Co-authors

Number of documents

127

Publication B. Mourrain


Journal articles55 documents

  • Cédric Josz, Jean-Bernard Lasserre, Bernard Mourrain. Sparse polynomial interpolation: sparse recovery, super resolution, or Prony?. Advances in Computational Mathematics, Springer Verlag, 2019, ⟨10.1007/s10444-019-09672-2⟩. ⟨hal-01575325v2⟩
  • Agostino Martinelli, Alexander Oliva, Bernard Mourrain. Cooperative Visual-Inertial Sensor Fusion: the Analytic Solution. IEEE Robotics and Automation Letters, IEEE 2019, 4 (2), pp.453-460. ⟨10.1109/LRA.2019.2891025⟩. ⟨hal-01966542⟩
  • Ioannis Emiris, Bernard Mourrain, Elias Tsigaridas. Separation bounds for polynomial systems. Journal of Symbolic Computation, Elsevier, 2019. ⟨hal-01105276v5⟩
  • Gang Xu, Yaoli Jin, Zhoufang Xiao, Qing Wu, Bernard Mourrain, et al.. Exact conversion from Bézier tetrahedra to Bézier hexahedra. Computer Aided Geometric Design, Elsevier, 2018, 62, pp.154 - 165. ⟨10.1016/j.cagd.2018.03.022⟩. ⟨hal-01936167⟩
  • Bernard Mourrain. Polynomial-Exponential Decomposition from Moments. Foundations of Computational Mathematics, Springer Verlag, 2018, 18 (6), pp.1435-1492. ⟨10.1007/s10208-017-9372-x⟩. ⟨hal-01367730v3⟩
  • Simon Telen, Bernard Mourrain, Marc van Barel. Solving Polynomial Systems via a Stabilized Representation of Quotient Algebras. SIAM Journal on Matrix Analysis and Applications, Society for Industrial and Applied Mathematics, 2018, 39 (3), pp.1421-1447. ⟨10.1137/17M1162433⟩. ⟨hal-01630425⟩
  • Gang Xu, Ming Li, Bernard Mourrain, Timon Rabczuk, Jinlan Xu, et al.. Constructing IGA-suitable planar parameterization from complex CAD boundary by domain partition and global/local optimization. Computer Methods in Applied Mechanics and Engineering, Elsevier, 2018, 328, pp.175 - 200. ⟨10.1016/j.cma.2017.08.052⟩. ⟨hal-01599319⟩
  • Jouhayna Harmouch, Houssam Khalil, Bernard Mourrain. Structured low rank decomposition of multivariate Hankel matrices. Linear Algebra and Applications, Elsevier - Academic Press, 2017, ⟨10.1016/j.laa.2017.04.015⟩. ⟨hal-01440063⟩
  • Meng Wu, Bernard Mourrain, André Galligo, Boniface Nkonga. H1-parametrizations of complex planar physical domains in Isogeometric analysis. Computer Methods in Applied Mechanics and Engineering, Elsevier, 2017, 318, pp.296-318. ⟨10.1016/j.cma.2017.01.025⟩. ⟨hal-01196435v3⟩
  • Elisa Berrini, Bernard Mourrain, Yann Roux, Mathieu Durand, Guillaume Fontaine. Geometric Modelling and Deformation for Shape Optimization of Ship Hulls and Appendages. Journal of Ship Research, 2017, 61 (2), pp.91-106. ⟨10.5957/JOSR.61.2.160059⟩. ⟨hal-01373249v4⟩
  • Ahmed Blidia, Bernard Mourrain, Nelly Villamizar. $G^1$-smooth splines on quad meshes with 4-split macro-patch elements. Computer Aided Geometric Design, Elsevier, 2017, 52–53, pp.106-125. ⟨10.1016/j.cagd.2017.03.003⟩. ⟨hal-01491676⟩
  • Meng Wu, Yicao Wang, Bernard Mourrain, Boniface Nkonga, Changzheng Cheng. Convergence rates with singular parameterizations for solving elliptic boundary value problems in isogeometric analysis. Computer Aided Geometric Design, Elsevier, 2017, 52–53, pp.170-189. ⟨10.1016/j.cagd.2017.02.006⟩. ⟨hal-01276699v2⟩
  • Meng Wu, Bernard Mourrain, André Galligo, Boniface Nkonga. Hermite type Spline spaces over rectangular meshes with complex topological structures. Communications in Computational Physics, Global Science Press, 2017, 21 (3), pp.835-866. ⟨10.4208/cicp.OA-2016-0030⟩. ⟨hal-01196428v4⟩
  • Alessandra Bernardi, Noah S. Daleo, Jonathan D. Hauenstein, Bernard Mourrain. Tensor decomposition and homotopy continuation. Differential Geometry and its Applications, Elsevier, 2017, 55, pp.78-105. ⟨10.1016/j.difgeo.2017.07.009⟩. ⟨hal-01250398⟩
  • Bernard Mourrain, Konrad Schmüdgen. Flat extensions in ∗-algebras. Proceedings of the American Mathematical Society, American Mathematical Society, 2016, 144 (11), pp.4873-4885. ⟨10.1090/proc/13158⟩. ⟨hal-01009909⟩
  • Bernard Mourrain, Raimundas Vidunas, Nelly Villamizar. Geometrically continuous splines for surfaces of arbitrary topology. Computer Aided Geometric Design, Elsevier, 2016, 45, pp.108-133. ⟨10.1016/j.cagd.2016.03.003⟩. ⟨hal-01196996v2⟩
  • Marta Abril Bucero, Chandrajit Bajaj, Bernard Mourrain. On the construction of general cubature formula by flat extensions. Linear Algebra and its Applications, Elsevier, 2016, 502, pp.104-125. ⟨10.1016/j.laa.2015.09.052⟩. ⟨hal-01158099v3⟩
  • Marta Abril Bucero, Bernard Mourrain. Border Basis relaxation for polynomial optimization. Journal of Symbolic Computation, Elsevier, 2015, 74, pp.378-399. ⟨10.1016/j.jsc.2015.08.004⟩. ⟨hal-00981546v3⟩
  • Jerome Brachat, Paolo Lella, Bernard Mourrain, Margherita Roggero. Extensors and the Hilbert scheme. Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, Scuola Normale Superiore 2014, pp. 23. ⟨10.2422/2036-2145.201407_003 ⟩. ⟨hal-00816528⟩
  • Alessandra Bernardi, Jérôme Brachat, Bernard Mourrain. A comparison of different notions of ranks of symmetric tensors. Linear Algebra and its Applications, Elsevier, 2014, 460, pp.205-230. ⟨hal-00746967v2⟩
  • Bernard Mourrain. On the dimension of spline spaces on planar T-meshes. Mathematics of Computation, American Mathematical Society, 2014, 83, pp.847-871. ⟨inria-00533187v3⟩
  • Dmitry Berdinsky, Taiwan Kim, Cesare Bracco, Durkbin Cho, Bernard Mourrain, et al.. Dimensions and bases of hierarchical tensor-product splines. Journal of Computational and Applied Mathematics, Elsevier, 2014, 257, pp.86-104. ⟨10.1016/j.cam.2013.08.019⟩. ⟨hal-00876557⟩
  • Gang Xu, Bernard Mourrain, André Galligo, Timon Rabczuk. High-quality construction of analysis-suitable trivariate NURBS solids by reparameterization methods. Computational Mechanics, Springer Verlag, 2014, 54 (5), pp.1303-1313. ⟨10.1007/s00466-014-1060-y⟩. ⟨hal-00922544v2⟩
  • Bernard Mourrain, Nelly Villamizar. Bounds on the dimension of trivariate spline spaces: A homological approach. Mathematics in Computer Science, Springer, 2014, 8 (2), pp.157-174. ⟨10.1007/s11786-014-0187-8⟩. ⟨hal-00879100v2⟩
  • Gang Xu, Bernard Mourrain, Régis Duvigneau, André Galligo. Constructing analysis-suitable parameterization of computational domain from CAD boundary by variational harmonic method. Journal of Computational Physics, Elsevier, 2013, 252, pp.275-289. ⟨10.1016/j.jcp.2013.06.029⟩. ⟨hal-00836413⟩
  • Ioannis Z. Emiris, Angelos Mantzaflaris, Bernard Mourrain. Voronoi Diagrams of Algebraic Distance Fields. Computer-Aided Design, Elsevier, 2013, 45 (2), pp.511-516. ⟨10.1016/j.cad.2012.10.043⟩. ⟨hal-00722406⟩
  • Gang Xu, Bernard Mourrain, Régis Duvigneau, André Galligo. Optimal analysis-aware parameterization of computational domain in 3D isogeometric analysis. Computer-Aided Design, Elsevier, 2013, 45 (4), ⟨10.1016/j.cad.2011.05.007⟩. ⟨inria-00539616⟩
  • Gang Xu, Bernard Mourrain, Régis Duvigneau, André Galligo. Analysis-suitable volume parameterization of multi-block computational domain in isogeometric applications. Computer-Aided Design, Elsevier, 2013, Special Issue on Solid and Physical Modeling 2012, 45 (2), pp.395-404. ⟨10.1016/j.cad.2012.10.022⟩. ⟨hal-00685002v2⟩
  • Houssam Khalil, Bernard Mourrain, Michelle Schatzman. Superfast solution of Toeplitz systems based on syzygy reduction. Linear Algebra and its Applications, Elsevier, 2013, 438 (9), pp.3563-3575. ⟨10.1016/j.laa.2013.01.015⟩. ⟨hal-00780556⟩
  • Alessandra Bernardi, Jerome Brachat, Pierre Comon, Bernard Mourrain. General Tensor Decomposition, Moment Matrices and Applications. Journal of Symbolic Computation, Elsevier, 2013, 52 (May), pp.51-71. ⟨10.1016/j.jsc.2012.05.012⟩. ⟨inria-00590965v3⟩
  • Bernard Mourrain, Nelly Villamizar. Homological techniques for the analysis of the dimension of triangular spline spaces. Journal of Symbolic Computation, Elsevier, 2013, 50, pp.564-577. ⟨10.1016/j.jsc.2012.10.002⟩. ⟨hal-00742636⟩
  • Gang Xu, Bernard Mourrain, Régis Duvigneau, André Galligo. A New Error Assessment Method in Isogeometric Analysis of 2D Heat Conduction Problems. Advanced Science Letters, American Scientific Publishers, 2012, 10 (1), pp.508-512. ⟨10.1166/asl.2012.3321⟩. ⟨hal-00742955⟩
  • Berdinsky Dmitry, Oh Min-Jae, Kim Taewan, Bernard Mourrain. On the problem of instability in the dimension of a spline space over a T-mesh. Computers and Graphics, Elsevier, 2012, 36 (5), pp.507-513. ⟨10.1016/j.cag.2012.03.005⟩. ⟨hal-00742505⟩
  • Itnuit Janovitz-Freireich, Bernard Mourrain, Lajos Ronayi, Agnes Szanto. On the Computation of Matrices of Traces and Radicals of Ideals. Journal of Symbolic Computation, Elsevier, 2012, 47 (1), pp.102-122. ⟨10.1016/j.jsc.2011.08.020⟩. ⟨inria-00354120⟩
  • Daouda Diatta, Bernard Mourrain, Olivier Ruatta. On the isotopic meshing of an algebraic implicit surface. Journal of Symbolic Computation, Elsevier, 2012, 47 (8), pp.903-925. ⟨10.1016/j.jsc.2011.09.010⟩. ⟨hal-00421214⟩
  • Gang Xu, Bernard Mourrain, Régis Duvigneau, André Galligo. Parametrization of computational domain in isogeometric analysis: methods and comparison. Computer Methods in Applied Mechanics and Engineering, Elsevier, 2011, 200 (23-24), pp.2021-2031. ⟨10.1016/j.cma.2011.03.005⟩. ⟨inria-00530758v2⟩
  • Angelos Mantzaflaris, Bernard Mourrain, Elias Tsigaridas. On Continued Fraction Expansion of Real Roots of Polynomial Systems, Complexity and Condition Numbers. Theoretical Computer Science, Elsevier, 2011, 412 (22), pp.2312-2330. ⟨10.1016/j.tcs.2011.01.009⟩. ⟨inria-00530756⟩
  • Guillaume Chèze, André Galligo, Bernard Mourrain, Jean-Claude Yakoubsohn. A Subdivision Method for Computing Nearest Gcd with Certification. Theoretical Computer Science, Elsevier, 2011, 412 (35), pp.4493-4503. ⟨10.1016/j.tcs.2011.04.018⟩. ⟨inria-00589062⟩
  • Xiaohong Jia, Yi-King Choi, Bernard Mourrain, Wenping Wang. An Algebraic Approach to Continuous Collision Detection for Ellipsoids. Computer Aided Geometric Design, Elsevier, 2011, 28 (3), pp.164-176. ⟨10.1016/j.cagd.2011.01.004⟩. ⟨hal-00646511⟩
  • Jérôme Brachat, Pierre Comon, Bernard Mourrain, Elias P. Tsigaridas. Symmetric tensor decomposition. Linear Algebra and Applications, Elsevier - Academic Press, 2010, 433 (11-12), pp.1851-1872. ⟨inria-00355713v2⟩
  • Laurent Busé, Bernard Mourrain. Explicit factors of some iterated resultants and discriminants. Mathematics of Computation, American Mathematical Society, 2009, 78 (265), pp.345--386. ⟨inria-00119287v2⟩
  • Changhe Tu, Wenping Wang, Bernard Mourrain, Jiaye Wang. Signature Sequence of Intersection Curve of Two Quadrics for Exact Morphological Classification. Computer Aided Geometric Design, Elsevier, 2009, 26 (3), pp.317-335. ⟨10.1016/j.cagd.2008.08.004⟩. ⟨hal-00123473v2⟩
  • Monique Laurent, Bernard Mourrain. A Sparse Flat Extension Theorem for Moment Matrices. Archiv der Mathematik, Springer Verlag, 2009, 93, pp.87-98. ⟨10.1007/s00013-009-0007-6⟩. ⟨inria-00347022v2⟩
  • Bernard Mourrain, Jean-Pascal Pavone. Subdivision methods for solving polynomial equations. Journal of Symbolic Computation, Elsevier, 2009, 44 (3), pp.292-306. ⟨10.1016⟩. ⟨inria-00070350⟩
  • Lionel Alberti, Bernard Mourrain, Jean-Pierre Técourt. Isotopic triangulation of a real algebraic surface. Journal of Symbolic Computation, Elsevier, 2009, 44 (9), pp.1291-1310. ⟨10.1016/j.jsc.2008.02.007⟩. ⟨inria-00433141⟩
  • Lionel Alberti, Bernard Mourrain, Julien Wintz. Topology and arrangement computation of semi-algebraic planar curves. Computer Aided Geometric Design, Elsevier, 2008, Computer Graphics and Applications, 25 (8), pp.631-651. ⟨10.1016/j.cagd.2008.06.009⟩. ⟨inria-00343110⟩
  • Pierre Comon, Gene Golub, Lek-Heng Lim, Bernard Mourrain. Symmetric tensors and symmetric tensor rank. SIAM Journal on Matrix Analysis and Applications, Society for Industrial and Applied Mathematics, 2008, 30 (3), pp.1254-1279. ⟨hal-00327599⟩
  • Bernard Mourrain, Jean-Pierre Técourt, Monique Teillaud. On the Computation of an Arrangement of Quadrics in 3D. Computational Geometry, Elsevier, 2005, 30 (2), pp.145-164. ⟨10.1016/j.comgeo.2004.05.003⟩. ⟨inria-00350858⟩
  • Laurent Busé, Mohamed Elkadi, Bernard Mourrain. Using projection operators in computer aided geometric design. Comtemporary Mathematics, American Mathematical Society, 2003, 334, pp.321--342. ⟨inria-00098681⟩
  • Olivier Devillers, Alexandra Fronville, Bernard Mourrain, Monique Teillaud. Algebraic methods and arithmetic filtering for exact predicates on circle arcs. Computational Geometry, Elsevier, 2002, 22, pp.119-142. ⟨10.1016/S0925-7721(01)00050-5⟩. ⟨inria-00166709⟩
  • Olivier Devillers, Bernard Mourrain, Franco Preparata, Philippe Trebuchet. Circular Cylinders by Four or Five Points in Space. Discrete and Computational Geometry, Springer Verlag, 2002, 29 (1), pp.83--104. ⟨10.1007/s00454-002-2811-7⟩. ⟨inria-00090648⟩
  • Laurent Busé, Mohamed Elkadi, Bernard Mourrain. Resultant over the residual of a complete intersection. Journal of Pure and Applied Algebra, Elsevier, 2001, Effective methods in algebraic geometry (Bath, 2000), 164 (1-2), pp.35--57. ⟨inria-00099487⟩
  • Bernard Mourrain, Victor Pan. Multivariate Polynomials, Duality, and Structured Matrices. Journal of Complexity, Elsevier, 2000, 16 (1), pp.110 - 180. ⟨10.1006/jcom.1999.0530⟩. ⟨hal-00739512⟩
  • Laurent Busé, Mohamed Elkadi, Bernard Mourrain. Generalized resultants over unirational algebraic varieties. Journal of Symbolic Computation, Elsevier, 2000, J. Symbolic Comput., 29 (4-5), pp.515--526. ⟨inria-00096842⟩
  • Bernard Mourrain. Isolated points, duality and residues. Journal of Pure and Applied Algebra, Elsevier, 1996, 117&118, pp.469--493. ⟨inria-00125278⟩

Conference papers32 documents

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

Books1 document

  • Mohamed Elkadi, Bernard Mourrain. Introduction à la résolution des systèmes polynomiaux. Springer, 59, pp.307, 2007, Mathématiques et Applications, 978-3-540-71646-4. ⟨inria-00170536⟩

Book sections7 documents

  • Stefanie Hahmann, Alexander Belyaev, Laurent Busé, Gershon Elber, Bernard Mourrain, et al.. Shape Interrogation. 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⟩. ⟨inria-00193551⟩
  • Jean-Daniel Boissonnat, David Cohen-Steiner, Bernard Mourrain, Guenter Rote, Gert Vegter. Meshing of Surfaces. Effective Computational Geometry for Curves and Surfaces, Springer, pp.181-230, 2007, Mathematics and Visualization. ⟨hal-00488274⟩
  • Bernard Mourrain, Jean-Pascal Pavone, Philippe Trebuchet, Elias P. Tsigaridas, Julien Wintz. SYNAPS: A library for dedicated applications in symbolic numeric computing,. 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. ⟨inria-00178498⟩
  • Chen Liang, Bernard Mourrain, Jean-Pascal Pavone. Subdivision Methods for the Topology of 2d and 3d Implicit Curves. Bert Juetller and Ragni Piene. Geometric Modeling and Algebraic Geometry, Springer, pp.199-214, 2007, 978-3-540-72184-0. ⟨inria-00130216⟩
  • Lionel Alberti, Bernard Mourrain. Regularity criteria for the topology of algebraic curves and surfaces. Ralph Martin and Malcom Sabin and Joab Winkler. Mathematics of Surfaces XII, 4647, Springer, pp.1-28, 2007, LNCS, 0302-9743. ⟨inria-00170886⟩
  • Marc-André Delsuc, Thérèse Malliavin, Antoine Marin, Bernard Mourrain. Biologie Moléculaire Structurale et Géométrie. Yves Gautier. La Science au Présent, Encyclopaedia Universalis, pp.128-131, 2007, 2-85229-514-8. ⟨inria-00175688⟩
  • Bernard Mourrain. Pythagore's Dilemma, Symbolic-Numeric Computation, and the Border Basis Method. Dongming Wang and Lihong Zhi. Symbolic-Numeric Computation, Birkhauser, pp.223--243, 2007, Trends in Mathematics. ⟨inria-00137424⟩

Directions of work or proceedings4 documents

  • Hannah Markwig, Bernard Mourrain, Giorgio Ottaviani. Special issue of JSC on the occasion of MEGA 2017. MEGA 2017 - International Conference on Effective Methods in Algebraic Geometry, Jun 2017, Nice, France. 91, pp.1-2, 2018, Journal of Symbolic Computation, ⟨10.1016/j.jsc.2018.05.001⟩. ⟨https://mega2017.inria.fr/⟩. ⟨hal-01829959⟩
  • d'Andrea Carlos, Bernard Mourrain. Special Issue on Symbolic and Algebraic Computation. C. D'andrea & B. Mourrain. 44, Elsevier, pp.135, 2008, 7, ⟨10.1016/j.jsc.2008.07.005⟩. ⟨inria-00558470⟩
  • Laurent Busé, Mohamed Elkadi, Bernard Mourrain. Computational Algebraic Geometry and its Applications. Laurent Busé, Mohamed Elkadi, Bernard Mourrain. 392, Elsevier, pp.178, 2008, Theoretical Computer Sciences. ⟨inria-00344404⟩
  • Bernard Mourrain, Ioannis Emiris, Victor Y. Pan. Special Issue on Algebraic and Numerical Algorithms. Emiris, I. and Mourrain, B. and Pan, Y. V. 315, Elsevier, pp.310, 2004. ⟨inria-00170535⟩

Other publications1 document

  • Long Quan, Bill Triggs, Marc-André Ameller, Bernard Mourrain. Uniqueness of Minimal Euclidean Reconstruction from 4 Points. Submitted to CVPR'01. 2001. 〈inria-00548269〉

Preprints, Working Papers, ...9 documents

  • Juan Elias, Roser Homs, Bernard Mourrain. Computing minimal Gorenstein covers. 2019. ⟨hal-01978906⟩
  • Deepesh Toshniwal, Bernard Mourrain, Thomas Hughes. Polynomial spline spaces of non-uniform bi-degree on T-meshes: Combinatorial bounds on the dimension. 2019. ⟨hal-02067534⟩
  • Bernard Mourrain, Alessandro Oneto. On minimal decompositions of low rank symmetric tensors. 2018. ⟨hal-01803571⟩
  • Enrique Arrondo, Alessandra Bernardi, Pedro Macias Marques, Bernard Mourrain. Skew-Symmetric Tensor Decomposition. 2018. ⟨hal-01940005⟩
  • Bernard Mourrain, Simon Telen, Marc Van Barel. Truncated Normal Forms for Solving Polynomial Systems: Generalized and Efficient Algorithms. 2018. ⟨hal-01738695v2⟩
  • Meng Wu, Bernard Mourrain, André Galligo, Boniface Nkonga. Spline Spaces over Quadrangle Meshes with Complex Topologies. 2014. ⟨hal-00952455⟩
  • Marta Abril Bucero, Bernard Mourrain. Exact relaxation for polynomial optimization on semi-algebraic sets. 2014. ⟨hal-00846977v4⟩
  • Marta Abril Bucero, Bernard Mourrain, Philippe Trébuchet. Unconstraint global polynomial optimization via Gradient Ideal. 2013. ⟨hal-00779666v3⟩
  • Mariemi Alonso, Jérome Brachat, Bernard Mourrain. The Hilbert scheme of points and its link with border basis. 2010. ⟨inria-00433127v2⟩

Reports18 documents

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