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Papers by Bernard Mourrain

Research paper thumbnail of Border Basis relaxation for polynomial optimization

Research paper thumbnail of A subdivision framework for solving polynomial systems

Research paper thumbnail of Algebraic methods and arithmetic filtering for exact predicates on circle arcs

Research paper thumbnail of Approche effective de la theorie des invariants des groupes classiques

Research paper thumbnail of Efficient construction of multi-block volumetric spline parameterization by discrete mask method

Journal of Computational and Applied Mathematics, 2015

Research paper thumbnail of Des formes aux formules, ou comment les singularités nous aident à mieux calculer

Research paper thumbnail of Certifying Isolated Singular Points and their Multiplicity Structure

Proceedings of the 2015 ACM on International Symposium on Symbolic and Algebraic Computation - ISSAC '15, 2015

Research paper thumbnail of Computable identities in the algebra of formal matrices

Theoretical Computer Science, 1992

Research paper thumbnail of Moment matrices, trace matrices and the radical of ideals

Proceedings of the twenty-first international symposium on Symbolic and algebraic computation - ISSAC '08, 2008

Research paper thumbnail of Computing Approximate Radicals using Bezoutians

Abstract Consider I ⊂ C[x1,...,xm], a zero dimensional complete intersection ideal, with I = (f1,... more Abstract Consider I ⊂ C[x1,...,xm], a zero dimensional complete intersection ideal, with I = (f1,...,fm). Assume that I has clusters of roots, each cluster of radius at most ε in the ∞-norm. We compute the “approxi-mate radical” of I, ie an ideal which contains one root for each ...

Research paper thumbnail of The 40 “generic” positions of a parallel robot

Proceedings of the 1993 international symposium on Symbolic and algebraic computation - ISSAC '93, 1993

Research paper thumbnail of A New Criterion for Normal Form Algorithms

Lecture Notes in Computer Science, 1999

Research paper thumbnail of Type II Codes over Z 4

Research paper thumbnail of Other Grants and Activities - International actions

Research paper thumbnail of A construction of injective parameterizations of domains for isogeometric applications

Proceedings of the 2011 International Workshop on Symbolic Numeric Computation, Jun 7, 2012

We present a new method to construct a B-spline parameterization of a domain defined by its bound... more We present a new method to construct a B-spline parameterization of a domain defined by its boundary curves or surfaces. The method is based on solving Laplace equations on the physical domain. The equations are then pulled back to the parameter domain to deduce an elliptic system of Partial Differential Equations with boundary conditions. This system, solved by relaxation techniques,

Research paper thumbnail of Yet another algorithm for generalized Vorono� Diagrams

We design and implement an efficient algorithm for the computation of generalized Voronoï Diagram... more We design and implement an efficient algorithm for the computation of generalized Voronoï Diagrams (VD's) constrained to a given domain. Our framework is general and applicable to any VD-type where the distance field is given by a polynomial. We use the Bernstein form of polynomials to subdivide the domain and isolate bisector domains or domains that contain a Voronoï vertex.

Research paper thumbnail of Isolation of Real Roots and Computation of the Topological Degree

Research paper thumbnail of Bulbous Bow Shape Optimization

Research paper thumbnail of Rankin-Cohen Brackets and Invariant Theory

Journal of Algebraic Combinatorics an International Journal, 2001

Research paper thumbnail of New Results - Algebraic Geometric computing

Research paper thumbnail of Border Basis relaxation for polynomial optimization

Research paper thumbnail of A subdivision framework for solving polynomial systems

Research paper thumbnail of Algebraic methods and arithmetic filtering for exact predicates on circle arcs

Research paper thumbnail of Approche effective de la theorie des invariants des groupes classiques

Research paper thumbnail of Efficient construction of multi-block volumetric spline parameterization by discrete mask method

Journal of Computational and Applied Mathematics, 2015

Research paper thumbnail of Des formes aux formules, ou comment les singularités nous aident à mieux calculer

Research paper thumbnail of Certifying Isolated Singular Points and their Multiplicity Structure

Proceedings of the 2015 ACM on International Symposium on Symbolic and Algebraic Computation - ISSAC '15, 2015

Research paper thumbnail of Computable identities in the algebra of formal matrices

Theoretical Computer Science, 1992

Research paper thumbnail of Moment matrices, trace matrices and the radical of ideals

Proceedings of the twenty-first international symposium on Symbolic and algebraic computation - ISSAC '08, 2008

Research paper thumbnail of Computing Approximate Radicals using Bezoutians

Abstract Consider I ⊂ C[x1,...,xm], a zero dimensional complete intersection ideal, with I = (f1,... more Abstract Consider I ⊂ C[x1,...,xm], a zero dimensional complete intersection ideal, with I = (f1,...,fm). Assume that I has clusters of roots, each cluster of radius at most ε in the ∞-norm. We compute the “approxi-mate radical” of I, ie an ideal which contains one root for each ...

Research paper thumbnail of The 40 “generic” positions of a parallel robot

Proceedings of the 1993 international symposium on Symbolic and algebraic computation - ISSAC '93, 1993

Research paper thumbnail of A New Criterion for Normal Form Algorithms

Lecture Notes in Computer Science, 1999

Research paper thumbnail of Type II Codes over Z 4

Research paper thumbnail of Other Grants and Activities - International actions

Research paper thumbnail of A construction of injective parameterizations of domains for isogeometric applications

Proceedings of the 2011 International Workshop on Symbolic Numeric Computation, Jun 7, 2012

We present a new method to construct a B-spline parameterization of a domain defined by its bound... more We present a new method to construct a B-spline parameterization of a domain defined by its boundary curves or surfaces. The method is based on solving Laplace equations on the physical domain. The equations are then pulled back to the parameter domain to deduce an elliptic system of Partial Differential Equations with boundary conditions. This system, solved by relaxation techniques,

Research paper thumbnail of Yet another algorithm for generalized Vorono� Diagrams

We design and implement an efficient algorithm for the computation of generalized Voronoï Diagram... more We design and implement an efficient algorithm for the computation of generalized Voronoï Diagrams (VD's) constrained to a given domain. Our framework is general and applicable to any VD-type where the distance field is given by a polynomial. We use the Bernstein form of polynomials to subdivide the domain and isolate bisector domains or domains that contain a Voronoï vertex.

Research paper thumbnail of Isolation of Real Roots and Computation of the Topological Degree

Research paper thumbnail of Bulbous Bow Shape Optimization

Research paper thumbnail of Rankin-Cohen Brackets and Invariant Theory

Journal of Algebraic Combinatorics an International Journal, 2001

Research paper thumbnail of New Results - Algebraic Geometric computing

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