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Bernard Mourrain

153
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On the Effective Putinar’s Positivstellensatz and Moment Approximation

Lorenzo Baldi , Bernard Mourrain
Mathematical Programming, Series A, 2022, ⟨10.1007/s10107-022-01877-6⟩
Journal articles hal-03437328v3
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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⟩
Journal articles hal-03244448v2
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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⟩
Journal articles hal-02958248v2
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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⟩
Journal articles hal-03656945v2
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Newton-Type Methods For Simultaneous Matrix Diagonalization

Rima Khouja , Bernard Mourrain , Jean-Claude Yakoubsohn
Journal articles hal-03390265v2
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A certified iterative method for isolated singular roots

Angelos Mantzaflaris , Bernard Mourrain , Agnes Szanto
Journal of Symbolic Computation, 2022, 115, pp.223-247
Journal articles hal-03079910v1
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Univariate Rational Sums of Squares

Teresa Krick , Bernard Mourrain , Agnes Szanto
Revista de la Union Matematica Argentina, 2022, 64 (2), pp.215-237. ⟨10.33044/revuma.2904⟩
Journal articles hal-03442193v2
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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⟩
Journal articles hal-03200138v1
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Riemannian Newton optimization methods for the symmetric tensor approximation problem

Rima Khouja , Houssam Khalil , Bernard Mourrain
Linear Algebra and its Applications, inPress, 637C, pp.175-211. ⟨10.1016/j.laa.2021.12.008⟩
Journal articles hal-02494172v3
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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⟩
Journal articles hal-02927010v1
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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⟩
Journal articles hal-01803571v1
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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⟩
Journal articles hal-02480959v1
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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⟩
Journal articles hal-01105276v5
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Interpolatory Catmull-Clark volumetric subdivision over unstructured hexahedral meshes for modeling and simulation applications

Jin Xie , Jinlan Xu , Zhenyu Dong , Gang Xu , Chongyang Deng et al.
Computer Aided Geometric Design, 2020, 80, pp.101867. ⟨10.1016/j.cagd.2020.101867⟩
Journal articles hal-02958501v1
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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⟩
Journal articles hal-01738695v2
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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⟩
Journal articles hal-01940005v1
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Computing minimal Gorenstein covers

Juan Elias , Roser Homs , Bernard Mourrain
Journal of Pure and Applied Algebra, 2019, ⟨10.1016/j.jpaa.2019.106280⟩
Journal articles hal-01978906v2
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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⟩
Journal articles hal-01966542v1
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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⟩
Journal articles hal-01575325v2
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Exact conversion from Bézier tetrahedra to Bézier hexahedra

Gang Xu , Yaoli Jin , Zhoufang Xiao , Qing Wu , Bernard Mourrain et al.
Computer Aided Geometric Design, 2018, 62, pp.154 - 165. ⟨10.1016/j.cagd.2018.03.022⟩
Journal articles hal-01936167v1
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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⟩
Journal articles hal-01630425v1
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Polynomial-Exponential Decomposition from Moments

Bernard Mourrain
Foundations of Computational Mathematics, 2018, 18 (6), pp.1435-1492. ⟨10.1007/s10208-017-9372-x⟩
Journal articles hal-01367730v3
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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 Xu et al.
Computer Methods in Applied Mechanics and Engineering, 2018, 328, pp.175 - 200. ⟨10.1016/j.cma.2017.08.052⟩
Journal articles hal-01599319v1
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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⟩
Journal articles hal-01440063v1
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$G^1$-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⟩
Journal articles hal-01491676v1
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Convergence rates with singular parameterizations for solving elliptic boundary value problems in isogeometric analysis

Meng Wu , Yicao Wang , Bernard Mourrain , Boniface Nkonga , Changzheng Cheng et al.
Computer Aided Geometric Design, 2017, 52–53, pp.170-189. ⟨10.1016/j.cagd.2017.02.006⟩
Journal articles hal-01276699v2
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Geometric Modelling and Deformation for Shape Optimization of Ship Hulls and Appendages

Elisa Berrini , Bernard Mourrain , Yann Roux , Mathieu Durand , Guillaume Fontaine et al.
Journal of Ship Research, 2017, 61 (2), pp.91-106. ⟨10.5957/JOSR.61.2.160059⟩
Journal articles hal-01373249v4
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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⟩
Journal articles hal-01250398v1
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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⟩
Journal articles hal-01196435v3
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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⟩
Journal articles hal-01196428v4
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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⟩
Journal articles hal-01158099v3
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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⟩
Journal articles hal-01250388v1
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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⟩
Journal articles hal-01196996v2
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Flat extensions in ∗-algebras

Bernard Mourrain , Konrad Schmüdgen
Proceedings of the American Mathematical Society, 2016, 144 (11), pp.4873-4885. ⟨10.1090/proc/13158⟩
Journal articles hal-01009909v1
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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⟩
Journal articles hal-00981546v3
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Dimensions and bases of hierarchical tensor-product splines

Dmitry Berdinsky , Taiwan Kim , Cesare Bracco , Durkbin Cho , Bernard Mourrain et al.
Journal of Computational and Applied Mathematics, 2014, 257, pp.86-104. ⟨10.1016/j.cam.2013.08.019⟩
Journal articles hal-00876557v1
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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
Journal articles hal-00746967v2

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⟩
Journal articles hal-00816528v1
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On the dimension of spline spaces on planar T-meshes

Bernard Mourrain
Mathematics of Computation, 2014, 83, pp.847-871
Journal articles inria-00533187v3
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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⟩
Journal articles hal-00922544v2
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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⟩
Journal articles hal-00879100v2
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Moment Matrices, Border Bases and Real Radical Computation

Jean-Bernard Lasserre , Monique Laurent , Bernard Mourrain , Philipp Rostalski , Philippe Trébuchet et al.
Journal of Symbolic Computation, 2013, 51, pp.63-85. ⟨10.1016/j.jsc.2012.03.007⟩
Journal articles hal-00651759v1
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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⟩
Journal articles inria-00590965v3
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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⟩
Journal articles hal-00836413v1
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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⟩
Journal articles inria-00539616v1
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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⟩
Journal articles hal-00722406v1
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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⟩
Journal articles hal-00742636v1
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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⟩
Journal articles hal-00685002v2

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⟩
Journal articles hal-00815120v1
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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⟩
Journal articles hal-00780556v1
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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⟩
Journal articles hal-00421214v1
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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⟩
Journal articles inria-00354120v1

Mathemagix

Joris van Der Hoeven , Grégoire Lecerf , Bernard Mourrain , Philippe Trebuchet , Jérémy Berthomieu et al.
ACM Communications in Computer Algebra, 2012, 45 (3/4), pp.186-188. ⟨10.1145/2110170.2110180⟩
Journal articles hal-02350521v1
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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⟩
Journal articles hal-00742955v1
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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⟩
Journal articles hal-00742505v1
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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⟩
Journal articles inria-00589062v1
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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⟩
Journal articles inria-00530758v2
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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⟩
Journal articles hal-00646511v1
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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⟩
Journal articles inria-00530756v1
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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⟩
Journal articles inria-00355713v2
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Explicit factors of some iterated resultants and discriminants

Laurent Busé , Bernard Mourrain
Mathematics of Computation, 2009, 78 (265), pp.345--386
Journal articles inria-00119287v2
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Subdivision methods for solving polynomial equations

Bernard Mourrain , Jean-Pascal Pavone
Journal of Symbolic Computation, 2009, 44 (3), pp.292-306
Journal articles inria-00070350v1
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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⟩
Journal articles hal-00123473v2
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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⟩
Journal articles inria-00433141v1
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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⟩
Journal articles inria-00347022v2
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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⟩
Journal articles inria-00343103v1
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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⟩
Journal articles inria-00343110v1
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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
Journal articles hal-00327599v1
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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⟩
Journal articles inria-00350858v1
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Using projection operators in computer aided geometric design

Laurent Busé , Mohamed Elkadi , Bernard Mourrain
Contemporary mathematics, 2003, 334, pp.321--342
Journal articles inria-00098681v1
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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⟩
Journal articles inria-00166709v1
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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⟩
Journal articles inria-00090648v1
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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
Journal articles inria-00099487v1
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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
Journal articles 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⟩
Journal articles hal-00739512v1
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Isolated points, duality and residues

Bernard Mourrain
Journal of Pure and Applied Algebra, 1996, 117&118, pp.469--493
Journal articles inria-00125278v1
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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⟩
Conference papers hal-03145501v2
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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⟩
Conference papers hal-02478768v2
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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⟩
Conference papers hal-01848546v1
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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⟩
Conference papers hal-01579079v1
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Geometric model for automated multi-objective optimization of foils

Elisa Berrini , Bernard Mourrain , Regis Duvigneau , Matthieu Sacher , Yann Roux et al.
Marine 2017, May 2017, Nantes, France. pp.473-484
Conference papers hal-01524287v1
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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⟩
Conference papers hal-01515366v1
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Parametric shape modeler for hulls and appendages

Elisa Berrini , Bernard Mourrain , Yann Roux , Guillaume Fontaine , Eric Jean et al.
COMPIT'16, May 2016, Lecce, Italy. pp.255-263
Conference papers hal-01373867v1
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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⟩
Conference papers hal-01356869v1
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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⟩
Conference papers hal-01107541v2
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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⟩
Conference papers hal-00994683v1
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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, United States. pp.1-4, ⟨10.1109/WASPAA.2013.6701896⟩
Conference papers hal-00848876v1
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Bulbous Bow Shape Optimization

Louis Blanchard , Elisa Berrini , Régis Duvigneau , Yann Roux , Bernard Mourrain et al.
5th International Conference on Computational Methods in Marine Engineering, May 2013, Hamburg, Germany
Conference papers hal-00873272v1
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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⟩
Conference papers hal-00709962v1
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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⟩
Conference papers inria-00556021v1
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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⟩
Conference papers hal-00646566v1
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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⟩
Conference papers inria-00638837v1
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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
Conference papers inria-00440130v3
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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
Conference papers inria-00542193v1
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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⟩
Conference papers inria-00393833v4
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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⟩
Conference papers inria-00463491v2
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Efficient and robust reconstruction of botanical branching structure from laser scanned points

Dong-Ming Yan , Julien Wintz , Bernard Mourrain , Wenping Wang , Frédéric Boudon et al.
CAD/Graphics 2009, Aug 2009, Yellow Mountain City, China. pp.572-575
Conference papers inria-00436480v1
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Experimental evaluation and cross-benchmarking of univariate real solvers

Ioannis Z. Emiris , Michael Hemmer , Menelaos Karavelas , Bernard Mourrain , Elias P. P. Tsigaridas et al.
International Workshop SNC, ACM, Aug 2009, Kyoto, Japan. pp.85-94, ⟨10.1145/1577190.1577202⟩
Conference papers inria-00340887v2
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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⟩
Conference papers inria-00387399v2
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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
Conference papers inria-00437559v1
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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
Conference papers hal-00435908v1
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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⟩
Conference papers inria-00418403v1
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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
Conference papers inria-00071370v1
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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
Conference papers inria-00343126v1
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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⟩
Conference papers hal-00218271v1
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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 Mourrain et al.
11th International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), Sep 2008, New York, United States. p. 237-248
Conference papers hal-00340600v1
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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
Conference papers hal-00366292v1
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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⟩
Conference papers inria-00189560v1
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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
Conference papers inria-00175062v1
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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
Conference papers inria-00100288v1
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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
Conference papers inria-00350878v1
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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⟩
Conference papers inria-00070537v1

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
Conference papers 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⟩
Conference papers hal-01179417v1

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
Books 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⟩
Books 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
Books 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
Books inria-00170535v1

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⟩
Book sections hal-02350517v1
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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⟩
Book sections hal-02958889v1
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Shape Interrogation

Stefanie Hahmann , Alexander Belyaev , Laurent Busé , Gershon Elber , Bernard Mourrain et 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⟩
Book sections inria-00193551v1
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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
Book sections inria-00137424v1
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SYNAPS: A library for dedicated applications in symbolic numeric computing,

Bernard Mourrain , Jean-Pascal Pavone , Philippe Trebuchet , Elias P. Tsigaridas , Julien Wintz et al.
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
Book sections inria-00178498v1
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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
Book sections inria-00170886v1

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
Book sections inria-00175688v1
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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
Book sections inria-00130216v1
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Meshing of Surfaces

Jean-Daniel Boissonnat , David Cohen-Steiner , Bernard Mourrain , Guenter Rote , Gert Vegter et al.
Effective Computational Geometry for Curves and Surfaces, Springer, pp.181-230, 2007, Mathematics and Visualization
Book sections hal-00488274v1
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Automated Generation of Geometric Models for a Bulbous Trawler Ship

Louis Blanchard , Régis Duvigneau , Bernard Mourrain
[Research Report] RR-8011, INRIA. 2012
Reports hal-00714791v1
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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
Reports inria-00585663v2
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Hierarchical Optimization in Isogeometric Analysis : Application to Thermal Conduction

Louis Blanchard , Régis Duvigneau , Gang Xu , Bernard Mourrain
[Research Report] RR-7470, INRIA. 2010
Reports inria-00542271v1
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Isotopic meshing of a real algebraic surface

Bernard Mourrain , Jean-Pierre Técourt
[Research Report] RR-5508, INRIA. 2006, pp.21
Reports inria-00070499v1
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Bernstein's basis and real root isolation

Bernard Mourrain , Fabrice Rouillier , Marie-Françoise Roy
[Research Report] RR-5149, INRIA. 2004
Reports inria-00071434v1
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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
Reports inria-00070798v1
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On circular Cylinders by Four or Five Points in Space

Olivier Devillers , Bernard Mourrain , Franco P. Preparata , Philippe Trebuchet
RR-4195, INRIA. 2001
Reports inria-00072427v1
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Isolation of Real Roots and Computation of the Topological Degree

Bernard Mourrain , Michael N. Vrahatis , Jean-Claude Yakoubsohn
[Research Report] RR-4300, INRIA. 2001
Reports inria-00072287v1
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A framework for Symbolic and Numeric Computations

Bernard Mourrain , Hélène Prieto
[Research Report] RR-4013, INRIA. 2000, pp.96
Reports inria-00072629v1

Certificated and Efficient Solver for Intersection of three quadric surfaces

Abhishek Pandey , Bernard Mourrain , Sylvain Lazard
[Internship report] A00-R-393 || pandey00a, 2000
Reports inria-00099246v1
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Sign Methods for Counting and Computing Real Roots of Algebraic Systems

Ioannis Z. Emiris , Bernard Mourrain , Mihail N. Vrahatis
RR-3669, INRIA. 1999
Reports inria-00073003v1
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Algebraic Methods and Arithmetic Filtering for Exact Predicates on Circle Arcs

Olivier Devillers , Alexandra Fronville , Bernard Mourrain , Monique Teillaud
RR-3826, INRIA. 1999
Reports inria-00072832v1
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Some Applications of Bezoutians in Effective Algebraic Geometry

Mohamed Elkadi , Bernard Mourrain
RR-3572, INRIA. 1998
Reports inria-00073109v1
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Multivariate Polynomials, Duality and Structured Matrices

Bernard Mourrain , Victor Y. Y. Pan
RR-3513, INRIA. 1998
Reports inria-00073171v1
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Approche effective des résidus algébriques

Mohamed Elkadi , Bernard Mourrain
RR-2884, INRIA. 1996
Reports inria-00073806v1
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Polynomial System Solving: the Case of a Six-Atom Molecule

Ioannis Z. Emiris , Bernard Mourrain
RR-3075, INRIA. 1996
Reports inria-00073617v1
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On the Geometry and Algebra of the Point and Line Correspondences between $N$ Images

Olivier Faugeras , Bernard Mourrain
RR-2665, INRIA. 1995
Reports inria-00074025v1
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About the rational map

Bernard Mourrain
RR-2141, INRIA. 1993
Reports inria-00074531v1