a paradigm and progress towards its implementation. Zbl 1143.65344Bates, Daniel J.; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler, Charles W. II 66 2008 Adaptive multiprecision path tracking. Zbl 1162.65026Bates, Daniel J.; Hauenstein, Jonathan D.; Sommese, Andrew J.; Wampler II, Charles W. 41 2008 all cited Publications top 5 cited Publications all top 5 Cited by 604 Authors 55 Hauenstein, Jonathan D. 26 Hao, Wenrui 22 Sommese, Andrew John 17 Sottile, Frank 16 Sturmfels, Bernd 15 Hu, Bei 15 Rodriguez, Jose Israel 13 Bates, Daniel J. 12 Peterson, Chris 11 Bernardi, Alessandra 11 Leykin, Anton 11 Wampler, Charles W. II 10 Wu, Wenyuan 9 Eklund, David 9 Mehta, Dhagash 9 Michałek, Mateusz 8 He, Yang-Hui Evariste 7 Landsberg, Joseph Montague 7 Szántó, Ágnes 6 Blekherman, Grigoriy 6 Di Rocco, Sandra 6 Mourrain, Bernard 6 Safey El Din, Mohab 6 Telen, Simon 6 Zhang, Yongtao 5 Angelini, Elena 5 Ballico, Edoardo 5 Breiding, Paul 5 Chen, Tianran 5 Helmer, Martin 5 Huang, Yaodan 5 Kubjas, Kaie 5 Niemerg, Matthew E. 5 Ottaviani, Giorgio Maria 5 Verschelde, Jan 5 Zhang, Zhengce 4 Brysiewicz, Taylor 4 Chen, Changbo 4 Chiantini, Luca 4 del Campo, Abraham Martín 4 Feng, Yong 4 Heaton, Alexander 4 Hein, Nickolas 4 Ikenmeyer, Christian 4 Krone, Robert 4 Lee, Tsung-Lin 4 Li, Tien-Yien 4 Regan, Margaret H. 4 Timme, Sascha 4 Townsend, Alex 4 Vannieuwenhoven, Nick 4 Vázquez-Leal, Héctor 4 Wu, Junde 4 Xing, Ruixiang 4 Zeng, Zhonggang 4 Zhang, Lei 3 Améndola, Carlos 3 Ayyildiz Akoglu, Tulay 3 Batselier, Kim 3 Beltrán, Carlos E. 3 Burr, Michael A. 3 Chen, Hongbin 3 Chen, Qipin 3 Daleo, Noah S. 3 Delabays, Robin 3 DeVille, Lee 3 Draisma, Jan 3 Faugère, Jean-Charles 3 Gesmundo, Fulvio 3 Gross, Elizabeth 3 Harrington, Heather A. 3 He, Yinnian 3 Horobeţ, Emil 3 Jacquod, Philippe 3 Jejjala, Vishnu 3 Lairez, Pierre 3 Li, Shuwang 3 Liddell, Alan C. jun. 3 Lim, Lek-Heng 3 Lin, Guang 3 Matti, Cyril 3 Mella, Massimiliano 3 Nelson, Brent D. 3 Oeding, Luke 3 Ranestad, Kristian 3 Schost, Éric 3 Sertöz, Emre Can 3 Sherman, Samantha N. 3 Shu, Chi-Wang 3 Song, Huijuan 3 Van Barel, Marc 3 Vinzant, Cynthia 3 Vu, Thi Xuan 3 Wang, Botong 3 Wang, Dongming 3 Wang, Zejia 3 Weinstein, Madeleine 3 Yin, Jianyuan 3 Yu, Bo 3 Zhang, Pingwen ...and 504 more Authors all top 5 Cited in 141 Serials 48 Journal of Symbolic Computation 15 Mathematics of Computation 13 Journal of High Energy Physics 13 Foundations of Computational Mathematics 12 Applied Mathematics and Computation 12 Journal of Computational and Applied Mathematics 12 SIAM Journal on Applied Algebra and Geometry 11 Journal of Scientific Computing 10 Advances in Applied Mathematics 10 Chaos 9 Journal of Computational Physics 8 Journal of Pure and Applied Algebra 8 Numerical Algorithms 8 Experimental Mathematics 7 Journal of Differential Equations 6 Linear Algebra and its Applications 5 Computers & Mathematics with Applications 5 Mechanism and Machine Theory 5 Nonlinear Analysis. Real World Applications 5 Journal of Algebra and its Applications 5 Mathematics in Computer Science 4 Journal of Algebra 4 Theoretical Computer Science 4 SIAM Journal on Optimization 4 SIAM Journal on Applied Dynamical Systems 4 Arnold Mathematical Journal 4 European Journal of Mathematics 3 Journal of Mathematical Analysis and Applications 3 Journal of Mathematical Biology 3 Journal of Mathematical Physics 3 Nonlinearity 3 Bulletin of Mathematical Biology 3 Annali di Matematica Pura ed Applicata. Serie Quarta 3 Transactions of the American Mathematical Society 3 SIAM Journal on Matrix Analysis and Applications 3 SIAM Journal on Scientific Computing 3 Vietnam Journal of Mathematics 3 Advances in Geometry 3 Discrete and Continuous Dynamical Systems. Series B 3 Journal of Systems Science and Complexity 2 Computers and Fluids 2 Linear and Multilinear Algebra 2 Physics Letters. B 2 Advances in Mathematics 2 Automatica 2 Compositio Mathematica 2 Journal für die Reine und Angewandte Mathematik 2 Numerische Mathematik 2 Proceedings of the American Mathematical Society 2 Rendiconti del Circolo Matemàtico di Palermo. Serie II 2 SIAM Journal on Numerical Analysis 2 Applied Numerical Mathematics 2 Journal of Complexity 2 Discrete & Computational Geometry 2 Applied Mathematics Letters 2 Journal of the American Mathematical Society 2 Differential Geometry and its Applications 2 SIAM Review 2 Mathematical Programming. Series A. Series B 2 Journal of Dynamics and Differential Equations 2 Computational and Applied Mathematics 2 Advances in Computational Mathematics 2 Discrete and Continuous Dynamical Systems 2 Mediterranean Journal of Mathematics 2 Acta Numerica 2 Communications in Computational Physics 2 Bollettino dell’Unione Matematica Italiana 1 Communications in Algebra 1 Communications in Mathematical Physics 1 Computer Physics Communications 1 Discrete Mathematics 1 Journal of Engineering Mathematics 1 Journal of the Franklin Institute 1 Journal of Statistical Physics 1 Nuclear Physics. B 1 Rocky Mountain Journal of Mathematics 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Beiträge zur Algebra und Geometrie 1 The Annals of Statistics 1 Bulletin of the London Mathematical Society 1 Computing 1 Glasgow Mathematical Journal 1 Journal of Economic Theory 1 Le Matematiche 1 Mathematics of Operations Research 1 Mathematika 1 Meccanica 1 Proceedings of the London Mathematical Society. Third Series 1 SIAM Journal on Control and Optimization 1 Acta Applicandae Mathematicae 1 Computer Aided Geometric Design 1 Physica D 1 Neural Computation 1 Computational Geometry 1 IMRN. International Mathematics Research Notices 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 SIAM Journal on Mathematical Analysis 1 Bulletin of the American Mathematical Society. New Series 1 Celestial Mechanics and Dynamical Astronomy ...and 41 more Serials all top 5 Cited in 51 Fields 199 Algebraic geometry (14-XX) 188 Numerical analysis (65-XX) 88 Computer science (68-XX) 82 Commutative algebra (13-XX) 58 Partial differential equations (35-XX) 47 Linear and multilinear algebra; matrix theory (15-XX) 43 Biology and other natural sciences (92-XX) 31 Ordinary differential equations (34-XX) 23 Convex and discrete geometry (52-XX) 22 Quantum theory (81-XX) 20 Operations research, mathematical programming (90-XX) 17 Mechanics of particles and systems (70-XX) 15 Statistics (62-XX) 13 Combinatorics (05-XX) 13 Field theory and polynomials (12-XX) 11 Dynamical systems and ergodic theory (37-XX) 11 Fluid mechanics (76-XX) 10 Systems theory; control (93-XX) 7 Number theory (11-XX) 7 Calculus of variations and optimal control; optimization (49-XX) 7 Statistical mechanics, structure of matter (82-XX) 6 Geometry (51-XX) 6 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 6 Information and communication theory, circuits (94-XX) 5 Real functions (26-XX) 5 Functions of a complex variable (30-XX) 4 Associative rings and algebras (16-XX) 4 Several complex variables and analytic spaces (32-XX) 4 Algebraic topology (55-XX) 4 Global analysis, analysis on manifolds (58-XX) 3 Group theory and generalizations (20-XX) 3 Probability theory and stochastic processes (60-XX) 3 Relativity and gravitational theory (83-XX) 2 General and overarching topics; collections (00-XX) 2 Approximations and expansions (41-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Operator theory (47-XX) 2 Differential geometry (53-XX) 2 Manifolds and cell complexes (57-XX) 2 Mechanics of deformable solids (74-XX) 1 Mathematical logic and foundations (03-XX) 1 Nonassociative rings and algebras (17-XX) 1 Topological groups, Lie groups (22-XX) 1 Special functions (33-XX) 1 Difference and functional equations (39-XX) 1 Integral transforms, operational calculus (44-XX) 1 Integral equations (45-XX) 1 Functional analysis (46-XX) 1 General topology (54-XX) 1 Optics, electromagnetic theory (78-XX) 1 Mathematics education (97-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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