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- Bernard Mourrain

Discipline name
D-index
D-index (Discipline H-index) only includes papers and citation values for an examined
discipline in contrast to General H-index which accounts for publications across all
disciplines.
Citations
Publications
World Ranking
National Ranking

Mathematics
D-index
40
Citations
6,716
224
World Ranking
1381
National Ranking
71

- Algebra
- Geometry
- Mathematical analysis

Bernard Mourrain spends much of his time researching Algebra, Polynomial, Computation, Topology and Combinatorics. The Polynomial study combines topics in areas such as Monomial, Discrete mathematics, Dual space and Differential operator. His work in Computation addresses subjects such as Algebraic number, which are connected to disciplines such as Geometry, Trifocal tensor, Epipolar geometry and Algebraic relations.

Bernard Mourrain combines subjects such as Box spline, Basis function, Algebraic curve, Differentiable function and Piecewise with his study of Topology. His Combinatorics research is multidisciplinary, incorporating elements of Hankel matrix and Symmetric tensor. His Elementary symmetric polynomial research incorporates themes from Triple system and Ring of symmetric functions.

- Symmetric Tensors and Symmetric Tensor Rank (435 citations)
- On the geometry and algebra of the point and line correspondences between N images (213 citations)
- Decomposition of quantics in sums of powers of linear forms (201 citations)

Bernard Mourrain mainly focuses on Algebra, Polynomial, Pure mathematics, Discrete mathematics and Algebraic number. His Polynomial research incorporates elements of Basis and Monomial, Combinatorics. His Pure mathematics research is multidisciplinary, relying on both Ring, Spline and Rank.

Particularly relevant to Algebraic curve is his body of work in Discrete mathematics. Bernard Mourrain works mostly in the field of Algebraic number, limiting it down to topics relating to Computation and, in certain cases, Theoretical computer science, as a part of the same area of interest. His biological study deals with issues like Domain, which deal with fields such as Applied mathematics.

- Algebra (25.58%)
- Polynomial (23.64%)
- Pure mathematics (17.83%)

- Pure mathematics (17.83%)
- Polynomial (23.64%)
- Applied mathematics (13.18%)

His primary scientific interests are in Pure mathematics, Polynomial, Applied mathematics, Algebraic number and Algebra. The concepts of his Pure mathematics study are interwoven with issues in Basis, Basis function, Polygon mesh and Rank. His work deals with themes such as Discrete mathematics, Infimum and supremum, Quotient, Ring and Relaxation, which intersect with Polynomial.

His studies in Applied mathematics integrate themes in fields like Multiplicity, Relaxation, Inverse system, Isogeometric analysis and Newton's method. Bernard Mourrain has researched Algebraic number in several fields, including Intersection, Semidefinite programming, Interpolation, Noise and Restricted isometry property. His Algebra research is multidisciplinary, incorporating perspectives in Cylinder and Polyhedron.

- Constructing IGA-suitable planar parameterization from complex CAD boundary by domain partition and global/local optimization (57 citations)
- Dimension and bases for geometrically continuous splines on surfaces of arbitrary topology (39 citations)
- $G^1$-smooth splines on quad meshes with 4-split macro-patch elements (21 citations)

- Algebra
- Geometry
- Mathematical analysis

His main research concerns Pure mathematics, Polynomial, Basis function, Spline and Rank. His work focuses on many connections between Pure mathematics and other disciplines, such as Ring, that overlap with his field of interest in Matrix, Affine transformation and Ideal. To a larger extent, Bernard Mourrain studies Algebra with the aim of understanding Polynomial.

The various areas that he examines in his Algebra study include Generalization and Truncated normal distribution. His studies deal with areas such as Differentiable function, Piecewise and Topology as well as Spline. His work carried out in the field of Rank brings together such families of science as Elimination theory, Tensor decomposition, Variety and Joins.

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

Symmetric Tensors and Symmetric Tensor Rank

Pierre Comon;Gene Golub;Lek-Heng Lim;Bernard Mourrain.

SIAM Journal on Matrix Analysis and Applications **(2008)**

563 Citations

Symmetric Tensors and Symmetric Tensor Rank

Pierre Comon;Gene Golub;Lek-Heng Lim;Bernard Mourrain.

SIAM Journal on Matrix Analysis and Applications **(2008)**

563 Citations

On the geometry and algebra of the point and line correspondences between N images

O. Faugeras;B. Mourrain.

international conference on computer vision **(1995)**

378 Citations

On the geometry and algebra of the point and line correspondences between N images

O. Faugeras;B. Mourrain.

international conference on computer vision **(1995)**

378 Citations

Decomposition of quantics in sums of powers of linear forms

P. Comon;B. Mourrain.

Signal Processing **(1996)**

265 Citations

Decomposition of quantics in sums of powers of linear forms

P. Comon;B. Mourrain.

Signal Processing **(1996)**

265 Citations

Symmetric tensor decomposition

Jérôme Brachat;Pierre Comon;Bernard Mourrain;Elias P. Tsigaridas;Elias P. Tsigaridas.

Linear Algebra and its Applications **(2010)**

241 Citations

Symmetric tensor decomposition

Jérôme Brachat;Pierre Comon;Bernard Mourrain;Elias P. Tsigaridas;Elias P. Tsigaridas.

Linear Algebra and its Applications **(2010)**

241 Citations

Parameterization of computational domain in isogeometric analysis: Methods and comparison

Gang Xu;Gang Xu;Bernard Mourrain;Régis Duvigneau;André Galligo.

Computer Methods in Applied Mechanics and Engineering **(2011)**

219 Citations

Parameterization of computational domain in isogeometric analysis: Methods and comparison

Gang Xu;Gang Xu;Bernard Mourrain;Régis Duvigneau;André Galligo.

Computer Methods in Applied Mechanics and Engineering **(2011)**

219 Citations

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