Bernard Mourrain

Publications

Article dans une revue (86)

An Effective Positivstellensatz over the Rational Numbers for Finite Semialgebraic Sets Lorenzo Baldi,Térésa Krick,Bernard Mourrain Mathematics of Computation, 2025, ⟨10.1090/mcom/4153⟩ Article dans une revue hal-04723493v2
An algebraic framework for geometrically continuous splines Angelos Mantzaflaris,Bernard Mourrain,Nelly Villamizar,Beihui Yuan Mathematics of Computation, 2025, ⟨10.1090/mcom/4068⟩ Article dans une revue hal-04100465v1
Exact Moment Representation in Polynomial Optimization Lorenzo Baldi,Bernard Mourrain Journal of Symbolic Computation, 2024, 129, pp.102403. ⟨10.1016/j.jsc.2024.102403⟩ Article dans une revue hal-03082531v5
A spline-based regularized method for the reconstruction of complex geological models Ayoub Belhachmi,Azeddine Benabbou,Bernard Mourrain Mathematical Geosciences, 2024, ⟨10.1007/s11004-024-10149-2⟩ Article dans une revue hal-04327756v1
On Łojasiewicz Inequalities and the Effective Putinar's Positivstellensatz Lorenzo Baldi,Bernard Mourrain,Adam Parusiński Journal of Algebra, 2024, 662, pp.741-767. ⟨10.1016/j.jalgebra.2024.08.022⟩ Article dans une revue hal-03899373v2
From CAD to Representations Suitable for Isogeometric Analysis: a Complete Pipeline Michelangelo Marsala,Angelos Mantzaflaris,Bernard Mourrain,Sam Whyman,Mark Gammon Engineering with Computers, 2024, ⟨10.1007/s00366-024-02065-0⟩ Article dans une revue hal-04185850v2
G1 Spline Functions for Point Cloud Fitting Michelangelo Marsala,Angelos Mantzaflaris,Bernard Mourrain Applied Mathematics and Computation, 2023, 460, pp.128279. ⟨10.1016/j.amc.2023.128279⟩ Article dans une revue hal-04002985v2
Tensor decomposition for learning Gaussian mixtures from moments Rima Khouja,Pierre-Alexandre Mattei,Bernard Mourrain Journal of Symbolic Computation, 2022, 113, pp.193-210. ⟨10.1016/j.jsc.2022.04.002⟩ Article dans une revue hal-03244448v2
Riemannian Newton optimization methods for the symmetric tensor approximation problem Rima Khouja,Houssam Khalil,Bernard Mourrain Linear Algebra and its Applications, 2022, 637C, pp.175-211. ⟨10.1016/j.laa.2021.12.008⟩ Article dans une revue hal-02494172v3
Univariate Rational Sums of Squares Teresa Krick,Bernard Mourrain,Agnes Szanto Revista de la Unión Matemática Argentina, 2022, 64 (2), pp.215-237. ⟨10.33044/revuma.2904⟩ Article dans une revue hal-03442193v2
A certified iterative method for isolated singular roots Angelos Mantzaflaris,Bernard Mourrain,Agnes Szanto Journal of Symbolic Computation, 2022, 115, pp.223-247. ⟨10.1016/j.jsc.2022.08.006⟩ Article dans une revue hal-03079910v1
Flux-aligned quad mesh generation in magnetohydrodynamic simulation Meng Wu,Xuhui Wang,Boniface Nkonga,Bernard Mourrain,Gang Xuet al. Journal of Computational Physics, 2022, 466, pp.111393. ⟨10.1016/j.jcp.2022.111393⟩ Article dans une revue hal-03714937v1
Newton-Type Methods For Simultaneous Matrix Diagonalization Rima Khouja,Bernard Mourrain,Jean-Claude Yakoubsohn Calcolo, 2022, ⟨10.1007/s10092-022-00484-3⟩ Article dans une revue hal-03390265v2
G1-smooth Biquintic Approximation of Catmull-Clark Subdivision Surfaces Michelangelo Marsala,Angelos Mantzaflaris,Bernard Mourrain Computer Aided Geometric Design, 2022, 99, ⟨10.1016/j.cagd.2022.102158⟩ Article dans une revue hal-03656945v2
Curve Valuations and Mixed Volumes in the Implicitization of Rational Varieties Alicia Dickenstein,Maria Isabel Herrero,Bernard Mourrain Journal of Algebra, 2022, 612, pp.691-721. ⟨10.1016/j.jalgebra.2022.08.026⟩ Article dans une revue hal-02958248v2
On the Effective Putinar’s Positivstellensatz and Moment Approximation Lorenzo Baldi,Bernard Mourrain Mathematical Programming, Series A, 2022, ⟨10.1007/s10107-022-01877-6⟩ Article dans une revue hal-03437328v4
Computing the Topology of Voronoi Diagrams of Parallel Half-Lines Ibrahim Adamou,Bernard Mourrain Mathematics in Computer Science, 2021, 15, pp.859-876. ⟨10.1007/s11786-021-00508-1⟩ Article dans une revue hal-03200138v1
Polynomial spline spaces of non-uniform bi-degree on T-meshes: Combinatorial bounds on the dimension Deepesh Toshniwal,Bernard Mourrain,Thomas J.R. Hughes Advances in Computational Mathematics, 2021, 47 (1), pp.16. ⟨10.1007/s10444-020-09829-4⟩ Article dans une revue hal-02067534v1
Interpolatory Catmull-Clark volumetric subdivision over unstructured hexahedral meshes for modeling and simulation applications Jin Xie,Jinlan Xu,Zhenyu Dong,Gang Xu,Chongyang Denget al. Computer Aided Geometric Design, 2020, 80, pp.101867. ⟨10.1016/j.cagd.2020.101867⟩ Article dans une revue hal-02958501v1
Geometrically smooth spline bases for data fitting and simulation Ahmed Blidia,Bernard Mourrain,Gang Xu Computer Aided Geometric Design, 2020, 78, pp.101814. ⟨10.1016/j.cagd.2020.101814⟩ Article dans une revue hal-02480959v1
On minimal decompositions of low rank symmetric tensors Bernard Mourrain,Alessandro Oneto Linear Algebra and its Applications, 2020, 607, pp.347-377. ⟨10.1016/j.laa.2020.06.029⟩ Article dans une revue hal-01803571v1
Complete Classification and Efficient Determination of Arrangements Formed by Two Ellipsoids Xiaohong Jia,Changhe Tu,Bernard Mourrain,Wenping Wang ACM Transactions on Graphics, 2020, 39 (3), pp.1-12. ⟨10.1145/3388540⟩ Article dans une revue hal-02927010v1
Separation bounds for polynomial systems Ioannis Z. Emiris,Bernard Mourrain,Elias Tsigaridas Journal of Symbolic Computation, 2020, 101, pp.128-151. ⟨10.1016/j.jsc.2019.07.001⟩ Article dans une revue hal-01105276v5
Enumerating the morphologies of non-degenerate Darboux cyclides Mingyang Zhao,Xiaohong Jia,Changhe Tu,Bernard Mourrain,Wenping Wang Computer Aided Geometric Design, 2019, 75, pp.101776. ⟨10.1016/j.cagd.2019.101776⟩ Article dans une revue hal-02400652v1
Sparse polynomial interpolation: sparse recovery, super resolution, or Prony? Cédric Josz,Jean-Bernard Lasserre,Bernard Mourrain Advances in Computational Mathematics, 2019, 45 (3), pp.1401-1437. ⟨10.1007/s10444-019-09672-2⟩ Article dans une revue hal-01575325v2
Skew-Symmetric Tensor Decomposition Enrique Arrondo,Alessandra Bernardi,Pedro Macias Marques,Bernard Mourrain Communications in Contemporary Mathematics, 2019, 23 (02), pp.1950061. ⟨10.1142/S0219199719500615⟩ Article dans une revue hal-01940005v1
Cooperative Visual-Inertial Sensor Fusion: the Analytic Solution Agostino Martinelli,Alexander Oliva,Bernard Mourrain IEEE Robotics and Automation Letters, 2019, 4 (2), pp.453-460. ⟨10.1109/LRA.2019.2891025⟩ Article dans une revue hal-01966542v1
Computing minimal Gorenstein covers Juan Elias,Roser Homs,Bernard Mourrain Journal of Pure and Applied Algebra, 2019, ⟨10.1016/j.jpaa.2019.106280⟩ Article dans une revue hal-01978906v2
Truncated Normal Forms for Solving Polynomial Systems: Generalized and Efficient Algorithms Bernard Mourrain,Simon Telen,Marc van Barel Journal of Symbolic Computation, 2019, ⟨10.1016/j.jsc.2019.10.009⟩ Article dans une revue hal-01738695v2
Constructing IGA-suitable planar parameterization from complex CAD boundary by domain partition and global/local optimization Gang Xu,Ming Li,Bernard Mourrain,Timon Rabczuk,Jinlan Xuet al. Computer Methods in Applied Mechanics and Engineering, 2018, 328, pp.175 - 200. ⟨10.1016/j.cma.2017.08.052⟩ Article dans une revue hal-01599319v1
Polynomial-Exponential Decomposition from Moments Bernard Mourrain Foundations of Computational Mathematics, 2018, 18 (6), pp.1435-1492. ⟨10.1007/s10208-017-9372-x⟩ Article dans une revue hal-01367730v3
Exact conversion from Bézier tetrahedra to Bézier hexahedra Gang Xu,Yaoli Jin,Zhoufang Xiao,Qing Wu,Bernard Mourrainet al. Computer Aided Geometric Design, 2018, 62, pp.154 - 165. ⟨10.1016/j.cagd.2018.03.022⟩ Article dans une revue hal-01936167v1
Solving Polynomial Systems via a Stabilized Representation of Quotient Algebras Simon Telen,Bernard Mourrain,Marc van Barel SIAM Journal on Matrix Analysis and Applications, 2018, 39 (3), pp.1421-1447. ⟨10.1137/17M1162433⟩ Article dans une revue hal-01630425v1
$G^1$-smooth splines on quad meshes with 4-split macro-patch elements Ahmed Blidia,Bernard Mourrain,Nelly Villamizar Computer Aided Geometric Design, 2017, 52–53, pp.106-125. ⟨10.1016/j.cagd.2017.03.003⟩ Article dans une revue hal-01491676v1
Structured low rank decomposition of multivariate Hankel matrices Jouhayna Harmouch,Houssam Khalil,Bernard Mourrain Linear Algebra and its Applications, 2017, ⟨10.1016/j.laa.2017.04.015⟩ Article dans une revue hal-01440063v1
H1-parametrizations of complex planar physical domains in Isogeometric analysis Meng Wu,Bernard Mourrain,André Galligo,Boniface Nkonga Computer Methods in Applied Mechanics and Engineering, 2017, 318, pp.296-318. ⟨10.1016/j.cma.2017.01.025⟩ Article dans une revue hal-01196435v3
Convergence rates with singular parameterizations for solving elliptic boundary value problems in isogeometric analysis Meng Wu,Yicao Wang,Bernard Mourrain,Boniface Nkonga,Changzheng Cheng Computer Aided Geometric Design, 2017, 52–53, pp.170-189. ⟨10.1016/j.cagd.2017.02.006⟩ Article dans une revue hal-01276699v2
Tensor decomposition and homotopy continuation Alessandra Bernardi,Noah S. Daleo,Jonathan D. Hauenstein,Bernard Mourrain Differential Geometry and its Applications, 2017, 55, pp.78-105. ⟨10.1016/j.difgeo.2017.07.009⟩ Article dans une revue hal-01250398v1
Geometric Modelling and Deformation for Shape Optimization of Ship Hulls and Appendages Elisa Berrini,Bernard Mourrain,Yann Roux,Mathieu Durand,Guillaume Fontaine Journal of Ship Research, 2017, 61 (2), pp.91-106. ⟨10.5957/JOSR.61.2.160059⟩ Article dans une revue hal-01373249v4
Hermite type Spline spaces over rectangular meshes with complex topological structures Meng Wu,Bernard Mourrain,André Galligo,Boniface Nkonga Communications in Computational Physics, 2017, 21 (3), pp.835-866. ⟨10.4208/cicp.OA-2016-0030⟩ Article dans une revue hal-01196428v4
On the construction of general cubature formula by flat extensions Marta Abril Bucero,Chandrajit Bajaj,Bernard Mourrain Linear Algebra and its Applications, 2016, 502, pp.104-125. ⟨10.1016/j.laa.2015.09.052⟩ Article dans une revue hal-01158099v3
On deflation and multiplicity structure Jonathan D. Hauenstein,Bernard Mourrain,Agnes Szanto Journal of Symbolic Computation, 2016, 83, pp.228-253. ⟨10.1016/j.jsc.2016.11.013⟩ Article dans une revue hal-01250388v1
Geometrically continuous splines for surfaces of arbitrary topology Bernard Mourrain,Raimundas Vidunas,Nelly Villamizar Computer Aided Geometric Design, 2016, 45, pp.108-133. ⟨10.1016/j.cagd.2016.03.003⟩ Article dans une revue hal-01196996v2
Flat extensions in ∗-algebras Bernard Mourrain,Konrad Schmüdgen Proceedings of the American Mathematical Society, 2016, 144 (11), pp.4873-4885. ⟨10.1090/proc/13158⟩ Article dans une revue hal-01009909v1
Border Basis relaxation for polynomial optimization Marta Abril Bucero,Bernard Mourrain Journal of Symbolic Computation, 2015, 74, pp.378-399. ⟨10.1016/j.jsc.2015.08.004⟩ Article dans une revue hal-00981546v3
Bounds on the dimension of trivariate spline spaces: A homological approach Bernard Mourrain,Nelly Villamizar Mathematics in Computer Science, 2014, 8 (2), pp.157-174. ⟨10.1007/s11786-014-0187-8⟩ Article dans une revue hal-00879100v2
On the dimension of spline spaces on planar T-meshes Bernard Mourrain Mathematics of Computation, 2014, 83, pp.847-871 Article dans une revue inria-00533187v3
Extensors and the Hilbert scheme Jerome Brachat,Paolo Lella,Bernard Mourrain,Margherita Roggero Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 2014, pp. 23. ⟨10.2422/2036-2145.201407_003⟩ Article dans une revue hal-00816528v1
A comparison of different notions of ranks of symmetric tensors Alessandra Bernardi,Jérôme Brachat,Bernard Mourrain Linear Algebra and its Applications, 2014, 460, pp.205-230 Article dans une revue hal-00746967v2
Dimensions and bases of hierarchical tensor-product splines Dmitry Berdinsky,Taiwan Kim,Cesare Bracco,Durkbin Cho,Bernard Mourrainet al. Journal of Computational and Applied Mathematics, 2014, 257, pp.86-104. ⟨10.1016/j.cam.2013.08.019⟩ Article dans une revue hal-00876557v1
High-quality construction of analysis-suitable trivariate NURBS solids by reparameterization methods Gang Xu,Bernard Mourrain,André Galligo,Timon Rabczuk Computational Mechanics, 2014, 54 (5), pp.1303-1313. ⟨10.1007/s00466-014-1060-y⟩ Article dans une revue hal-00922544v2
A polynomial approach for extracting the extrema of a spherical function and its application in diffusion MRI Aurobrata Ghosh,Elias Tsigaridas,Bernard Mourrain,Rachid Deriche Medical Image Analysis, 2013, 17 (5), pp.503-514. ⟨10.1016/j.media.2013.03.004⟩ Article dans une revue istex hal-00815120v1
Analysis-suitable volume parameterization of multi-block computational domain in isogeometric applications Gang Xu,Bernard Mourrain,Régis Duvigneau,André Galligo Computer-Aided Design, 2013, Special Issue on Solid and Physical Modeling 2012, 45 (2), pp.395-404. ⟨10.1016/j.cad.2012.10.022⟩ Article dans une revue hal-00685002v2
Optimal analysis-aware parameterization of computational domain in 3D isogeometric analysis Gang Xu,Bernard Mourrain,Régis Duvigneau,André Galligo Computer-Aided Design, 2013, 45 (4), ⟨10.1016/j.cad.2011.05.007⟩ Article dans une revue inria-00539616v1
Homological techniques for the analysis of the dimension of triangular spline spaces Bernard Mourrain,Nelly Villamizar Journal of Symbolic Computation, 2013, 50, pp.564-577. ⟨10.1016/j.jsc.2012.10.002⟩ Article dans une revue hal-00742636v1
Voronoi Diagrams of Algebraic Distance Fields Ioannis Z. Emiris,Angelos Mantzaflaris,Bernard Mourrain Computer-Aided Design, 2013, 45 (2), pp.511-516. ⟨10.1016/j.cad.2012.10.043⟩ Article dans une revue hal-00722406v1
General Tensor Decomposition, Moment Matrices and Applications Alessandra Bernardi,Jerome Brachat,Pierre Comon,Bernard Mourrain Journal of Symbolic Computation, 2013, 52 (May), pp.51-71. ⟨10.1016/j.jsc.2012.05.012⟩ Article dans une revue inria-00590965v3
Constructing analysis-suitable parameterization of computational domain from CAD boundary by variational harmonic method Gang Xu,Bernard Mourrain,Régis Duvigneau,André Galligo Journal of Computational Physics, 2013, 252, pp.275-289. ⟨10.1016/j.jcp.2013.06.029⟩ Article dans une revue hal-00836413v1
Moment Matrices, Border Bases and Real Radical Computation Jean-Bernard Lasserre,Monique Laurent,Bernard Mourrain,Philipp Rostalski,Philippe Trébuchet Journal of Symbolic Computation, 2013, 51, pp.63-85. ⟨10.1016/j.jsc.2012.03.007⟩ Article dans une revue hal-00651759v1
Superfast solution of Toeplitz systems based on syzygy reduction Houssam Khalil,Bernard Mourrain,Michelle Schatzman Linear Algebra and its Applications, 2013, 438 (9), pp.3563-3575. ⟨10.1016/j.laa.2013.01.015⟩ Article dans une revue hal-00780556v1
On the isotopic meshing of an algebraic implicit surface Daouda Niang Diatta,Bernard Mourrain,Olivier Ruatta Journal of Symbolic Computation, 2012, 47 (8), pp.903-925. ⟨10.1016/j.jsc.2011.09.010⟩ Article dans une revue hal-00421214v1
On the problem of instability in the dimension of a spline space over a T-mesh Berdinsky Dmitry,Oh Min-Jae,Kim Taewan,Bernard Mourrain Computers and Graphics, 2012, 36 (5), pp.507-513. ⟨10.1016/j.cag.2012.03.005⟩ Article dans une revue hal-00742505v1
Mathemagix Joris van der Hoeven,Grégoire Lecerf,Bernard Mourrain,Philippe Trebuchet,Jérémy Berthomieuet al. ACM Communications in Computer Algebra, 2012, 45 (3/4), pp.186-188. ⟨10.1145/2110170.2110180⟩ Article dans une revue hal-02350521v1
On the Computation of Matrices of Traces and Radicals of Ideals Itnuit Janovitz-Freireich,Bernard Mourrain,Lajos Ronayi,Agnes Szanto Journal of Symbolic Computation, 2012, 47 (1), pp.102-122. ⟨10.1016/j.jsc.2011.08.020⟩ Article dans une revue inria-00354120v1
A New Error Assessment Method in Isogeometric Analysis of 2D Heat Conduction Problems Gang Xu,Bernard Mourrain,Régis Duvigneau,André Galligo Advanced Science Letters, 2012, 10 (1), pp.508-512. ⟨10.1166/asl.2012.3321⟩ Article dans une revue hal-00742955v1
On Continued Fraction Expansion of Real Roots of Polynomial Systems, Complexity and Condition Numbers Angelos Mantzaflaris,Bernard Mourrain,Elias Tsigaridas Theoretical Computer Science, 2011, 412 (22), pp.2312-2330. ⟨10.1016/j.tcs.2011.01.009⟩ Article dans une revue inria-00530756v1
An Algebraic Approach to Continuous Collision Detection for Ellipsoids Xiaohong Jia,Yi-King Choi,Bernard Mourrain,Wenping Wang Computer Aided Geometric Design, 2011, 28 (3), pp.164-176. ⟨10.1016/j.cagd.2011.01.004⟩ Article dans une revue hal-00646511v1
Parametrization of computational domain in isogeometric analysis: methods and comparison Gang Xu,Bernard Mourrain,Régis Duvigneau,André Galligo Computer Methods in Applied Mechanics and Engineering, 2011, 200 (23-24), pp.2021-2031. ⟨10.1016/j.cma.2011.03.005⟩ Article dans une revue inria-00530758v2
A Subdivision Method for Computing Nearest Gcd with Certification Guillaume Chèze,André Galligo,Bernard Mourrain,Jean-Claude Yakoubsohn Theoretical Computer Science, 2011, 412 (35), pp.4493-4503. ⟨10.1016/j.tcs.2011.04.018⟩ Article dans une revue inria-00589062v1
Symmetric tensor decomposition Jérôme Brachat,Pierre Comon,Bernard Mourrain,Elias P. P. Tsigaridas Linear Algebra and its Applications, 2010, 433 (11-12), pp.1851-1872. ⟨10.1016/j.laa.2010.06.046⟩ Article dans une revue inria-00355713v2
Subdivision methods for solving polynomial equations Bernard Mourrain,Jean-Pascal Pavone Journal of Symbolic Computation, 2009, 44 (3), pp.292-306 Article dans une revue inria-00070350v1
Explicit factors of some iterated resultants and discriminants Laurent Busé,Bernard Mourrain Mathematics of Computation, 2009, 78 (265), pp.345--386 Article dans une revue inria-00119287v2
Signature Sequence of Intersection Curve of Two Quadrics for Exact Morphological Classification Changhe Tu,Wenping Wang,Bernard Mourrain,Jiaye Wang Computer Aided Geometric Design, 2009, 26 (3), pp.317-335. ⟨10.1016/j.cagd.2008.08.004⟩ Article dans une revue hal-00123473v2
Isotopic triangulation of a real algebraic surface Lionel Alberti,Bernard Mourrain,Jean-Pierre Técourt Journal of Symbolic Computation, 2009, 44 (9), pp.1291-1310. ⟨10.1016/j.jsc.2008.02.007⟩ Article dans une revue inria-00433141v1
A Sparse Flat Extension Theorem for Moment Matrices Monique Laurent,Bernard Mourrain Archiv der Mathematik, 2009, 93, pp.87-98. ⟨10.1007/s00013-009-0007-6⟩ Article dans une revue inria-00347022v2
Symmetric tensors and symmetric tensor rank Pierre Comon,Gene Golub,Lek-Heng Lim,Bernard Mourrain SIAM Journal on Matrix Analysis and Applications, 2008, 30 (3), pp.1254-1279 Article dans une revue hal-00327599v1
Stable normal forms for polynomial system solving Bernard Mourrain,Philippe Trébuchet Theoretical Computer Science, 2008, 409 (2), pp.229-240. ⟨10.1016/j.tcs.2008.09.004⟩ Article dans une revue inria-00343103v1
Topology and arrangement computation of semi-algebraic planar curves Lionel Alberti,Bernard Mourrain,Julien Wintz Computer Aided Geometric Design, 2008, Computer Graphics and Applications, 25 (8), pp.631-651. ⟨10.1016/j.cagd.2008.06.009⟩ Article dans une revue inria-00343110v1
On the Computation of an Arrangement of Quadrics in 3D Bernard Mourrain,Jean-Pierre Técourt,Monique Teillaud Computational Geometry, 2005, 30 (2), pp.145-164. ⟨10.1016/j.comgeo.2004.05.003⟩ Article dans une revue inria-00350858v1
Using projection operators in computer aided geometric design Laurent Busé,Mohamed Elkadi,Bernard Mourrain Contemporary mathematics, 2003, 334, pp.321--342 Article dans une revue inria-00098681v1
Algebraic methods and arithmetic filtering for exact predicates on circle arcs Olivier Devillers,Alexandra Fronville,Bernard Mourrain,Monique Teillaud Computational Geometry, 2002, 22, pp.119-142. ⟨10.1016/S0925-7721(01)00050-5⟩ Article dans une revue inria-00166709v1
Circular Cylinders by Four or Five Points in Space Olivier Devillers,Bernard Mourrain,Franco P. Preparata,Philippe Trebuchet Discrete and Computational Geometry, 2002, 29 (1), pp.83--104. ⟨10.1007/s00454-002-2811-7⟩ Article dans une revue inria-00090648v1
Resultant over the residual of a complete intersection Laurent Busé,Mohamed Elkadi,Bernard Mourrain Journal of Pure and Applied Algebra, 2001, Effective methods in algebraic geometry (Bath, 2000), 164 (1-2), pp.35--57 Article dans une revue inria-00099487v1
Generalized resultants over unirational algebraic varieties Laurent Busé,Mohamed Elkadi,Bernard Mourrain Journal of Symbolic Computation, 2000, J. Symbolic Comput., 29 (4-5), pp.515--526 Article dans une revue inria-00096842v1
Multivariate Polynomials, Duality, and Structured Matrices Bernard Mourrain,Victor Y. Pan Journal of Complexity, 2000, 16 (1), pp.110 - 180. ⟨10.1006/jcom.1999.0530⟩ Article dans une revue istex hal-00739512v1
Isolated points, duality and residues Bernard Mourrain Journal of Pure and Applied Algebra, 1996, 117&118, pp.469--493 Article dans une revue inria-00125278v1

Communication dans un congrès (39)

Computing real radicals by moment optimization Lorenzo Baldi,Bernard Mourrain ISSAC 2021 - 46th International Symposium on Symbolic and Algebraic Computation, Jul 2021, Saint-Pétersbourg, Russia. ⟨10.1145/3452143.3465541⟩ Communication dans un congrès hal-03145501v2
Polynomial optimization based schemes for solving AC Optimal Power Flow problems Edgar Fuentes,Bernard Mourrain,Michaël Gabay EURO 2021, Jul 2021, Athens, Greece Communication dans un congrès hal-04050425v1
Punctual Hilbert Schemes and Certified Approximate Singularities Angelos Mantzaflaris,Bernard Mourrain,Agnes Szanto ISSAC 2020 - International Symposium on Symbolic and Algebraic Computation, Jul 2020, Kalamata, Greece. ⟨10.1145/3373207.3404024⟩ Communication dans un congrès hal-02478768v2
Axl, a geometric modeler for semi-algebraic shapes Emmanouil Christoforou,Angelos Mantzaflaris,Bernard Mourrain,Julien Wintz ICMS 2018 - 6th International Conference on Mathematical Software, Jul 2018, Notre Dame, United States. pp.128-136, ⟨10.1007/978-3-319-96418-8_16⟩ Communication dans un congrès hal-01848546v1
Fast algorithm for border bases of Artinian Gorenstein algebras Bernard Mourrain ISSAC'17 -- International Symposium on Symbolic and Algebraic Computation, Jul 2017, Kaiserslautern, Germany. pp.333--340, ⟨10.1145/3087604.3087632⟩ Communication dans un congrès hal-01515366v1
Geometric model for automated multi-objective optimization of foils Elisa Berrini,Bernard Mourrain,Regis Duvigneau,Matthieu Sacher,Yann Roux Marine 2017, May 2017, Nantes, France. pp.473-484 Communication dans un congrès hal-01524287v1
Efficient certication of numeric solutions to eigenproblems Joris van der Hoeven,Bernard Mourrain MACIS 2017 - 7th International Conference on Mathematical Aspects of Computer and Information Sciences, Nov 2017, Vienna, Austria. pp.81--94, ⟨10.1007/978-3-319-72453-9_6⟩ Communication dans un congrès hal-01579079v1
Border Basis for Polynomial System Solving and Optimization Philippe Trébuchet,Bernard Mourrain,Marta Abril Bucero ICMS 2016 - 5th International Conference on Mathematical Software, Jul 2016, Berlin, Germany. pp.212-220, ⟨10.1007/978-3-319-42432-3_27⟩ Communication dans un congrès hal-01356869v1
Parametric shape modeler for hulls and appendages Elisa Berrini,Bernard Mourrain,Yann Roux,Guillaume Fontaine,Eric Jean COMPIT'16, May 2016, Lecce, Italy. pp.255-263 Communication dans un congrès hal-01373867v1
Certifying isolated singular points and their multiplicity structure Jonathan D. Hauenstein,Bernard Mourrain,Agnes Szanto ISSAC'15, Jul 2015, Bath, United Kingdom. pp.213-220, ⟨10.1145/2755996.2756645⟩ Communication dans un congrès hal-01107541v2
Toric Border Basis Bernard Mourrain,Philippe Trebuchet ISSAC'14 - International Symposium on Symbolic and Algebraic Computation, Jul 2014, Kobe, Japan. pp.343-350, ⟨10.1145/2608628.2608652⟩ Communication dans un congrès hal-00994683v1
The Geometry of Sound-Source Localization using Non-Coplanar microphone Arrays Xavier Alameda-Pineda,Radu Horaud,Bernard Mourrain WASPAA 2013 - IEEE Workshop on Applications of Signal Processing to Audio and Acoustics, Oct 2013, New Paltz, NY, United States. pp.1-4, ⟨10.1109/WASPAA.2013.6701896⟩ Communication dans un congrès hal-00848876v1
Bulbous Bow Shape Optimization Louis Blanchard,Elisa Berrini,Régis Duvigneau,Yann Roux,Bernard Mourrainet al. 5th International Conference on Computational Methods in Marine Engineering, May 2013, Hamburg, Germany Communication dans un congrès hal-00873272v1
Border basis representation of a general quotient algebra Bernard Mourrain,Philippe Trebuchet International Conference on Symbolic and Algebraic Computation (ISSAC), Jul 2012, Grenoble, France. pp.265-272, ⟨10.1145/2442829.2442868⟩ Communication dans un congrès hal-00709962v1
Multihomogeneous Polynomial Decomposition using Moment Matrices Alessandra Bernardi,Jérôme Brachat,Pierre Comon,Bernard Mourrain 36th international symposium on Symbolic and algebraic computation (ISSAC 11), Jun 2011, San Jose, United States. pp.35-42, ⟨10.1145/1993886.1993898⟩ Communication dans un congrès inria-00638837v1
Deflation and Certified Isolation of Singular Zeros of Polynomial Systems Angelos Mantzaflaris,Bernard Mourrain International Symposium on Symbolic and Algebraic Computation (ISSAC), Jun 2011, San Jose, CA, United States. pp.249-256, ⟨10.1145/1993886.1993925⟩ Communication dans un congrès inria-00556021v1
An Adapted Version of the Bentley-Ottmann Algorithm for Invariants of Plane Curves Singularities Madalina Hodorog,Bernard Mourrain,Joseph Schicho 11th International Conference on Computational Science and Its Applications (ICCSA), Jun 2011, Santander, Spain. pp.121-131, ⟨10.1007/978-3-642-21931-3_10⟩ Communication dans un congrès hal-00646566v1
Optimal analysis-aware parameterization of computational domain in isogeometric analysis Gang Xu,Bernard Mourrain,Régis Duvigneau,André Galligo GMP, Jun 2010, Castro Urdiales, Spain. pp.236-254 Communication dans un congrès inria-00440130v3
A Subdivision Approach to Planar Semi-algebraic Sets Angelos Mantzaflaris,Bernard Mourrain 6th International Conference, GMP, Jun 2010, Castro Urdiales, Spain. pp.104-123, ⟨10.1007/978-3-642-13411-1_8⟩ Communication dans un congrès inria-00463491v2
The DMM bound: multivariate (aggregate) separation bounds Ioannis Z. Emiris,Bernard Mourrain,Elias Tsigaridas Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation, Jul 2010, Munich, Germany. pp.243-250, ⟨10.1145/1837934.1837981⟩ Communication dans un congrès inria-00393833v4
A Symbolic-Numeric Algorithm for Computing the Alexander Polynomial of a Plane Curve Singularity Mădălina Hodorog,Bernard Mourrain,Josef Schicho International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC), Sep 2010, Timisoara, Romania. pp.21-28 Communication dans un congrès inria-00542193v1
Curve/surface intersection problem by means of matrix representations Thang Luu Ba,Laurent Busé,Bernard Mourrain SNC, Aug 2009, Kyoto, Japan. pp.71-78, ⟨10.1145/1577190.1577205⟩ Communication dans un congrès inria-00418403v1
Symmetric tensor decomposition Jérôme Brachat,Pierre Comon,Bernard Mourrain,Elias P. P. Tsigaridas 17th European Signal Processing Conference 2009., Aug 2009, Glasgow, United Kingdom. pp.525-529 Communication dans un congrès hal-00435908v1
Continued Fraction Expansion of Real Roots of Polynomial Systems Angelos Mantzaflaris,Bernard Mourrain,Elias P. P. Tsigaridas SNC, conference on Symbolic-Numeric Computation, Aug 2009, Kyoto, Japan. pp.85-94, ⟨10.1145/1577190.1577207⟩ Communication dans un congrès inria-00387399v2
Computing Nearest Gcd with Certification Guillaume Chèze,Jean-Claude Yakoubsohn,André Galligo,Bernard Mourrain International Workshop Symbolic-Numeric Computation (SNC), Aug 2009, Kyoto, Japan. pp.29-34 Communication dans un congrès inria-00437559v1
Experimental evaluation and cross-benchmarking of univariate real solvers Ioannis Z. Emiris,Michael Hemmer,Menelaos Karavelas,Bernard Mourrain,Elias P. P. Tsigaridaset al. International Workshop SNC, ACM, Aug 2009, Kyoto, Japan. pp.85-94, ⟨10.1145/1577190.1577202⟩ Communication dans un congrès inria-00340887v2
Efficient and robust reconstruction of botanical branching structure from laser scanned points Dong-Ming Yan,Julien Wintz,Bernard Mourrain,Wenping Wang,Frédéric Boudonet al. CAD/Graphics 2009, Aug 2009, Yellow Mountain City, China. pp.572-575 Communication dans un congrès inria-00436480v1
Real Algebraic Numbers: Complexity Analysis and Experimentations Ioannis Z. Emiris,Bernard Mourrain,Elias P. P. Tsigaridas Reliable Implementations of Real Number Algorithms: Theory and Practice, 2008, Dagsthul, Germany. pp.57-82 Communication dans un congrès inria-00071370v1
Toeplitz and Toeplitz-block-Toeplitz matrices and their correlation with syzygies of polynomials. Houssam Khalil,Bernard Mourrain,Michelle Schatzman international seminar matrix methods and operator equations (MM&OE), Jul 2007, Moscou, Russia. pp.296-312 Communication dans un congrès hal-00366292v1
A polynomial based approach to extract the maxima of an antipodally symmetric spherical function and its application to extract fiber directions from the Orientation Distribution Function in Diffusion MRI Aurorata Ghosh,Elias P. P. Tsigaridas,Maxime Descoteaux,Pierre Comon,Bernard Mourrainet al. 11th International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), Sep 2008, New York, United States. p. 237-248 Communication dans un congrès hal-00340600v1
On the Computation of the Topology of a Non-Reduced Implicit Space Curve Daouda Niang Diatta,Bernard Mourrain,Olivier Ruatta ISSAC, Jul 2008, Linz, Austria. pp.47-54, ⟨10.1145/1390768.1390778⟩ Communication dans un congrès hal-00218271v1
Moment matrices, trace matrices and the radical of ideals Inuit Janovitz-Freireich,Agnes Szanto,Bernard Mourrain,Lajos Ronyai ISSAC, Jul 2008, Linz, Austria. pp.125-132 Communication dans un congrès inria-00343126v1
Visualisation of implicit algebraic curves Lionel Alberti,Bernard Mourrain Pacific Conference on Computer Graphics and Applications 2007, Ron Goldman, Oct 2007, Lahaina, Maui, Hawaii, United States. pp.303-312 Communication dans un congrès inria-00175062v1
A subdivision arrangement algorithm for semi-algebraic curves: an overview Julien Wintz,Bernard Mourrain 15th Pacific Conference on Computer Graphics and Applications, Ron Goldman, Oct 2007, Lahaina, Maui, Hawaii, United States. pp.449-452, ⟨10.1109/ISBN0-7695-3009-5⟩ Communication dans un congrès inria-00189560v1
Generalized normal forms and polynomial system solving Bernard Mourrain,Philippe Trebuchet ISSAC 2005 - International Symposium on Symbolic and Algebraic Computation , Jul 2005, Beijing, China. pp.253-260, ⟨10.1145/1073884.1073920⟩ Communication dans un congrès inria-00070537v1
The Offset to an Algebraic Curve and an Application to Conics François Anton,Ioannis Z. Emiris,Bernard Mourrain,Monique Teillaud International Conference on Computational Science and its Applications, May 2005, Singapore, Singapore. pp.683-696 Communication dans un congrès inria-00350878v1
Resultant-based methods for plane curves intersection problems Laurent Busé,Houssam Khalil,Bernard Mourrain Computer Algebra in Scientific Computing (CASC), Sep 2005, Kalamata, Greece, pp.75-92 Communication dans un congrès inria-00100288v1
An environment for Symbolic and Numeric Computation Gabriel dos Reis,Bernard Mourrain,Philippe Trebuchet,Fabrice Rouillier International Congress of Mathematical Software - ICMS'2002, 2002, Beijing, China. pp.239-249 Communication dans un congrès inria-00100984v1
Algebraic methods and arithmetic filtering for exact predicates on circle arcs Olivier Devillers,Alexandra Fronville,Bernard Mourrain,Monique Teillaud Proceedings of the 16th Annual Symposium on Computational Geometry, 2000, Hong Kong, China. pp.139-147, ⟨10.1145/336154.336194⟩ Communication dans un congrès hal-01179417v1

Ouvrages (5)

Polynomial Optimization, Moments, and Applications Michal Kočvara,Bernard Mourrain,Cordian Riener Springer. Springer, 206, pp.258, 2023, SOIA. Springer Optimization and Its Applications, 978-3-031-38658-9 Ouvrages hal-04087030v1
Computational Algebraic Geometry and its Applications Laurent Busé,Mohamed Elkadi,Bernard Mourrain Laurent Busé, Mohamed Elkadi, Bernard Mourrain. Elsevier, 392, pp.178, 2008, Theoretical Computer Sciences Ouvrages inria-00344404v1
Special Issue on Symbolic and Algebraic Computation d'Andrea Carlos,Bernard Mourrain C. D'andrea & B. Mourrain. Elsevier, 44, pp.135, 2008, 7, ⟨10.1016/j.jsc.2008.07.005⟩ Ouvrages istex inria-00558470v1
Introduction à la résolution des systèmes polynomiaux Mohamed Elkadi,Bernard Mourrain Springer, 59, pp.307, 2007, Mathématiques et Applications, 978-3-540-71646-4 Ouvrages inria-00170536v1
Special Issue on Algebraic and Numerical Algorithms Bernard Mourrain,Ioannis Z. Emiris,Victor Y. Y. Pan Emiris, I. and Mourrain, B. and Pan, Y. V. Elsevier, 315, pp.310, 2004 Ouvrages inria-00170535v1

Chapitre d'ouvrage (11)

Isolated singularities, inverse systems and the punctual Hilbert scheme Bernard Mourrain Anthony Iarrobino; Pedro Macias Marques; Maria Evelina Rossi; Jean Vallès. Deformation of Artinian Algebras and Jordan Type, 805, American Mathematical Society, pp.205-224, 2024, Contemporary Mathematics, ⟨10.1090/conm/805/16135⟩ Chapitre d'ouvrage hal-04059950v1
Polynomial optimization in geometric modeling Soodeh Habibi,Michal Kočvara,Bernard Mourrain Michal Kočvara; Bernard Mourrain; Cordian Riener. Polynomial Optimization, Moments, and Applications, Springer, pp.163-186, In press Chapitre d'ouvrage hal-04081849v1
Efficient Certification of Numeric Solutions to Eigenproblems Joris van der Hoeven,Bernard Mourrain Mathematical Aspects of Computer and Information Sciences, pp.81-94, 2017, ⟨10.1007/978-3-319-72453-9_6⟩ Chapitre d'ouvrage hal-02350517v1
Singular Zeros of Polynomial Systems Angelos Mantzaflaris,Bernard Mourrain SAGA – Advances in ShApes, Geometry, and Algebra. Geometry and Computing, vol 10., pp.77-103, 2014, ⟨10.1007/978-3-319-08635-4_5⟩ Chapitre d'ouvrage hal-02958889v1
Shape Interrogation Stefanie Hahmann,Alexander Belyaev,Laurent Busé,Gershon Elber,Bernard Mourrainet al. Leila De Floriani, Michela Spagnuolo. Shape Analysis and Structuring, Springer, pp.1-51, 2008, Mathematics and Visualization, 978-3-540-33265-7. ⟨10.1007/978-3-540-33265-7_1⟩ Chapitre d'ouvrage istex inria-00193551v1
Pythagore's Dilemma, Symbolic-Numeric Computation, and the Border Basis Method Bernard Mourrain Dongming Wang and Lihong Zhi. Symbolic-Numeric Computation, Birkhauser, pp.223--243, 2007, Trends in Mathematics Chapitre d'ouvrage inria-00137424v1
Meshing of Surfaces Jean-Daniel Boissonnat,David Cohen-Steiner,Bernard Mourrain,Guenter Rote,Gert Vegter Effective Computational Geometry for Curves and Surfaces, Springer, pp.181-230, 2007, Mathematics and Visualization Chapitre d'ouvrage hal-00488274v1
Biologie Moléculaire Structurale et Géométrie Marc-André Delsuc,Thérèse Malliavin,Antoine Marin,Bernard Mourrain Yves Gautier. La Science au Présent, Encyclopaedia Universalis, pp.128-131, 2007, 2-85229-514-8 Chapitre d'ouvrage inria-00175688v1
Regularity criteria for the topology of algebraic curves and surfaces Lionel Alberti,Bernard Mourrain Ralph Martin and Malcom Sabin and Joab Winkler. Mathematics of Surfaces XII, 4647, Springer, pp.1-28, 2007, LNCS, 0302-9743 Chapitre d'ouvrage inria-00170886v1
SYNAPS: A library for dedicated applications in symbolic numeric computing, Bernard Mourrain,Jean-Pascal Pavone,Philippe Trebuchet,Elias P. Tsigaridas,Julien Wintz M.E. Stillman and N. Takayama and J. Verschelde. Software for algebraic geometry, 148, Springer, pp.81-110, 2007, IMA Volumes in Mathematics and its Applications Chapitre d'ouvrage inria-00178498v1
Subdivision Methods for the Topology of 2d and 3d Implicit Curves Chen Liang,Bernard Mourrain,Jean-Pascal Pavone Bert Juetller and Ragni Piene. Geometric Modeling and Algebraic Geometry, Springer, pp.199-214, 2007, 978-3-540-72184-0 Chapitre d'ouvrage inria-00130216v1

Autre publication scientifique (1)

Uniqueness of Minimal Euclidean Reconstruction from 4 Points Long Quan,Bill Triggs,Marc-André Ameller,Bernard Mourrain 2001 Autre publication scientifique inria-00548269v1

Pré-publication, Document de travail (8)

The Effective Countable Generalized Moment Problem Lucas Gamertsfelder,Bernard Mourrain 2025 Pré-publication, Document de travail (preprint/prepublication) hal-04885482v4
Truncated Normal Forms for Solving Algebraic Equations Bernard Mourrain 2025 Pré-publication, Document de travail hal-05135952v1
Generalized additive decompositions of symmetric tensors Enrica Barrilli,Bernard Mourrain,Daniele Taufer 2025 Pré-publication, Document de travail hal-05339397v1
Weighted Moment-SoS Approach to POMDPs with Polynomial Data: Theory and Applications Konstantin Avrachenkov,Lucas Gamertsfelder,Bernard Mourrain 2025 Pré-publication, Document de travail hal-05355845v1
Spline Spaces over Quadrangle Meshes with Complex Topologies Meng Wu,Bernard Mourrain,André Galligo,Boniface Nkonga 2014 Pré-publication, Document de travail hal-00952455v1
Exact relaxation for polynomial optimization on semi-algebraic sets Marta Abril Bucero,Bernard Mourrain 2014 Pré-publication, Document de travail hal-00846977v4
Unconstraint global polynomial optimization via Gradient Ideal Marta Abril Bucero,Bernard Mourrain,Philippe Trébuchet 2013 Pré-publication, Document de travail hal-00779666v3
The Hilbert scheme of points and its link with border basis Mariemi Alonso,Jérome Brachat,Bernard Mourrain 2010 Pré-publication, Document de travail inria-00433127v2

Rapport (18)

Automated Generation of Geometric Models for a Bulbous Trawler Ship Louis Blanchard,Régis Duvigneau,Bernard Mourrain [Research Report] RR-8011, INRIA. 2012 Rapport (rapport de recherche) hal-00714791v1
Constructing analysis-suitable parameterization of computational domain from CAD boundary by variational harmonic method Gang Xu,Bernard Mourrain,Régis Duvigneau,André Galligo [Research Report] 2011 Rapport (rapport de recherche) inria-00585663v2
Hierarchical Optimization in Isogeometric Analysis : Application to Thermal Conduction Louis Blanchard,Régis Duvigneau,Gang Xu,Bernard Mourrain [Research Report] RR-7470, INRIA. 2010 Rapport (rapport de recherche) inria-00542271v1
Isotopic meshing of a real algebraic surface Bernard Mourrain,Jean-Pierre Técourt [Research Report] RR-5508, INRIA. 2006, pp.21 Rapport (rapport de recherche) inria-00070499v1
Computing the topology of three-dimensional algebraic curves Grégory Gatelier,Abder Labrouzy,Bernard Mourrain,Jean-Pierre Técourt [Research Report] RR-5194, INRIA. 2004, pp.21 Rapport (rapport de recherche) inria-00070798v1
Bernstein's basis and real root isolation Bernard Mourrain,Fabrice Rouillier,Marie-Françoise Roy [Research Report] RR-5149, INRIA. 2004 Rapport (rapport de recherche) inria-00071434v1
Isolation of Real Roots and Computation of the Topological Degree Bernard Mourrain,Michael N. Vrahatis,Jean-Claude Yakoubsohn [Research Report] RR-4300, INRIA. 2001 Rapport (rapport de recherche) inria-00072287v1
On circular Cylinders by Four or Five Points in Space Olivier Devillers,Bernard Mourrain,Franco P. Preparata,Philippe Trebuchet RR-4195, INRIA. 2001 Rapport inria-00072427v1
Certificated and Efficient Solver for Intersection of three quadric surfaces Abhishek Pandey,Bernard Mourrain,Sylvain Lazard [Internship report] A00-R-393 || pandey00a, 2000 Rapport inria-00099246v1
A framework for Symbolic and Numeric Computations Bernard Mourrain,Hélène Prieto [Research Report] RR-4013, INRIA. 2000, pp.96 Rapport (rapport de recherche) inria-00072629v1
Sign Methods for Counting and Computing Real Roots of Algebraic Systems Ioannis Z. Emiris,Bernard Mourrain,Mihail N. Vrahatis RR-3669, INRIA. 1999 Rapport inria-00073003v1
Algebraic Methods and Arithmetic Filtering for Exact Predicates on Circle Arcs Olivier Devillers,Alexandra Fronville,Bernard Mourrain,Monique Teillaud RR-3826, INRIA. 1999 Rapport inria-00072832v1
Multivariate Polynomials, Duality and Structured Matrices Bernard Mourrain,Victor Y. Y. Pan RR-3513, INRIA. 1998 Rapport inria-00073171v1
Some Applications of Bezoutians in Effective Algebraic Geometry Mohamed Elkadi,Bernard Mourrain RR-3572, INRIA. 1998 Rapport inria-00073109v1
Approche effective des résidus algébriques Mohamed Elkadi,Bernard Mourrain RR-2884, INRIA. 1996 Rapport inria-00073806v1
Polynomial System Solving: the Case of a Six-Atom Molecule Ioannis Z. Emiris,Bernard Mourrain RR-3075, INRIA. 1996 Rapport inria-00073617v1
On the Geometry and Algebra of the Point and Line Correspondences between $N$ Images Olivier Faugeras,Bernard Mourrain RR-2665, INRIA. 1995 Rapport inria-00074025v1
About the rational map Bernard Mourrain RR-2141, INRIA. 1993 Rapport inria-00074531v1

Cours (1)

From moments to sparse representations, an algebraic, geometric and algorithmic viewpoint Bernard Mourrain École thématique. France. 2019 Cours hal-04193946v1