Edit Profile (opens in new tab) Mourrain, Bernard Compute Distance To: Compute Author ID: mourrain.bernard Published as: Mourrain, Bernard; Mourrain, B. Documents Indexed: 147 Publications since 1991, including 1 Book 4 Contributions as Editor Co-Authors: 138 Co-Authors with 137 Joint Publications 3,962 Co-Co-Authors all top 5 Co-Authors 14 single-authored 12 Trébuchet, Philippe 11 Xu, Gang 9 Elkadi, Mohamed 9 Galligo, André 9 Pan, Victor Yakovlevich 8 Tsigaridas, Elias P. 7 Busé, Laurent 7 Khalil, Houssam 7 Mantzaflaris, Angelos 6 Comon, Pierre 5 Bernardi, Alessandra 5 Brachat, Jerome 5 Emiris, Ioannis Z. 5 Ruatta, Olivier 5 Szántó, Ágnes 5 Técourt, Jean-Pierre 5 Villamizar, Nelly 4 Alberti, Lionel F. 4 Nkonga, Boniface 4 Vrahatis, Michael N. 4 Wang, Wenping 4 Wintz, Julien 4 Wu, Meng 3 Abril Bucero, Marta 3 Devillers, Olivier 3 Diatta, Daouda Niang 3 Duvigneau, Régis 3 Hauenstein, Jonathan D. 3 Jia, Xiaohong 3 Pavone, Jean-Pascal 3 Rabczuk, Timon 3 Schatzman, Michelle 3 Solé, Patrick 3 Teillaud, Monique 3 Tu, Changhe 3 Yakoubsohn, Jean-Claude 2 Adamou, Ibrahim 2 Blidia, Ahmed 2 Bondyfalat, Didier 2 Bonnecaze, Alexis 2 Chèze, Guillaume 2 Choi, Yi-King 2 Fronville, Alexandra 2 Harmouch, Jouhayna 2 Khouja, Rima 2 Lasserre, Jean-Bernard 2 Laurent, Monique 2 Pavlidis, Nicos G. 2 Rónyai, Lajos 2 Rouillier, Fabrice 2 Stolfi, Noëlle 2 Tasoulis, Dimitris K. 2 Telen, Simon 2 Van Barel, Marc 2 van der Hoeven, Joris 2 Xu, Jinlan 1 Aries, Franck 1 Arrondo, Enrique 1 Bachoc, Christine 1 Bajaj, Chandrajit L. 1 Berdinskiĭ, Dmitriĭ Aleksandrovich 1 Berthomieu, Jérémy 1 Boissonnat, Jean-Daniel 1 Bordas, Stéphane Pierre Alain 1 Bracco, Cesare 1 Cardinal, Jean Paul 1 Chen, Long 1 Cheng, Changzheng 1 Cho, Durkbin 1 Choie, YoungJu 1 Christoforou, Emmanouil 1 Cohen-Steiner, David 1 Daleo, Noah S. 1 Deng, Chongyang 1 Dong, Zhenyu 1 Dos Reis, Gabriel 1 Elias, Juan 1 Fioravanti, Mario A. 1 Fournier, Robert 1 Garnier, Christelle 1 Gatellier, G. 1 Golub, Gene Howard 1 Gonzalez-Vega, Laureano 1 Grellier, Olivier 1 Hodorog, Mădălina 1 Homs Pons, Roser 1 Hughes, Thomas J. R. 1 Hui, Kinchuen 1 Janovitz-Freirech, Itnuit 1 Janovitz-Freireich, Itnuit 1 Jin, Yaoli 1 Josz, Cédric 1 Kajler, Norbert 1 Kiatpanichgij, Sutipong 1 Kim, Taewan 1 Labrouzy, A. 1 Lecerf, Grégoire 1 Lella, Paolo 1 Liang, Chen 1 Lim, Lek-Heng ...and 38 more Co-Authors all top 5 Serials 20 Journal of Symbolic Computation 10 Computer Aided Geometric Design 8 Linear Algebra and its Applications 5 Theoretical Computer Science 4 Journal of Pure and Applied Algebra 3 Computer Methods in Applied Mechanics and Engineering 3 Journal of Computational Physics 3 Journal of Complexity 2 Mathematics of Computation 2 Journal of Computational and Applied Mathematics 2 SIAM Journal on Matrix Analysis and Applications 2 Computational Geometry 2 Advances in Computational Mathematics 2 Mathematics in Computer Science 2 ACM Communications in Computer Algebra 1 Computers & Mathematics with Applications 1 IEEE Transactions on Information Theory 1 Archiv der Mathematik 1 Calcolo 1 Proceedings of the American Mathematical Society 1 SIAM Journal on Computing 1 Discrete & Computational Geometry 1 Computational Mechanics 1 Signal Processing 1 IEEE Transactions on Signal Processing 1 Differential Geometry and its Applications 1 Designs, Codes and Cryptography 1 Applicable Algebra in Engineering, Communication and Computing 1 Journal of Mathematical Imaging and Vision 1 Journal of Algebraic Combinatorics 1 Analele Universității din Timișoara. Seria Matematică-Informatică 1 Communications in Contemporary Mathematics 1 Foundations of Computational Mathematics 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 Lecture Notes in Computer Science 1 Mathématiques & Applications (Berlin) 1 Communications in Computational Physics 1 Confluentes Mathematici 1 Mathematics and Visualization all top 5 Fields 84 Numerical analysis (65-XX) 63 Computer science (68-XX) 38 Commutative algebra (13-XX) 38 Algebraic geometry (14-XX) 23 Linear and multilinear algebra; matrix theory (15-XX) 19 Field theory and polynomials (12-XX) 9 Real functions (26-XX) 7 Approximations and expansions (41-XX) 6 Functions of a complex variable (30-XX) 6 Information and communication theory, circuits (94-XX) 4 General and overarching topics; collections (00-XX) 4 Associative rings and algebras (16-XX) 4 Mechanics of particles and systems (70-XX) 3 Partial differential equations (35-XX) 3 Operator theory (47-XX) 3 Algebraic topology (55-XX) 3 Operations research, mathematical programming (90-XX) 2 Number theory (11-XX) 2 Integral transforms, operational calculus (44-XX) 2 Geometry (51-XX) 2 Manifolds and cell complexes (57-XX) 1 Combinatorics (05-XX) 1 General algebraic systems (08-XX) 1 Group theory and generalizations (20-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Ordinary differential equations (34-XX) 1 Functional analysis (46-XX) 1 Convex and discrete geometry (52-XX) 1 Differential geometry (53-XX) 1 Statistics (62-XX) 1 Fluid mechanics (76-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Geophysics (86-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 124 Publications have been cited 1,403 times in 887 Documents Cited by ▼ Year ▼ Symmetric tensors and symmetric tensor rank. Zbl 1181.15014Comon, Pierre; Golub, Gene; Lim, Lek-Heng; Mourrain, Bernard 154 2008 Parameterization of computational domain in isogeometric analysis: methods and comparison. Zbl 1228.65232Xu, Gang; Mourrain, Bernard; Duvigneau, Régis; Galligo, André 84 2011 Symmetric tensor decomposition. Zbl 1206.65141Brachat, Jerome; Comon, Pierre; Mourrain, Bernard; Tsigaridas, Elias 76 2010 Constructing analysis-suitable parameterization of computational domain from CAD boundary by variational harmonic method. Zbl 1349.65079Xu, Gang; Mourrain, Bernard; Duvigneau, Régis; Galligo, André 50 2013 Decomposition of quantics in sums of powers of linear forms. Zbl 0875.94079Comon, P.; Mourrain, B. 47 1996 A new criterion for normal form algorithms. Zbl 0976.12005Mourrain, B. 45 1999 Type II codes over \(\mathbb{Z}_4\). Zbl 0898.94009Bonnecaze, Alexis; Solé, Patrick; Bachoc, Christine; Mourrain, Bernard 45 1997 Multivariate polynomials, duality, and structured matrices. Zbl 0963.68232Mourrain, Bernard; Pan, Victor Y. 34 2000 Matrices in elimination theory. Zbl 0943.13005Emiris, Ioannis Z.; Mourrain, Bernard 33 1999 Subdivision methods for solving polynomial equations. Zbl 1158.13010Mourrain, B.; Pavone, J. P. 32 2009 Isolated points, duality and residues. Zbl 0896.13020Mourrain, B. 32 1997 Generalized normal forms and polynomial system solving. Zbl 1360.68947Mourrain, Bernard; Trebuchet, Philippe 28 2005 Introduction to the solution of polynomial systems. (Introduction à la résolution des systèmes polynomiaux.) Zbl 1127.13001Elkadi, Mohamed; Mourrain, Bernard 22 2007 Dimension and bases for geometrically continuous splines on surfaces of arbitrary topology. Zbl 1418.41010Mourrain, Bernard; Vidunas, Raimundas; Villamizar, Nelly 22 2016 On the dimension of spline spaces on planar T-meshes. Zbl 1360.65052Mourrain, Bernard 21 2014 Computing the isolated roots by matrix methods. Zbl 0934.68136Mourrain, B. 20 1998 General tensor decomposition, moment matrices and applications. Zbl 1275.15017Bernardi, A.; Brachat, J.; Comon, P.; Mourrain, B. 19 2013 Resultant-based methods for plane curves intersection problems. Zbl 1169.65316Busé, Laurent; Khalil, Houssam; Mourrain, Bernard 19 2005 A generalized flat extension theorem for moment matrices. Zbl 1183.30030Laurent, Monique; Mourrain, Bernard 18 2009 Generalized resultants over unirational algebraic varieties. Zbl 0983.14039Busé, Laurent; Elkadi, Mohamed; Mourrain, Bernard 18 2000 On the complexity of isolating real roots and computing with certainty the topological degree. Zbl 1008.65022Mourrain, B.; Vrahatis, M. N.; Yakoubsohn, J. C. 18 2002 High-quality construction of analysis-suitable trivariate NURBS solids by reparameterization methods. Zbl 1311.65020Xu, Gang; Mourrain, Bernard; Galligo, André; Rabczuk, Timon 18 2014 A comparison of different notions of ranks of symmetric tensors. Zbl 1298.15034Bernardi, Alessandra; Brachat, Jérôme; Mourrain, Bernard 17 2014 The DMM bound: multivariate (aggregate) separation bounds. Zbl 1321.68528Emiris, Ioannis Z.; Mourrain, Bernard; Tsigaridas, Elias P. 17 2010 On the computation of the topology of a non-reduced implicit space curve. Zbl 1238.14046Daouda, Diatta Niang; Mourrain, Bernard; Ruatta, Olivier 16 2008 Real algebraic numbers: Complexity analysis and experimentation. Zbl 1165.65315Emiris, Ioannis Z.; Mourrain, Bernard; Tsigaridas, Elias P. 15 2008 Topology and arrangement computation of semi-algebraic planar curves. Zbl 1172.14343Alberti, L.; Mourrain, B.; Wintz, J. 14 2008 Constructing IGA-suitable planar parameterization from complex CAD boundary by domain partition and global/local optimization. Zbl 1439.65200Xu, Gang; Li, Ming; Mourrain, Bernard; Rabczuk, Timon; Xu, Jinlan; Bordas, Stéphane P. A. 14 2018 On the computation of an arrangement of quadrics in 3D. Zbl 1063.65018Mourrain, Bernard; Técourt, Jean-Pierre; Teillaud, Monique 13 2005 \(G^1\)-smooth splines on quad meshes with 4-split macro-patch elements. Zbl 1366.65012Blidia, Ahmed; Mourrain, Bernard; Villamizar, Nelly 13 2017 Moment matrices, border bases and real radical computation. Zbl 1276.13021Lasserre, Jean-Bernard; Laurent, Monique; Mourrain, Bernard; Rostalski, Philipp; Trébuchet, Philippe 13 2013 Deflation and certified isolation of singular zeros of polynomial systems. Zbl 1323.65054Mantzaflaris, Angelos; Mourrain, Bernard 13 2011 The Bernstein-basis and real root isolation. Zbl 1094.14051Mourrain, Bernard; Rouillier, Fabrice; Roy, Marie-Françoise 13 2005 Stable normal forms for polynomial system solving. Zbl 1159.68045Mourrain, Bernard; Trébuchet, Philippe 12 2008 Computing the topology of three-dimensional algebraic curves. Zbl 1077.14089Gatellier, G.; Labrouzy, A.; Mourrain, B.; Técourt, J. P. 12 2005 Explicit factors of some iterated resultants and discriminants. Zbl 1200.13042Busé, Laurent; Mourrain, Bernard 11 2009 Algebraic approach of residues and applications. Zbl 0857.13026Cardinal, J. P.; Mourrain, B. 11 1996 Dimensions and bases of hierarchical tensor-product splines. Zbl 1292.65009Berdinsky, Dmitry; Kim, Tae-wan; Bracco, Cesare; Cho, Durkbin; Mourrain, Bernard; Oh, Min-jae; Kiatpanichgij, Sutipong 11 2014 Isotopic triangulation of a real algebraic surface. Zbl 1173.14344Alberti, Lionel; Mourrain, Bernard; Técourt, Jean-Pierre 10 2009 Solving special polynomial systems by using structured matrices and algebraic residues. Zbl 0922.65044Mourrain, Bernard; Pan, Victor Y. 10 1997 Tensor decomposition and homotopy continuation. Zbl 1377.65057Bernardi, Alessandra; Daleo, Noah S.; Hauenstein, Jonathan D.; Mourrain, Bernard 9 2017 On continued fraction expansion of real roots of polynomial systems, complexity and condition numbers. Zbl 1243.12005Mantzaflaris, Angelos; Mourrain, Bernard; Tsigaridas, Elias 9 2011 Polynomial-exponential decomposition from moments. Zbl 1427.14119Mourrain, Bernard 9 2018 Resultant over the residual of a complete intersection. Zbl 1075.14525Busé, L.; Elkadi, M.; Mourrain, B. 8 2001 Certifying isolated singular points and their multiplicity structure. Zbl 1345.68286Hauenstein, Jonathan D.; Mourrain, Bernard; Szanto, Agnes 8 2015 Using projection operators in computer aided geometric design. Zbl 1036.14500Busé, Laurent; Elkadi, Mohamed; Mourrain, Bernard 8 2003 Residue and implicitization problem for rational surfaces. Zbl 1058.14073Elkadi, Mohamed; Mourrain, Bernard 7 2004 Subdivision methods for the topology of 2d and 3d implicit curves. Zbl 1132.14335Liang, Chen; Mourrain, Bernard; Pavone, Jean-Pascal 7 2008 An algebraic approach to continuous collision detection for ellipsoids. Zbl 1233.65020Jia, Xiaohong; Choi, Yi-King; Mourrain, Bernard; Wang, Wenping 7 2011 Algorithms for residues and Łojasiewicz exponents. Zbl 0974.13021Elkadi, M.; Mourrain, B. 7 2000 Computation of a specified root of a polynomial system of equations using eigenvectors. Zbl 0973.65038Bondyfalat, Didier; Mourrain, Bernard; Pan, Victor Y. 7 2000 Extensors and the Hilbert scheme. Zbl 1342.14008Brachat, Jérôme; Lella, Paolo; Mourrain, Bernard; Roggero, Margherita 6 2016 Homological techniques for the analysis of the dimension of triangular spline spaces. Zbl 1370.41020Mourrain, Bernard; Villamizar, Nelly 6 2013 Using signature sequences to classify intersection curves of two quadrics. Zbl 1205.68473Tu, Changhe; Wang, Wenping; Mourrain, Bernard; Wang, Jiaye 6 2009 On the isotopic meshing of an algebraic implicit surface. Zbl 1237.14069Diatta, Daouda Niang; Mourrain, Bernard; Ruatta, Olivier 6 2012 Border basis representation of a general quotient algebra. Zbl 1323.68618Mourrain, Bernard; Trébuchet, Philippe 6 2012 Relations between roots and coefficients, interpolation and application to system solving. Zbl 1022.13007Mourrain, Bernard; Ruatta, Olivier 6 2002 Asymptotic acceleration of solving multivariate polynomial systems of equations. Zbl 1028.68216Mourrain, Bernard; Pan, Victor Y. 6 1998 Meshing implicit algebraic surfaces: the smooth case. Zbl 1080.65514Alberti, L.; Comte, G.; Mourrain, B. 6 2005 Enumeration problems in geometry, robotics and vision. Zbl 0915.14031Mourrain, B. 6 1996 Meshing of surfaces. Zbl 1116.65020Boissonnat, Jean-Daniel; Cohen-Steiner, David; Mourrain, Bernard; Rote, Günter; Vegter, Gert 6 2007 Pythagore’s dilemma, symbolic-numeric computation, and the border basis method. Zbl 1117.65076Mourrain, Bernard 6 2007 Multihomogeneous polynomial decomposition using moment matrices. Zbl 1323.15017Bernardi, Alessandra; Brachat, Jérôme; Comon, Pierre; Mourrain, Bernard 6 2011 Curve/surface intersection problem by means of matrix representations. Zbl 1356.65060Thang, Luu Ba; Busé, Laurent; Mourrain, Bernard 6 2009 On deflation and multiplicity structure. Zbl 1387.13063Hauenstein, Jonathan D.; Mourrain, Bernard; Szanto, Agnes 5 2017 A subdivision method for computing nearest gcd with certification. Zbl 1221.68297Chèze, Guillaume; Galligo, André; Mourrain, Bernard; Yakoubsohn, Jean-Claude 5 2011 Algebraic methods and arithmetic filtering for exact predicates on circle arcs. Zbl 1016.68142Devillers, Olivier; Fronville, Alexandra; Mourrain, Bernard; Teillaud, Monique 5 2002 Circular cylinders through four or five points in space. Zbl 1031.52008Devillers, Olivier; Mourrain, Bernard; Preparata, Franco P.; Trebuchet, Philippe 5 2003 Solving polynomial systems via truncated normal forms. Zbl 1401.65054Telen, Simon; Mourrain, Bernard; Barel, Marc Van 5 2018 Bezoutian and quotient ring structure. Zbl 1120.13035Mourrain, B. 4 2005 Regularity criteria for the topology of algebraic curves and surfaces. Zbl 1163.68342Alberti, Lionel; Mourrain, Bernard 4 2007 Controlled iterative methods for solving polynomial systems. Zbl 0924.65043Bondyfalat, Didier; Mourrain, Bernard; Pan, Victor Y. 4 1998 The 40 “generic” positions of a parallel robot. Zbl 0925.70047Mourrain, B. 4 1993 Rankin-Cohen brackets and invariant theory. Zbl 1039.11024Choie, Y.; Mourrain, B.; Solé, P. 4 2001 An introduction to linear algebra methods for solving polynomial equations. Zbl 0944.65054Mourrain, B. 4 1998 Efficient construction of multi-block volumetric spline parameterization by discrete mask method. Zbl 1321.65028Xu, Gang; Mourrain, Bernard; Wu, Xiangyang; Chen, Long; Hui, Kin-chuen 4 2015 Continuous detection of the variations of the intersection curve of two moving quadrics in 3-dimensional projective space. Zbl 1336.68309Jia, Xiaohong; Wang, Wenping; Choi, Yi-King; Mourrain, Bernard; Tu, Changhe 4 2016 Border basis relaxation for polynomial optimization. Zbl 1346.90655Abril Bucero, Marta; Mourrain, Bernard 4 2016 Geometrically smooth spline bases for data fitting and simulation. Zbl 1472.65015Blidia, Ahmed; Mourrain, Bernard; Xu, Gang 4 2020 Interpolatory Catmull-Clark volumetric subdivision over unstructured hexahedral meshes for modeling and simulation applications. Zbl 07207278Xie, Jin; Xu, Jinlan; Dong, Zhenyu; Xu, Gang; Deng, Chongyang; Mourrain, Bernard; Zhang, Yongjie Jessica 4 2020 Convergence rates for solving elliptic boundary value problems with singular parameterizations in isogeometric analysis. Zbl 1366.65098Wu, Meng; Wang, Yicao; Mourrain, Bernard; Nkonga, Boniface; Cheng, Changzheng 3 2017 Applications of Clifford algebras in robotics. Zbl 0900.70070Mourrain, B.; Stolfi, N. 3 1995 Analytical blind channel identification. Zbl 1369.94467Grellier, Olivier; Comon, Pierre; Mourrain, Bernard; Trébuchet, Philippe 3 2002 Algebraic methods and arithmetic filtering for exact predicates on circle arcs. Zbl 1374.68658Devillers, Olivier; Fronville, Alexandra; Mourrain, Bernard; Teillaud, Monique 3 2000 Bounds on the dimension of trivariate spline spaces: a homological approach. Zbl 1317.13035Mourrain, Bernard; Villamizar, Nelly 3 2014 Bisectors and Voronoï diagram of a family of parallel half-lines. Zbl 1331.65033Adamou, I.; Fioravanti, M.; Gonzalez-Vega, L.; Mourrain, B. 3 2014 Accelerated solution of multivariate polynomial systems of equations. Zbl 1030.65051Mourrain, B.; Pan, V. Y.; Ruatta, O. 3 2003 Flat extensions in \(\ast\)-algebras. Zbl 1364.46047Mourrain, Bernard; Schmüdgen, Konrad 3 2016 Computing nearest gcd with certification. Zbl 1356.68273Chèze, Guillaume; Yakoubsohn, Jean-Claude; Galligo, André; Mourrain, Bernard 3 2009 Structured low rank decomposition of multivariate Hankel matrices. Zbl 1417.15044Harmouch, J.; Khalil, H.; Mourrain, B. 3 2018 Exact conversion from Bézier tetrahedra to Bézier hexahedra. Zbl 06892785Xu, Gang; Jin, Yaoli; Xiao, Zhoufang; Wu, Qing; Mourrain, Bernard; Rabczuk, Timon 3 2018 Symbolic-numeric methods for solving polynomial equations and applications. Zbl 1152.68701Elkadi, Mohamed; Mourrain, Bernard 2 2005 Some algebra with formal matrices. Zbl 0736.16014Mourrain, Bernard 2 1991 Multidimensional structured matrices and polynomial systems. Zbl 0904.65050Mourrain, Bernard; Pan, Victor Y. 2 1996 Jacobi polynomials, type II codes, and designs. Zbl 1049.94018Bonnecaze, Alexis; Mourrain, Bernard; Solé, Patrick 2 1999 Algebraic issues in computational geometry. Zbl 1116.65029Mourrain, Bernard; Pion, Sylvain; Schmitt, Susanne; Técourt, Jean-Pierre; Tsigaridas, Elias; Wolpert, Nocola 2 2007 An environment for symbolic and numeric computation. Zbl 1057.68140Dos Reis, G.; Mourrain, B.; Trébuchet, Ph.; Rouillier, F. 2 2002 Toric border basis. Zbl 1325.68296Mourrain, Bernard; Trébuchet, Philippe 2 2014 Solving projective complete intersection faster. Zbl 1326.68363Mourrain, Bernard; Trebuchet, Philippe 2 2000 Singular zeros of polynomial systems. Zbl 1331.65074Mantzaflaris, Angelos; Mourrain, Bernard 2 2014 Riemannian Newton optimization methods for the symmetric tensor approximation problem. Zbl 1481.15028Khouja, Rima; Khalil, Houssam; Mourrain, Bernard 1 2022 Skew-symmetric tensor decomposition. Zbl 1458.15044Arrondo, Enrique; Bernardi, Alessandra; Marques, Pedro Macias; Mourrain, Bernard 2 2021 Truncated normal forms for solving polynomial systems: generalized and efficient algorithms. Zbl 1443.13024Mourrain, Bernard; Telen, Simon; Van Barel, Marc 1 2021 Geometrically smooth spline bases for data fitting and simulation. Zbl 1472.65015Blidia, Ahmed; Mourrain, Bernard; Xu, Gang 4 2020 Interpolatory Catmull-Clark volumetric subdivision over unstructured hexahedral meshes for modeling and simulation applications. Zbl 07207278Xie, Jin; Xu, Jinlan; Dong, Zhenyu; Xu, Gang; Deng, Chongyang; Mourrain, Bernard; Zhang, Yongjie Jessica 4 2020 Separation bounds for polynomial systems. Zbl 1446.68202Emiris, Ioannis; Mourrain, Bernard; Tsigaridas, Elias 2 2020 Computing minimal Gorenstein covers. Zbl 1452.13032Elias, Juan; Homs, Roser; Mourrain, Bernard 1 2020 On minimal decompositions of low rank symmetric tensors. Zbl 1460.13049Mourrain, Bernard; Oneto, Alessandro 1 2020 Sparse polynomial interpolation: sparse recovery, super-resolution, or Prony? Zbl 1417.90112Josz, Cédric; Lasserre, Jean Bernard; Mourrain, Bernard 2 2019 Constructing IGA-suitable planar parameterization from complex CAD boundary by domain partition and global/local optimization. Zbl 1439.65200Xu, Gang; Li, Ming; Mourrain, Bernard; Rabczuk, Timon; Xu, Jinlan; Bordas, Stéphane P. A. 14 2018 Polynomial-exponential decomposition from moments. Zbl 1427.14119Mourrain, Bernard 9 2018 Solving polynomial systems via truncated normal forms. Zbl 1401.65054Telen, Simon; Mourrain, Bernard; Barel, Marc Van 5 2018 Structured low rank decomposition of multivariate Hankel matrices. Zbl 1417.15044Harmouch, J.; Khalil, H.; Mourrain, B. 3 2018 Exact conversion from Bézier tetrahedra to Bézier hexahedra. Zbl 06892785Xu, Gang; Jin, Yaoli; Xiao, Zhoufang; Wu, Qing; Mourrain, Bernard; Rabczuk, Timon 3 2018 Axl, a geometric modeler for semi-algebraic shapes. Zbl 1396.65028Christoforou, Emmanouil; Mantzaflaris, Angelos; Mourrain, Bernard; Wintz, Julien 1 2018 \(G^1\)-smooth splines on quad meshes with 4-split macro-patch elements. Zbl 1366.65012Blidia, Ahmed; Mourrain, Bernard; Villamizar, Nelly 13 2017 Tensor decomposition and homotopy continuation. Zbl 1377.65057Bernardi, Alessandra; Daleo, Noah S.; Hauenstein, Jonathan D.; Mourrain, Bernard 9 2017 On deflation and multiplicity structure. Zbl 1387.13063Hauenstein, Jonathan D.; Mourrain, Bernard; Szanto, Agnes 5 2017 Convergence rates for solving elliptic boundary value problems with singular parameterizations in isogeometric analysis. Zbl 1366.65098Wu, Meng; Wang, Yicao; Mourrain, Bernard; Nkonga, Boniface; Cheng, Changzheng 3 2017 Fast algorithm for border bases of Artinian Gorenstein algebras. Zbl 1458.13036Mourrain, Bernard 2 2017 Hermite type spline spaces over rectangular meshes with complex topological structures. Zbl 07413973Wu, Meng; Mourrain, Bernard; Galligo, André; Nkonga, Boniface 1 2017 \(H^1\)-parametrizations of complex planar physical domains in isogeometric analysis. Zbl 1439.65198Wu, Meng; Mourrain, Bernard; Galligo, André; Nkonga, Boniface 1 2017 Decomposition of low rank multi-symmetric tensor. Zbl 07036042Harmouch, Jouhayna; Mourrain, Bernard; Khalil, Houssam 1 2017 Dimension and bases for geometrically continuous splines on surfaces of arbitrary topology. Zbl 1418.41010Mourrain, Bernard; Vidunas, Raimundas; Villamizar, Nelly 22 2016 Extensors and the Hilbert scheme. Zbl 1342.14008Brachat, Jérôme; Lella, Paolo; Mourrain, Bernard; Roggero, Margherita 6 2016 Continuous detection of the variations of the intersection curve of two moving quadrics in 3-dimensional projective space. Zbl 1336.68309Jia, Xiaohong; Wang, Wenping; Choi, Yi-King; Mourrain, Bernard; Tu, Changhe 4 2016 Border basis relaxation for polynomial optimization. Zbl 1346.90655Abril Bucero, Marta; Mourrain, Bernard 4 2016 Flat extensions in \(\ast\)-algebras. Zbl 1364.46047Mourrain, Bernard; Schmüdgen, Konrad 3 2016 On the construction of general cubature formula by flat extensions. Zbl 1386.65094Abril Bucero, Marta; Bajaj, Chandrajit; Mourrain, Bernard 1 2016 Certifying isolated singular points and their multiplicity structure. Zbl 1345.68286Hauenstein, Jonathan D.; Mourrain, Bernard; Szanto, Agnes 8 2015 Efficient construction of multi-block volumetric spline parameterization by discrete mask method. Zbl 1321.65028Xu, Gang; Mourrain, Bernard; Wu, Xiangyang; Chen, Long; Hui, Kin-chuen 4 2015 On the dimension of spline spaces on planar T-meshes. Zbl 1360.65052Mourrain, Bernard 21 2014 High-quality construction of analysis-suitable trivariate NURBS solids by reparameterization methods. Zbl 1311.65020Xu, Gang; Mourrain, Bernard; Galligo, André; Rabczuk, Timon 18 2014 A comparison of different notions of ranks of symmetric tensors. Zbl 1298.15034Bernardi, Alessandra; Brachat, Jérôme; Mourrain, Bernard 17 2014 Dimensions and bases of hierarchical tensor-product splines. Zbl 1292.65009Berdinsky, Dmitry; Kim, Tae-wan; Bracco, Cesare; Cho, Durkbin; Mourrain, Bernard; Oh, Min-jae; Kiatpanichgij, Sutipong 11 2014 Bounds on the dimension of trivariate spline spaces: a homological approach. Zbl 1317.13035Mourrain, Bernard; Villamizar, Nelly 3 2014 Bisectors and Voronoï diagram of a family of parallel half-lines. Zbl 1331.65033Adamou, I.; Fioravanti, M.; Gonzalez-Vega, L.; Mourrain, B. 3 2014 Toric border basis. Zbl 1325.68296Mourrain, Bernard; Trébuchet, Philippe 2 2014 Singular zeros of polynomial systems. Zbl 1331.65074Mantzaflaris, Angelos; Mourrain, Bernard 2 2014 Constructing analysis-suitable parameterization of computational domain from CAD boundary by variational harmonic method. Zbl 1349.65079Xu, Gang; Mourrain, Bernard; Duvigneau, Régis; Galligo, André 50 2013 General tensor decomposition, moment matrices and applications. Zbl 1275.15017Bernardi, A.; Brachat, J.; Comon, P.; Mourrain, B. 19 2013 Moment matrices, border bases and real radical computation. Zbl 1276.13021Lasserre, Jean-Bernard; Laurent, Monique; Mourrain, Bernard; Rostalski, Philipp; Trébuchet, Philippe 13 2013 Homological techniques for the analysis of the dimension of triangular spline spaces. Zbl 1370.41020Mourrain, Bernard; Villamizar, Nelly 6 2013 Superfast solution of Toeplitz systems based on syzygy reduction. Zbl 1267.65032Khalil, Houssam; Mourrain, Bernard; Schatzman, Michelle 1 2013 On the isotopic meshing of an algebraic implicit surface. Zbl 1237.14069Diatta, Daouda Niang; Mourrain, Bernard; Ruatta, Olivier 6 2012 Border basis representation of a general quotient algebra. Zbl 1323.68618Mourrain, Bernard; Trébuchet, Philippe 6 2012 On the computation of matrices of traces and radicals of ideals. Zbl 1230.13002Janovitz-Freireich, Itnuit; Mourrain, Bernard; Rónyai, Lajos; Szántó, Ágnes 1 2012 Parameterization of computational domain in isogeometric analysis: methods and comparison. Zbl 1228.65232Xu, Gang; Mourrain, Bernard; Duvigneau, Régis; Galligo, André 84 2011 Deflation and certified isolation of singular zeros of polynomial systems. Zbl 1323.65054Mantzaflaris, Angelos; Mourrain, Bernard 13 2011 On continued fraction expansion of real roots of polynomial systems, complexity and condition numbers. Zbl 1243.12005Mantzaflaris, Angelos; Mourrain, Bernard; Tsigaridas, Elias 9 2011 An algebraic approach to continuous collision detection for ellipsoids. Zbl 1233.65020Jia, Xiaohong; Choi, Yi-King; Mourrain, Bernard; Wang, Wenping 7 2011 Multihomogeneous polynomial decomposition using moment matrices. Zbl 1323.15017Bernardi, Alessandra; Brachat, Jérôme; Comon, Pierre; Mourrain, Bernard 6 2011 A subdivision method for computing nearest gcd with certification. Zbl 1221.68297Chèze, Guillaume; Galligo, André; Mourrain, Bernard; Yakoubsohn, Jean-Claude 5 2011 A construction of injective parameterizations of domains for isogeometric applications. Zbl 1350.65128Nguyen, Thien; Mourrain, Bernard; Galligo, André; Xu, Gang 1 2011 Symmetric tensor decomposition. Zbl 1206.65141Brachat, Jerome; Comon, Pierre; Mourrain, Bernard; Tsigaridas, Elias 76 2010 The DMM bound: multivariate (aggregate) separation bounds. Zbl 1321.68528Emiris, Ioannis Z.; Mourrain, Bernard; Tsigaridas, Elias P. 17 2010 A subdivision method for arrangement computation of semi-algebraic curves. Zbl 1191.68890Mourrain, Bernard; Wintz, Julien 1 2010 GENOM3CK: a library for genus computation of plane complex algebraic curves using knot theory. Zbl 1308.68173Hodorog, Mădălina; Mourrain, Bernard; Schicho, Josef 1 2010 Subdivision methods for solving polynomial equations. Zbl 1158.13010Mourrain, B.; Pavone, J. P. 32 2009 A generalized flat extension theorem for moment matrices. Zbl 1183.30030Laurent, Monique; Mourrain, Bernard 18 2009 Explicit factors of some iterated resultants and discriminants. Zbl 1200.13042Busé, Laurent; Mourrain, Bernard 11 2009 Isotopic triangulation of a real algebraic surface. Zbl 1173.14344Alberti, Lionel; Mourrain, Bernard; Técourt, Jean-Pierre 10 2009 Using signature sequences to classify intersection curves of two quadrics. Zbl 1205.68473Tu, Changhe; Wang, Wenping; Mourrain, Bernard; Wang, Jiaye 6 2009 Curve/surface intersection problem by means of matrix representations. Zbl 1356.65060Thang, Luu Ba; Busé, Laurent; Mourrain, Bernard 6 2009 Computing nearest gcd with certification. Zbl 1356.68273Chèze, Guillaume; Yakoubsohn, Jean-Claude; Galligo, André; Mourrain, Bernard 3 2009 Continued fraction expansion of real roots of polynomial systems. Zbl 1356.65124Mantzaflaris, Angelos; Mourrain, Bernard; Tsigaridas, Elias 2 2009 Symmetric tensors and symmetric tensor rank. Zbl 1181.15014Comon, Pierre; Golub, Gene; Lim, Lek-Heng; Mourrain, Bernard 154 2008 On the computation of the topology of a non-reduced implicit space curve. Zbl 1238.14046Daouda, Diatta Niang; Mourrain, Bernard; Ruatta, Olivier 16 2008 Real algebraic numbers: Complexity analysis and experimentation. Zbl 1165.65315Emiris, Ioannis Z.; Mourrain, Bernard; Tsigaridas, Elias P. 15 2008 Topology and arrangement computation of semi-algebraic planar curves. Zbl 1172.14343Alberti, L.; Mourrain, B.; Wintz, J. 14 2008 Stable normal forms for polynomial system solving. Zbl 1159.68045Mourrain, Bernard; Trébuchet, Philippe 12 2008 Subdivision methods for the topology of 2d and 3d implicit curves. Zbl 1132.14335Liang, Chen; Mourrain, Bernard; Pavone, Jean-Pascal 7 2008 SYNAPS: a library for dedicated applications in symbolic numeric computing. Zbl 1161.68882Mourrain, Bernard; Pavone, Jean-Pascal; Trebuchet, Philippe; Tsigaridas, Elias P.; Wintz, Julien 1 2008 Introduction to the solution of polynomial systems. (Introduction à la résolution des systèmes polynomiaux.) Zbl 1127.13001Elkadi, Mohamed; Mourrain, Bernard 22 2007 Meshing of surfaces. Zbl 1116.65020Boissonnat, Jean-Daniel; Cohen-Steiner, David; Mourrain, Bernard; Rote, Günter; Vegter, Gert 6 2007 Pythagore’s dilemma, symbolic-numeric computation, and the border basis method. Zbl 1117.65076Mourrain, Bernard 6 2007 Regularity criteria for the topology of algebraic curves and surfaces. Zbl 1163.68342Alberti, Lionel; Mourrain, Bernard 4 2007 Algebraic issues in computational geometry. Zbl 1116.65029Mourrain, Bernard; Pion, Sylvain; Schmitt, Susanne; Técourt, Jean-Pierre; Tsigaridas, Elias; Wolpert, Nocola 2 2007 Determining the number of real roots of polynomials through neural networks. Zbl 1100.65044Mourrain, B.; Pavlidis, N. G.; Tasoulis, D. K.; Vrahatis, M. N. 1 2006 Generalized normal forms and polynomial system solving. Zbl 1360.68947Mourrain, Bernard; Trebuchet, Philippe 28 2005 Resultant-based methods for plane curves intersection problems. Zbl 1169.65316Busé, Laurent; Khalil, Houssam; Mourrain, Bernard 19 2005 On the computation of an arrangement of quadrics in 3D. Zbl 1063.65018Mourrain, Bernard; Técourt, Jean-Pierre; Teillaud, Monique 13 2005 The Bernstein-basis and real root isolation. Zbl 1094.14051Mourrain, Bernard; Rouillier, Fabrice; Roy, Marie-Françoise 13 2005 Computing the topology of three-dimensional algebraic curves. Zbl 1077.14089Gatellier, G.; Labrouzy, A.; Mourrain, B.; Técourt, J. P. 12 2005 Meshing implicit algebraic surfaces: the smooth case. Zbl 1080.65514Alberti, L.; Comte, G.; Mourrain, B. 6 2005 Bezoutian and quotient ring structure. Zbl 1120.13035Mourrain, B. 4 2005 Symbolic-numeric methods for solving polynomial equations and applications. Zbl 1152.68701Elkadi, Mohamed; Mourrain, Bernard 2 2005 Residue and implicitization problem for rational surfaces. Zbl 1058.14073Elkadi, Mohamed; Mourrain, Bernard 7 2004 Quadratically parametrized surfaces: algorithms and applications. Zbl 1060.65528Aries, Franck; Mourrain, Bernard; Técourt, Jean-Pierre 1 2004 Using projection operators in computer aided geometric design. Zbl 1036.14500Busé, Laurent; Elkadi, Mohamed; Mourrain, Bernard 8 2003 Circular cylinders through four or five points in space. Zbl 1031.52008Devillers, Olivier; Mourrain, Bernard; Preparata, Franco P.; Trebuchet, Philippe 5 2003 Accelerated solution of multivariate polynomial systems of equations. Zbl 1030.65051Mourrain, B.; Pan, V. Y.; Ruatta, O. 3 2003 On the complexity of isolating real roots and computing with certainty the topological degree. Zbl 1008.65022Mourrain, B.; Vrahatis, M. N.; Yakoubsohn, J. C. 18 2002 Relations between roots and coefficients, interpolation and application to system solving. Zbl 1022.13007Mourrain, Bernard; Ruatta, Olivier 6 2002 Algebraic methods and arithmetic filtering for exact predicates on circle arcs. Zbl 1016.68142Devillers, Olivier; Fronville, Alexandra; Mourrain, Bernard; Teillaud, Monique 5 2002 Analytical blind channel identification. Zbl 1369.94467Grellier, Olivier; Comon, Pierre; Mourrain, Bernard; Trébuchet, Philippe 3 2002 An environment for symbolic and numeric computation. Zbl 1057.68140Dos Reis, G.; Mourrain, B.; Trébuchet, Ph.; Rouillier, F. 2 2002 Asymptotic acceleration of the solution of multivariate polynomial systems of equations. Zbl 1015.65022Mourrain, B.; Pan, V. Y.; Ruatta, O. 1 2002 Resultant over the residual of a complete intersection. Zbl 1075.14525Busé, L.; Elkadi, M.; Mourrain, B. 8 2001 Rankin-Cohen brackets and invariant theory. Zbl 1039.11024Choie, Y.; Mourrain, B.; Solé, P. 4 2001 ...and 24 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,184 Authors 65 Mourrain, Bernard 26 Ballico, Edoardo 22 Bernardi, Alessandra 19 Tsigaridas, Elias P. 17 Xu, Gang 16 Harada, Masaaki 16 Jüttler, Bert 15 Busé, Laurent 15 Pan, Victor Yakovlevich 12 Cheng, Jinsan 11 Comon, Pierre 11 Deng, Jiansong 11 Emiris, Ioannis Z. 11 Kapl, Mario 10 Sagraloff, Michael 10 Solé, Patrick 9 Galligo, André 9 Hauenstein, Jonathan D. 9 Qi, Liqun 8 Alcazar, Juan Gerardo 8 Chen, Falai 8 Faugère, Jean-Charles 8 Nie, Jiawang 8 Speleers, Hendrik 8 Szántó, Ágnes 7 Bordas, Stéphane Pierre Alain 7 D’Andrea, Carlos 7 De Lathauwer, Lieven 7 Gonzalez-Vega, Laureano 7 Kreuzer, Martin 7 Mantzaflaris, Angelos 7 Oneto, Alessandro 7 Sangalli, Giancarlo 7 Takacs, Thomas 7 Teitler, Zach 7 Zhi, Lihong 7 Zhu, Chungang 6 Bracco, Cesare 6 Chiantini, Luca 6 Deng, Fang 6 Díaz-Toca, Gema María 6 Elkadi, Mohamed 6 Hughes, Thomas J. R. 6 Lasserre, Jean-Bernard 6 Manni, Carla 6 Minimair, Manfred 6 Ottaviani, Giorgio Maria 6 Rabczuk, Timon 6 Roggero, Margherita 6 Schost, Éric 6 Toshniwal, Deepesh 6 Usevich, Konstantin 6 Vitrih, Vito 6 Wang, Yiju 6 Wu, Meng 5 Caravantes, Jorge 5 Carlini, Enrico 5 Chu, Moody T. 5 Dougherty, Steven T. 5 Fan, Jinyan 5 Gao, Xiaoshan 5 Jeronimo, Gabriela 5 Ji, Ye 5 Jin, Kai 5 Lazard, Sylvain 5 Massarenti, Alex 5 Rouillier, Fabrice 5 Safey El Din, Mohab 5 Schicho, Josef 5 Scott, Michael A. 5 Ventura, Emanuele 5 Villamizar, Nelly 5 Vrahatis, Michael N. 5 Wu, Wenyuan 5 Xu, Changqing 5 Xu, Jinlan 5 Zeng, Chao 5 Zhou, Anwa 4 Berthomieu, Jérémy 4 Bertone, Cristina 4 Bouzidi, Yacine 4 Buczyński, Jarosław 4 Chen, Long 4 Cioffi, Francesca 4 Dipasquale, Michael R. 4 Duvigneau, Régis 4 Feng, Yong 4 Gaborit, Philippe 4 Giannelli, Carlotta 4 Goldman, Ronald N. 4 Hu, ShengLong 4 Jia, Xiaohong 4 Johannessen, Kjetil André 4 Kleiss, Stefan K. 4 Kvamsdal, Trond 4 Landsberg, Joseph Montague 4 Laurent, Monique 4 Lazard, Daniel 4 Lewis, Robert H. 4 Leykin, Anton ...and 1,084 more Authors all top 5 Cited in 194 Serials 117 Journal of Symbolic Computation 62 Computer Aided Geometric Design 54 Computer Methods in Applied Mechanics and Engineering 41 Linear Algebra and its Applications 28 Journal of Computational and Applied Mathematics 27 Theoretical Computer Science 19 SIAM Journal on Matrix Analysis and Applications 17 Journal of Pure and Applied Algebra 16 Computers & Mathematics with Applications 14 Journal of Complexity 13 Applied Mathematics and Computation 13 Mathematics in Computer Science 12 Linear and Multilinear Algebra 12 Mathematics of Computation 11 Computational Geometry 11 Foundations of Computational Mathematics 10 Applicable Algebra in Engineering, Communication and Computing 10 Finite Fields and their Applications 10 SIAM Journal on Applied Algebra and Geometry 9 Journal of Computational Physics 9 Collectanea Mathematica 9 Journal of Algebra 8 SIAM Journal on Scientific Computing 8 Frontiers of Mathematics in China 7 Mathematics and Computers in Simulation 7 Mathematical Programming. 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Series B (English Edition) 3 Annals of Mathematics and Artificial Intelligence 3 Mediterranean Journal of Mathematics 3 Advances in Mathematics of Communications 3 Bollettino dell’Unione Matematica Italiana 3 SMAI Journal of Computational Mathematics 2 Communications in Algebra 2 International Journal of Control 2 Journal of the Franklin Institute 2 Letters in Mathematical Physics 2 Acta Mathematica Vietnamica 2 Archiv der Mathematik 2 Journal of Geometry 2 Journal of Multivariate Analysis 2 Mathematische Annalen 2 Numerical Functional Analysis and Optimization 2 Proceedings of the American Mathematical Society 2 Bulletin of the Korean Mathematical Society 2 Graphs and Combinatorics 2 Applied Mathematics Letters 2 SIAM Journal on Discrete Mathematics 2 Signal Processing 2 Japan Journal of Industrial and Applied Mathematics 2 International Journal of Algebra and Computation 2 Designs, Codes and Cryptography 2 International Journal of Computer Mathematics 2 SIAM Journal on Optimization 2 Computational Complexity 2 Experimental Mathematics 2 Journal de Théorie des Nombres de Bordeaux 2 Complex Analysis and Operator Theory 2 Optimization Letters 2 Discrete Mathematics, Algorithms and Applications 2 The Journal of Software for Algebra and Geometry 2 Communications in Mathematics and Statistics 1 Applicable Analysis 1 Archive for Rational Mechanics and Analysis 1 Journal of Fluid Mechanics 1 Journal of Statistical Physics 1 Theoretical and Mathematical Physics 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 1 Beiträge zur Algebra und Geometrie 1 Annales de l’Institut Fourier 1 The Annals of Statistics 1 BIT 1 Duke Mathematical Journal ...and 94 more Serials all top 5 Cited in 55 Fields 425 Numerical analysis (65-XX) 216 Algebraic geometry (14-XX) 200 Computer science (68-XX) 198 Linear and multilinear algebra; matrix theory (15-XX) 189 Commutative algebra (13-XX) 68 Information and communication theory, circuits (94-XX) 54 Field theory and polynomials (12-XX) 52 Number theory (11-XX) 45 Operations research, mathematical programming (90-XX) 39 Approximations and expansions (41-XX) 33 Mechanics of deformable solids (74-XX) 28 Real functions (26-XX) 26 Functions of a complex variable (30-XX) 22 Partial differential equations (35-XX) 20 Statistics (62-XX) 17 Combinatorics (05-XX) 17 Operator theory (47-XX) 16 Fluid mechanics (76-XX) 16 Systems theory; control (93-XX) 14 Differential geometry (53-XX) 12 Convex and discrete geometry (52-XX) 11 Integral transforms, operational calculus (44-XX) 10 Functional analysis (46-XX) 9 Several complex variables and analytic spaces (32-XX) 9 Quantum theory (81-XX) 8 Harmonic analysis on Euclidean spaces (42-XX) 7 Biology and other natural sciences (92-XX) 6 Dynamical systems and ergodic theory (37-XX) 6 Probability theory and stochastic processes (60-XX) 6 Mechanics of particles and systems (70-XX) 5 Ordinary differential equations (34-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 5 Geometry (51-XX) 5 Global analysis, analysis on manifolds (58-XX) 4 Mathematical logic and foundations (03-XX) 4 Associative rings and algebras (16-XX) 4 Group theory and generalizations (20-XX) 4 Manifolds and cell complexes (57-XX) 3 Topological groups, Lie groups (22-XX) 3 Special functions (33-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 General and overarching topics; collections (00-XX) 2 Measure and integration (28-XX) 2 General topology (54-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Statistical mechanics, structure of matter (82-XX) 2 Relativity and gravitational theory (83-XX) 2 Mathematics education (97-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Nonassociative rings and algebras (17-XX) 1 Potential theory (31-XX) 1 Difference and functional equations (39-XX) 1 Algebraic topology (55-XX) 1 Optics, electromagnetic theory (78-XX) 1 Geophysics (86-XX) Citations by Year