×
Author ID: villard.gilles Recent zbMATH articles by "Villard, Gilles"
Published as: Villard, Gilles; Villard, G.

Publications by Year

Citations contained in zbMATH Open

45 Publications have been cited 484 times in 287 Documents Cited by Year
On the complexity of computing determinants. Zbl 1061.68185
Kaltofen, Erich; Villard, Gilles
56
2004
On the complexity of polynomial matrix computations. Zbl 1072.68708
Giorgi, Pascal; Jeannerod, Claude-Pierre; Villard, Gilles
52
2003
Normal forms for general polynomial matrices. Zbl 1128.15005
Beckermann, Bernhard; Labahn, George; Villard, Gilles
28
2006
An LLL-reduction algorithm with quasi-linear time complexity, extended abstract. Zbl 1288.68294
Novocin, Andrew; Stehlé, Damien; Villard, Gilles
23
2011
Efficient matrix preconditioners for black box linear algebra. Zbl 0997.65073
Chen, Li; Eberly, Wayne; Kaltofen, Erich; Saunders, B. David; Turner, William J.; Villard, Gilles
22
2002
Further analysis of Coppersmith’s block Wiedemann algorithm for the solution of sparse linear systems. (Extended abstract). Zbl 0917.65041
Villard, G.
22
1997
On efficient sparse integer matrix Smith normal form computations. Zbl 1050.65044
Dumas, Jean-Guillaume; Saunders, B. David; Villard, Gilles
20
2001
LinBox: A generic library for exact linear algebra. Zbl 1011.68182
Dumas, J.-G.; Gautier, T.; Giesbrecht, M.; Giorgi, P.; Hovinen, B.; Kaltofen, E.; Saunders, B. D.; Turner, W. J.; Villard, G.
18
2002
Fast computation of minimal interpolation bases in Popov form for arbitrary shifts. Zbl 1360.65049
Jeannerod, Claude-Pierre; Neiger, Vincent; Schost, Éric; Villard, Gilles
13
2016
Solving sparse rational linear systems. Zbl 1356.65118
Eberly, Wayne; Giesbrecht, Mark; Giorgi, Pascal; Storjohann, Arne; Villard, Gilles
13
2006
On computing the resultant of generic bivariate polynomials. Zbl 1467.13061
Villard, Gilles
13
2018
Computing Popov and Hermite forms of polynomial matrices. Zbl 0914.65045
Villard, G.
11
1996
Computing minimal interpolation bases. Zbl 1375.65013
Jeannerod, Claude-Pierre; Neiger, Vincent; Schost, Éric; Villard, Gilles
11
2017
Linear time interactive certificates for the minimal polynomial and the determinant of a sparse matrix. Zbl 1365.65138
Dumas, Jean-Guillaume; Kaltofen, Erich; Thomé, Emmanuel; Villard, Gilles
11
2016
Computing the rank and a small nullspace basis of a polynomial matrix. Zbl 1360.68957
Storjohann, Arne; Villard, Gilles
11
2005
Perturbation analysis of the QR factor R in the context of LLL lattice basis reduction. Zbl 1260.11082
Chang, Xiao-Wen; Stehlé, Damien; Villard, Gilles
10
2012
Faster algorithms for multivariate interpolation with multiplicities and simultaneous polynomial approximations. Zbl 1359.94683
Chowdhury, Muhammad F. I.; Jeannerod, Claude-Pierre; Neiger, Vincent; Schost, Éric; Villard, Gilles
10
2015
Computing the Frobenius normal form of a sparse matrix. Zbl 0976.65042
Villard, Gilles
9
2000
An algorithm for the reduction of linear DAE. Zbl 0915.65078
Quéré, M. P.; Villard, G.
9
1995
Essentially optimal computation of the inverse of generic polynomial matrices. Zbl 1101.68956
Jeannerod, Claude-Pierre; Villard, Gilles
9
2005
LLL reducing with the most significant bits. Zbl 1325.68298
Saruchi; Morel, Ivan; Stehlé, Damien; Villard, Gilles
9
2014
On the complexity of computing determinants. (Extended abstract). Zbl 1012.65505
Kaltofen, Erich; Villard, Gilles
8
2001
Generalized subresultants for computing the Smith normal form of polynomial matrices. Zbl 0851.68048
Villard, Gilles
8
1995
H-LLL: using Householder inside LLL. Zbl 1237.65041
Morel, Ivan; Stehlé, Damien; Villard, Gilles
8
2009
Asymptotically fast polynomial matrix algorithms for multivariable systems. Zbl 1133.93319
Jeannerod, C.-P.; Villard, G.
8
2006
Computing the sign or the value of the determinant of an integer matrix, a complexity survey. Zbl 1037.65044
Kaltofen, Erich; Villard, Gilles
7
2004
Matrix rank certification. Zbl 1038.65038
Saunders, B. David; Storjohann, Arne; Villard, Gilles
7
2004
Faster inversion and other black box matrix computations using efficient block projections. Zbl 1190.65072
Eberly, Wayne; Giesbrecht, Mark; Giorgi, Pascal; Storjohann, Arne; Villard, Gilles
7
2007
Fast computation of approximant bases in canonical form. Zbl 1450.65040
Jeannerod, Claude-Pierre; Neiger, Vincent; Villard, Gilles
7
2020
Computation of the Smith normal form of polynomial matrices. Zbl 0964.65507
Villard, Gilles
5
1993
A new view on HJLS and PSLQ: sums and projections of lattices. Zbl 1360.11141
Chen, Jingwei; Stehlé, Damien; Villard, Gilles
5
2013
Integer Smith form via the valence: experience with large sparse matrices from homology. Zbl 1326.65059
Dumas, Jean-Guillaume; Saunders, B. David; Villard, Gilles
5
2000
Certification of the QR factor \(R\) and of lattice basis reducedness. Zbl 1190.65059
Villard, Gilles
5
2007
Parallel lattice basis reduction. Zbl 0921.11075
Villard, Gilles
4
1992
Fast parallel algorithms for matrix reduction to normal forms. Zbl 0905.65054
Villard, Gilles
4
1997
Fast parallel computation of the Smith normal form of polynomial matrices. Zbl 0978.65501
Villard, Gilles
3
1994
Elimination ideal and bivariate resultant over finite fields. Zbl 07760799
Villard, Gilles
3
2023
Computing an LLL-reduced basis of the orthogonal latice. Zbl 1467.11121
Chen, Jingwei; Stehlé, Damien; Villard, Gilles
2
2018
Block solution of sparse linear systems over \(\text{GF}(q)\): the singular case. Zbl 1097.65525
Villard, Gilles
2
1998
Processor efficient parallel solution of linear systems of equations. Zbl 0954.68024
Villard, Gilles
1
2000
Parallel algorithms: analysis and design. (Algorithmes parallèles: analyse et conception.) Zbl 0855.68037
1
1994
Data allocation strategies for the Gauss and Jordan algorithms on a ring of processors. Zbl 0681.65015
Robert, Yves; Tourancheau, Bernard; Villard, Gilles
1
1989
A rank theorem for Vandermonde matrices. Zbl 1059.15002
Koiran, Pascal; Portier, Natacha; Villard, Gilles
1
2004
Polynomial time interactive proofs for linear algebra with exponential matrix dimensions and scalars given by polynomial time circuits. Zbl 1457.68111
Dumas, Jean-Guillaume; Kaltofen, Erich L.; Villard, Gilles; Zhi, Lihong
1
2017
High-order lifting for polynomial Sylvester matrices. Zbl 07799850
Pernet, Clément; Signargout, Hippolyte; Villard, Gilles
1
2024
High-order lifting for polynomial Sylvester matrices. Zbl 07799850
Pernet, Clément; Signargout, Hippolyte; Villard, Gilles
1
2024
Elimination ideal and bivariate resultant over finite fields. Zbl 07760799
Villard, Gilles
3
2023
Fast computation of approximant bases in canonical form. Zbl 1450.65040
Jeannerod, Claude-Pierre; Neiger, Vincent; Villard, Gilles
7
2020
On computing the resultant of generic bivariate polynomials. Zbl 1467.13061
Villard, Gilles
13
2018
Computing an LLL-reduced basis of the orthogonal latice. Zbl 1467.11121
Chen, Jingwei; Stehlé, Damien; Villard, Gilles
2
2018
Computing minimal interpolation bases. Zbl 1375.65013
Jeannerod, Claude-Pierre; Neiger, Vincent; Schost, Éric; Villard, Gilles
11
2017
Polynomial time interactive proofs for linear algebra with exponential matrix dimensions and scalars given by polynomial time circuits. Zbl 1457.68111
Dumas, Jean-Guillaume; Kaltofen, Erich L.; Villard, Gilles; Zhi, Lihong
1
2017
Fast computation of minimal interpolation bases in Popov form for arbitrary shifts. Zbl 1360.65049
Jeannerod, Claude-Pierre; Neiger, Vincent; Schost, Éric; Villard, Gilles
13
2016
Linear time interactive certificates for the minimal polynomial and the determinant of a sparse matrix. Zbl 1365.65138
Dumas, Jean-Guillaume; Kaltofen, Erich; Thomé, Emmanuel; Villard, Gilles
11
2016
Faster algorithms for multivariate interpolation with multiplicities and simultaneous polynomial approximations. Zbl 1359.94683
Chowdhury, Muhammad F. I.; Jeannerod, Claude-Pierre; Neiger, Vincent; Schost, Éric; Villard, Gilles
10
2015
LLL reducing with the most significant bits. Zbl 1325.68298
Saruchi; Morel, Ivan; Stehlé, Damien; Villard, Gilles
9
2014
A new view on HJLS and PSLQ: sums and projections of lattices. Zbl 1360.11141
Chen, Jingwei; Stehlé, Damien; Villard, Gilles
5
2013
Perturbation analysis of the QR factor R in the context of LLL lattice basis reduction. Zbl 1260.11082
Chang, Xiao-Wen; Stehlé, Damien; Villard, Gilles
10
2012
An LLL-reduction algorithm with quasi-linear time complexity, extended abstract. Zbl 1288.68294
Novocin, Andrew; Stehlé, Damien; Villard, Gilles
23
2011
H-LLL: using Householder inside LLL. Zbl 1237.65041
Morel, Ivan; Stehlé, Damien; Villard, Gilles
8
2009
Faster inversion and other black box matrix computations using efficient block projections. Zbl 1190.65072
Eberly, Wayne; Giesbrecht, Mark; Giorgi, Pascal; Storjohann, Arne; Villard, Gilles
7
2007
Certification of the QR factor \(R\) and of lattice basis reducedness. Zbl 1190.65059
Villard, Gilles
5
2007
Normal forms for general polynomial matrices. Zbl 1128.15005
Beckermann, Bernhard; Labahn, George; Villard, Gilles
28
2006
Solving sparse rational linear systems. Zbl 1356.65118
Eberly, Wayne; Giesbrecht, Mark; Giorgi, Pascal; Storjohann, Arne; Villard, Gilles
13
2006
Asymptotically fast polynomial matrix algorithms for multivariable systems. Zbl 1133.93319
Jeannerod, C.-P.; Villard, G.
8
2006
Computing the rank and a small nullspace basis of a polynomial matrix. Zbl 1360.68957
Storjohann, Arne; Villard, Gilles
11
2005
Essentially optimal computation of the inverse of generic polynomial matrices. Zbl 1101.68956
Jeannerod, Claude-Pierre; Villard, Gilles
9
2005
On the complexity of computing determinants. Zbl 1061.68185
Kaltofen, Erich; Villard, Gilles
56
2004
Computing the sign or the value of the determinant of an integer matrix, a complexity survey. Zbl 1037.65044
Kaltofen, Erich; Villard, Gilles
7
2004
Matrix rank certification. Zbl 1038.65038
Saunders, B. David; Storjohann, Arne; Villard, Gilles
7
2004
A rank theorem for Vandermonde matrices. Zbl 1059.15002
Koiran, Pascal; Portier, Natacha; Villard, Gilles
1
2004
On the complexity of polynomial matrix computations. Zbl 1072.68708
Giorgi, Pascal; Jeannerod, Claude-Pierre; Villard, Gilles
52
2003
Efficient matrix preconditioners for black box linear algebra. Zbl 0997.65073
Chen, Li; Eberly, Wayne; Kaltofen, Erich; Saunders, B. David; Turner, William J.; Villard, Gilles
22
2002
LinBox: A generic library for exact linear algebra. Zbl 1011.68182
Dumas, J.-G.; Gautier, T.; Giesbrecht, M.; Giorgi, P.; Hovinen, B.; Kaltofen, E.; Saunders, B. D.; Turner, W. J.; Villard, G.
18
2002
On efficient sparse integer matrix Smith normal form computations. Zbl 1050.65044
Dumas, Jean-Guillaume; Saunders, B. David; Villard, Gilles
20
2001
On the complexity of computing determinants. (Extended abstract). Zbl 1012.65505
Kaltofen, Erich; Villard, Gilles
8
2001
Computing the Frobenius normal form of a sparse matrix. Zbl 0976.65042
Villard, Gilles
9
2000
Integer Smith form via the valence: experience with large sparse matrices from homology. Zbl 1326.65059
Dumas, Jean-Guillaume; Saunders, B. David; Villard, Gilles
5
2000
Processor efficient parallel solution of linear systems of equations. Zbl 0954.68024
Villard, Gilles
1
2000
Block solution of sparse linear systems over \(\text{GF}(q)\): the singular case. Zbl 1097.65525
Villard, Gilles
2
1998
Further analysis of Coppersmith’s block Wiedemann algorithm for the solution of sparse linear systems. (Extended abstract). Zbl 0917.65041
Villard, G.
22
1997
Fast parallel algorithms for matrix reduction to normal forms. Zbl 0905.65054
Villard, Gilles
4
1997
Computing Popov and Hermite forms of polynomial matrices. Zbl 0914.65045
Villard, G.
11
1996
An algorithm for the reduction of linear DAE. Zbl 0915.65078
Quéré, M. P.; Villard, G.
9
1995
Generalized subresultants for computing the Smith normal form of polynomial matrices. Zbl 0851.68048
Villard, Gilles
8
1995
Fast parallel computation of the Smith normal form of polynomial matrices. Zbl 0978.65501
Villard, Gilles
3
1994
Parallel algorithms: analysis and design. (Algorithmes parallèles: analyse et conception.) Zbl 0855.68037
1
1994
Computation of the Smith normal form of polynomial matrices. Zbl 0964.65507
Villard, Gilles
5
1993
Parallel lattice basis reduction. Zbl 0921.11075
Villard, Gilles
4
1992
Data allocation strategies for the Gauss and Jordan algorithms on a ring of processors. Zbl 0681.65015
Robert, Yves; Tourancheau, Bernard; Villard, Gilles
1
1989
all top 5

Cited by 375 Authors

24 Villard, Gilles
22 Storjohann, Arne
16 Labahn, George
16 Schost, Éric
15 Neiger, Vincent
13 Saunders, B. David
12 Dumas, Jean-Guillaume
12 Kaltofen, Erich L.
9 Pernet, Clément
8 Bostan, Alin
8 Eberly, Wayne
8 Giesbrecht, Mark W.
7 Jeannerod, Claude-Pierre
7 Stehlé, Damien
6 Abramov, Sergeĭ Aleksandrovich
6 Rosenkilde, Johan
6 Zhou, Wei
5 Emiris, Ioannis Z.
5 Giorgi, Pascal
5 Lecerf, Grégoire
5 Thomé, Emmanuel
5 Tsigaridas, Elias P.
4 Hu, Lei
4 Lebreton, Romain
4 Li, Hanyu
4 Wan, Zhendong
3 Barkatou, Moulay A.
3 Beckermann, Bernhard
3 Bertolazzi, Enrico
3 Chen, Jingwei
3 El Bacha, Carole
3 Faugère, Jean-Charles
3 Feng, Yong
3 Fisikopoulos, Vissarion
3 Gunnells, Paul E.
3 Harrison, Gavin
3 Heninger, Nadia
3 Hyun, Seung Gyu
3 Koiran, Pascal
3 Lucas, David E.
3 Mantzaflaris, Angelos
3 Moreno-Centeno, Erick
3 Roche, Daniel S.
3 Nielsen, Johan Sebastian Rosenkilde
3 Sarkar, Santanu
3 Turner, William J.
3 van der Hoeven, Joris
3 Wang, Huaxiong
3 Wei, Yimin
3 Xu, Jun
2 Abelard, Simon
2 Alonso Rodríguez, Ana
2 Ash, Avner
2 Biasse, Jean-François
2 Birmpilis, Stavros
2 Caruso, Xavier
2 Chen, Shaoshi
2 Cheng, Howard
2 Cluzeau, Thomas
2 Couvreur, Alain
2 Dahan, Xavier
2 Escobedo, Adolfo R.
2 Espitau, Thomas
2 Fouque, Pierre-Alain
2 Gallopoulos, Efstratios
2 Gaudry, Pierrick
2 Gawrychowski, Paweł
2 Ghiloni, Riccardo
2 Guerrini, Eleonora
2 Gupta, Somit
2 Haraldson, Joseph
2 Hofmann, Tommy
2 Jamshidpey, Armin
2 Jing, Rui-Juan
2 Kirchner, Paul
2 Krieger, Dalia
2 McConnell, Mark
2 Morel, Ivan
2 Mrozek, Marian
2 Mulders, Thom
2 Musleh, Yossef
2 Nehring, Michael
2 Neumaier, Arnold
2 Novocin, Andrew
2 Pan, Yanbin
2 Peñaranda, Luis Mariano
2 Pflügel, Eckhard
2 Rahkooy, Hamid
2 Rampersad, Narad
2 Real, Pedro
2 Renault, Guénaël
2 Salvy, Bruno
2 Sarkar, Soumojit
2 Shallit, Jeffrey Outlaw
2 Shao, Hua
2 Sobczyk, Aleksandros
2 Solomatov, Grigory
2 Specogna, Ruben
2 van Hoeij, Mark
2 Wu, Wenyuan
...and 275 more Authors
all top 5

Cited in 65 Serials

43 Journal of Symbolic Computation
14 Linear Algebra and its Applications
12 Journal of Complexity
10 Mathematics of Computation
10 Theoretical Computer Science
9 Designs, Codes and Cryptography
4 Programming and Computer Software
3 SIAM Journal on Matrix Analysis and Applications
3 Computational Complexity
2 Computers & Mathematics with Applications
2 International Journal of Control
2 Information Processing Letters
2 Linear and Multilinear Algebra
2 ACM Transactions on Mathematical Software
2 Applied Mathematics and Computation
2 Journal of Computational and Applied Mathematics
2 Discrete & Computational Geometry
2 Computational Geometry
2 Applicable Algebra in Engineering, Communication and Computing
2 Journal of Mathematical Sciences (New York)
2 Advances in Computational Mathematics
2 Foundations of Computational Mathematics
2 Advances in Mathematics of Communications
2 ACM Communications in Computer Algebra
1 Classical and Quantum Gravity
1 Discrete Applied Mathematics
1 Journal of Mathematical Physics
1 Archiv der Mathematik
1 Information Sciences
1 International Journal of Mathematics and Mathematical Sciences
1 Journal of Algebra
1 Journal of Number Theory
1 Journal of Pure and Applied Algebra
1 Mathematics and Computers in Simulation
1 Quarterly of Applied Mathematics
1 SIAM Journal on Numerical Analysis
1 European Journal of Combinatorics
1 Applied Numerical Mathematics
1 Algorithmica
1 COMPEL
1 Random Structures & Algorithms
1 Japan Journal of Industrial and Applied Mathematics
1 International Journal of Computational Geometry & Applications
1 International Journal of Foundations of Computer Science
1 Computational Mathematics and Mathematical Physics
1 European Journal of Operational Research
1 Computational Statistics and Data Analysis
1 Journal of Mathematical Imaging and Vision
1 Applied Categorical Structures
1 Journal de Théorie des Nombres de Bordeaux
1 Numerical Linear Algebra with Applications
1 INFORMS Journal on Computing
1 LMS Journal of Computation and Mathematics
1 Journal of the European Mathematical Society (JEMS)
1 Algebraic & Geometric Topology
1 Journal of Systems Science and Complexity
1 International Journal of Number Theory
1 Mathematics in Computer Science
1 Discrete Mathematics, Algorithms and Applications
1 Acta Crystallographica. Section A
1 Forum of Mathematics, Sigma
1 International Journal of Engineering Mathematics
1 International Journal of Applied and Computational Mathematics
1 Open Mathematics
1 SIAM Journal on Applied Algebra and Geometry
all top 5

Cited in 37 Fields

149 Computer science (68-XX)
105 Numerical analysis (65-XX)
86 Linear and multilinear algebra; matrix theory (15-XX)
50 Number theory (11-XX)
30 Information and communication theory, circuits (94-XX)
27 Commutative algebra (13-XX)
19 Field theory and polynomials (12-XX)
13 Ordinary differential equations (34-XX)
12 Algebraic geometry (14-XX)
9 Combinatorics (05-XX)
8 Approximations and expansions (41-XX)
6 Special functions (33-XX)
6 Convex and discrete geometry (52-XX)
6 Algebraic topology (55-XX)
5 Associative rings and algebras (16-XX)
5 Difference and functional equations (39-XX)
5 Operations research, mathematical programming (90-XX)
4 Manifolds and cell complexes (57-XX)
3 Group theory and generalizations (20-XX)
3 Probability theory and stochastic processes (60-XX)
3 Statistics (62-XX)
3 Biology and other natural sciences (92-XX)
3 Systems theory; control (93-XX)
2 Category theory; homological algebra (18-XX)
2 Dynamical systems and ergodic theory (37-XX)
1 General and overarching topics; collections (00-XX)
1 Topological groups, Lie groups (22-XX)
1 Functions of a complex variable (30-XX)
1 Several complex variables and analytic spaces (32-XX)
1 Partial differential equations (35-XX)
1 Operator theory (47-XX)
1 Differential geometry (53-XX)
1 Mechanics of particles and systems (70-XX)
1 Mechanics of deformable solids (74-XX)
1 Quantum theory (81-XX)
1 Statistical mechanics, structure of matter (82-XX)
1 Relativity and gravitational theory (83-XX)

Citations by Year