Bernard Mourrain
Publications
Publications
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Computing real radicals by moment optimizationISSAC 2021 - 46th International Symposium on Symbolic and Algebraic Computation, Jul 2021, Saint-Pétersbourg, Russia. ⟨10.1145/3452143.3465541⟩ |
Polynomial optimization based schemes for solving AC Optimal Power Flow problemsEURO 2021, Jul 2021, Athens, Greece |
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Punctual Hilbert Schemes and Certified Approximate SingularitiesISSAC 2020 - International Symposium on Symbolic and Algebraic Computation, Jul 2020, Kalamata, Greece. ⟨10.1145/3373207.3404024⟩ |
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Axl, a geometric modeler for semi-algebraic shapesICMS 2018 - 6th International Conference on Mathematical Software, Jul 2018, Notre Dame, United States. pp.128-136, ⟨10.1007/978-3-319-96418-8_16⟩ |
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Fast algorithm for border bases of Artinian Gorenstein algebrasISSAC'17 -- International Symposium on Symbolic and Algebraic Computation, Jul 2017, Kaiserslautern, Germany. pp.333--340, ⟨10.1145/3087604.3087632⟩ |
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Efficient certication of numeric solutions to eigenproblemsMACIS 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⟩ |
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Geometric model for automated multi-objective optimization of foilsMarine 2017, May 2017, Nantes, France. pp.473-484 |
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Parametric shape modeler for hulls and appendagesCOMPIT'16, May 2016, Lecce, Italy. pp.255-263 |
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Border Basis for Polynomial System Solving and OptimizationICMS 2016 - 5th International Conference on Mathematical Software, Jul 2016, Berlin, Germany. pp.212-220, ⟨10.1007/978-3-319-42432-3_27⟩ |
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Certifying isolated singular points and their multiplicity structureISSAC'15, Jul 2015, Bath, United Kingdom. pp.213-220, ⟨10.1145/2755996.2756645⟩ |
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Toric Border BasisISSAC'14 - International Symposium on Symbolic and Algebraic Computation, Jul 2014, Kobe, Japan. pp.343-350, ⟨10.1145/2608628.2608652⟩ |
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Bulbous Bow Shape Optimization5th International Conference on Computational Methods in Marine Engineering, May 2013, Hamburg, Germany |
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The Geometry of Sound-Source Localization using Non-Coplanar microphone ArraysWASPAA 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⟩ |
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Border basis representation of a general quotient algebraInternational Conference on Symbolic and Algebraic Computation (ISSAC), Jul 2012, Grenoble, France. pp.265-272, ⟨10.1145/2442829.2442868⟩ |
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An Adapted Version of the Bentley-Ottmann Algorithm for Invariants of Plane Curves Singularities11th International Conference on Computational Science and Its Applications (ICCSA), Jun 2011, Santander, Spain. pp.121-131, ⟨10.1007/978-3-642-21931-3_10⟩ |
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Multihomogeneous Polynomial Decomposition using Moment Matrices36th international symposium on Symbolic and algebraic computation (ISSAC 11), Jun 2011, San Jose, United States. pp.35-42, ⟨10.1145/1993886.1993898⟩ |
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Deflation and Certified Isolation of Singular Zeros of Polynomial SystemsInternational Symposium on Symbolic and Algebraic Computation (ISSAC), Jun 2011, San Jose, CA, United States. pp.249-256, ⟨10.1145/1993886.1993925⟩ |
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A Subdivision Approach to Planar Semi-algebraic Sets6th International Conference, GMP, Jun 2010, Castro Urdiales, Spain. pp.104-123, ⟨10.1007/978-3-642-13411-1_8⟩ |
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The DMM bound: multivariate (aggregate) separation boundsProceedings of the 2010 International Symposium on Symbolic and Algebraic Computation, Jul 2010, Munich, Germany. pp.243-250, ⟨10.1145/1837934.1837981⟩ |
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Optimal analysis-aware parameterization of computational domain in isogeometric analysisGMP, Jun 2010, Castro Urdiales, Spain. pp.236-254 |
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A Symbolic-Numeric Algorithm for Computing the Alexander Polynomial of a Plane Curve SingularityInternational Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC), Sep 2010, Timisoara, Romania. pp.21-28 |
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Curve/surface intersection problem by means of matrix representationsSNC, Aug 2009, Kyoto, Japan. pp.71-78, ⟨10.1145/1577190.1577205⟩ |
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Symmetric tensor decomposition17th European Signal Processing Conference 2009., Aug 2009, Glasgow, United Kingdom. pp.525-529 |
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Continued Fraction Expansion of Real Roots of Polynomial SystemsSNC, conference on Symbolic-Numeric Computation, Aug 2009, Kyoto, Japan. pp.85-94, ⟨10.1145/1577190.1577207⟩ |
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Computing Nearest Gcd with CertificationInternational Workshop Symbolic-Numeric Computation (SNC), Aug 2009, Kyoto, Japan. pp.29-34 |
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Experimental evaluation and cross-benchmarking of univariate real solversInternational Workshop SNC, ACM, Aug 2009, Kyoto, Japan. pp.85-94, ⟨10.1145/1577190.1577202⟩ |
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Efficient and robust reconstruction of botanical branching structure from laser scanned pointsCAD/Graphics 2009, Aug 2009, Yellow Mountain City, China. pp.572-575 |
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On the Computation of the Topology of a Non-Reduced Implicit Space CurveISSAC, Jul 2008, Linz, Austria. pp.47-54, ⟨10.1145/1390768.1390778⟩ |
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Moment matrices, trace matrices and the radical of idealsISSAC, Jul 2008, Linz, Austria. pp.125-132 |
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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 MRI11th International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), Sep 2008, New York, United States. p. 237-248 |
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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 |
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Real Algebraic Numbers: Complexity Analysis and ExperimentationsReliable Implementations of Real Number Algorithms: Theory and Practice, 2008, Dagsthul, Germany. pp.57-82 |
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Visualisation of implicit algebraic curvesPacific Conference on Computer Graphics and Applications 2007, Ron Goldman, Oct 2007, Lahaina, Maui, Hawaii, United States. pp.303-312 |
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A subdivision arrangement algorithm for semi-algebraic curves: an overview15th 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⟩ |
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The Offset to an Algebraic Curve and an Application to ConicsInternational Conference on Computational Science and its Applications, May 2005, Singapore, Singapore. pp.683-696 |
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Generalized normal forms and polynomial system solvingISSAC 2005 - International Symposium on Symbolic and Algebraic Computation , Jul 2005, Beijing, China. pp.253-260, ⟨10.1145/1073884.1073920⟩ |
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Resultant-based methods for plane curves intersection problemsComputer Algebra in Scientific Computing (CASC), Sep 2005, Kalamata, Greece, pp.75-92 |
An environment for Symbolic and Numeric ComputationInternational Congress of Mathematical Software - ICMS'2002, 2002, Beijing, China. pp.239-249 |
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Algebraic methods and arithmetic filtering for exact predicates on circle arcsProceedings of the 16th Annual Symposium on Computational Geometry, 2000, Hong Kong, China. pp.139-147, ⟨10.1145/336154.336194⟩ |
Polynomial Optimization, Moments, and ApplicationsSpringer. Springer, 206, pp.258, 2023, SOIA. Springer Optimization and Its Applications, 978-3-031-38658-9 |
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Computational Algebraic Geometry and its ApplicationsLaurent Busé, Mohamed Elkadi, Bernard Mourrain. Elsevier, 392, pp.178, 2008, Theoretical Computer Sciences |
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Special Issue on Symbolic and Algebraic ComputationC. D'andrea & B. Mourrain. Elsevier, 44, pp.135, 2008, 7, ⟨10.1016/j.jsc.2008.07.005⟩ |
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Introduction à la résolution des systèmes polynomiauxSpringer, 59, pp.307, 2007, Mathématiques et Applications, 978-3-540-71646-4 |
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Special Issue on Algebraic and Numerical AlgorithmsEmiris, I. and Mourrain, B. and Pan, Y. V. Elsevier, 315, pp.310, 2004 |
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Isolated singularities, inverse systems and the punctual Hilbert schemeAnthony 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⟩ |
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Polynomial optimization in geometric modelingMichal Kočvara; Bernard Mourrain; Cordian Riener. Polynomial Optimization, Moments, and Applications, Springer, pp.163-186, In press |
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Efficient Certification of Numeric Solutions to EigenproblemsMathematical Aspects of Computer and Information Sciences, pp.81-94, 2017, ⟨10.1007/978-3-319-72453-9_6⟩ |
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Singular Zeros of Polynomial SystemsSAGA – Advances in ShApes, Geometry, and Algebra. Geometry and Computing, vol 10., pp.77-103, 2014, ⟨10.1007/978-3-319-08635-4_5⟩ |
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Shape InterrogationLeila 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⟩ |
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Subdivision Methods for the Topology of 2d and 3d Implicit CurvesBert Juetller and Ragni Piene. Geometric Modeling and Algebraic Geometry, Springer, pp.199-214, 2007, 978-3-540-72184-0 |
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Meshing of SurfacesEffective Computational Geometry for Curves and Surfaces, Springer, pp.181-230, 2007, Mathematics and Visualization |
Biologie Moléculaire Structurale et GéométrieYves Gautier. La Science au Présent, Encyclopaedia Universalis, pp.128-131, 2007, 2-85229-514-8 |
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Regularity criteria for the topology of algebraic curves and surfacesRalph Martin and Malcom Sabin and Joab Winkler. Mathematics of Surfaces XII, 4647, Springer, pp.1-28, 2007, LNCS, 0302-9743 |
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Pythagore's Dilemma, Symbolic-Numeric Computation, and the Border Basis MethodDongming Wang and Lihong Zhi. Symbolic-Numeric Computation, Birkhauser, pp.223--243, 2007, Trends in Mathematics |
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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 |
Uniqueness of Minimal Euclidean Reconstruction from 4 Points2001 |
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Truncated Normal Forms for Solving Algebraic Equations2025 |
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The Effective Countable Generalized Moment Problem2025 |
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Generalized additive decompositions of symmetric tensors2025 |
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Weighted Moment-SoS approach to POMDPs with polynomial data2025 |
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Spline Spaces over Quadrangle Meshes with Complex Topologies2014 |
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Exact relaxation for polynomial optimization on semi-algebraic sets2014 |
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Unconstraint global polynomial optimization via Gradient Ideal2013 |
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The Hilbert scheme of points and its link with border basis2010 |
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From moments to sparse representations, an algebraic, geometric and algorithmic viewpointÉcole thématique. France. 2019 |