On the complexity of computing determinants. Zbl 1061.68185
Kaltofen, Erich; Villard, Gilles |
|
2004
|
On the complexity of polynomial matrix computations. Zbl 1072.68708
Giorgi, Pascal; Jeannerod, Claude-Pierre; Villard, Gilles |
|
2003
|
Normal forms for general polynomial matrices. Zbl 1128.15005
Beckermann, Bernhard; Labahn, George; Villard, Gilles |
|
2006
|
An LLL-reduction algorithm with quasi-linear time complexity, extended abstract. Zbl 1288.68294
Novocin, Andrew; Stehlé, Damien; Villard, Gilles |
|
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 |
|
2002
|
Further analysis of Coppersmith’s block Wiedemann algorithm for the solution of sparse linear systems. (Extended abstract). Zbl 0917.65041
Villard, G. |
|
1997
|
On efficient sparse integer matrix Smith normal form computations. Zbl 1050.65044
Dumas, Jean-Guillaume; Saunders, B. David; Villard, Gilles |
|
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. |
|
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 |
|
2016
|
Solving sparse rational linear systems. Zbl 1356.65118
Eberly, Wayne; Giesbrecht, Mark; Giorgi, Pascal; Storjohann, Arne; Villard, Gilles |
|
2006
|
On computing the resultant of generic bivariate polynomials. Zbl 1467.13061
Villard, Gilles |
|
2018
|
Computing Popov and Hermite forms of polynomial matrices. Zbl 0914.65045
Villard, G. |
|
1996
|
Computing minimal interpolation bases. Zbl 1375.65013
Jeannerod, Claude-Pierre; Neiger, Vincent; Schost, Éric; Villard, Gilles |
|
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 |
|
2016
|
Computing the rank and a small nullspace basis of a polynomial matrix. Zbl 1360.68957
Storjohann, Arne; Villard, Gilles |
|
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 |
|
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 |
|
2015
|
Computing the Frobenius normal form of a sparse matrix. Zbl 0976.65042
Villard, Gilles |
|
2000
|
An algorithm for the reduction of linear DAE. Zbl 0915.65078
Quéré, M. P.; Villard, G. |
|
1995
|
Essentially optimal computation of the inverse of generic polynomial matrices. Zbl 1101.68956
Jeannerod, Claude-Pierre; Villard, Gilles |
|
2005
|
LLL reducing with the most significant bits. Zbl 1325.68298
Saruchi; Morel, Ivan; Stehlé, Damien; Villard, Gilles |
|
2014
|
On the complexity of computing determinants. (Extended abstract). Zbl 1012.65505
Kaltofen, Erich; Villard, Gilles |
|
2001
|
Generalized subresultants for computing the Smith normal form of polynomial matrices. Zbl 0851.68048
Villard, Gilles |
|
1995
|
H-LLL: using Householder inside LLL. Zbl 1237.65041
Morel, Ivan; Stehlé, Damien; Villard, Gilles |
|
2009
|
Asymptotically fast polynomial matrix algorithms for multivariable systems. Zbl 1133.93319
Jeannerod, C.-P.; Villard, G. |
|
2006
|
Computing the sign or the value of the determinant of an integer matrix, a complexity survey. Zbl 1037.65044
Kaltofen, Erich; Villard, Gilles |
|
2004
|
Matrix rank certification. Zbl 1038.65038
Saunders, B. David; Storjohann, Arne; Villard, Gilles |
|
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 |
|
2007
|
Fast computation of approximant bases in canonical form. Zbl 1450.65040
Jeannerod, Claude-Pierre; Neiger, Vincent; Villard, Gilles |
|
2020
|
Computation of the Smith normal form of polynomial matrices. Zbl 0964.65507
Villard, Gilles |
|
1993
|
A new view on HJLS and PSLQ: sums and projections of lattices. Zbl 1360.11141
Chen, Jingwei; Stehlé, Damien; Villard, Gilles |
|
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 |
|
2000
|
Certification of the QR factor \(R\) and of lattice basis reducedness. Zbl 1190.65059
Villard, Gilles |
|
2007
|
Parallel lattice basis reduction. Zbl 0921.11075
Villard, Gilles |
|
1992
|
Fast parallel algorithms for matrix reduction to normal forms. Zbl 0905.65054
Villard, Gilles |
|
1997
|
Fast parallel computation of the Smith normal form of polynomial matrices. Zbl 0978.65501
Villard, Gilles |
|
1994
|
Elimination ideal and bivariate resultant over finite fields. Zbl 07760799
Villard, Gilles |
|
2023
|
Computing an LLL-reduced basis of the orthogonal latice. Zbl 1467.11121
Chen, Jingwei; Stehlé, Damien; Villard, Gilles |
|
2018
|
Block solution of sparse linear systems over \(\text{GF}(q)\): the singular case. Zbl 1097.65525
Villard, Gilles |
|
1998
|
Processor efficient parallel solution of linear systems of equations. Zbl 0954.68024
Villard, Gilles |
|
2000
|
Parallel algorithms: analysis and design.
(Algorithmes parallèles: analyse et conception.) Zbl 0855.68037
|
|
1994
|
Data allocation strategies for the Gauss and Jordan algorithms on a ring of processors. Zbl 0681.65015
Robert, Yves; Tourancheau, Bernard; Villard, Gilles |
|
1989
|
A rank theorem for Vandermonde matrices. Zbl 1059.15002
Koiran, Pascal; Portier, Natacha; Villard, Gilles |
|
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 |
|
2017
|
High-order lifting for polynomial Sylvester matrices. Zbl 07799850
Pernet, Clément; Signargout, Hippolyte; Villard, Gilles |
|
2024
|
High-order lifting for polynomial Sylvester matrices. Zbl 07799850
Pernet, Clément; Signargout, Hippolyte; Villard, Gilles |
|
2024
|
Elimination ideal and bivariate resultant over finite fields. Zbl 07760799
Villard, Gilles |
|
2023
|
Fast computation of approximant bases in canonical form. Zbl 1450.65040
Jeannerod, Claude-Pierre; Neiger, Vincent; Villard, Gilles |
|
2020
|
On computing the resultant of generic bivariate polynomials. Zbl 1467.13061
Villard, Gilles |
|
2018
|
Computing an LLL-reduced basis of the orthogonal latice. Zbl 1467.11121
Chen, Jingwei; Stehlé, Damien; Villard, Gilles |
|
2018
|
Computing minimal interpolation bases. Zbl 1375.65013
Jeannerod, Claude-Pierre; Neiger, Vincent; Schost, Éric; Villard, Gilles |
|
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 |
|
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 |
|
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 |
|
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 |
|
2015
|
LLL reducing with the most significant bits. Zbl 1325.68298
Saruchi; Morel, Ivan; Stehlé, Damien; Villard, Gilles |
|
2014
|
A new view on HJLS and PSLQ: sums and projections of lattices. Zbl 1360.11141
Chen, Jingwei; Stehlé, Damien; Villard, Gilles |
|
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 |
|
2012
|
An LLL-reduction algorithm with quasi-linear time complexity, extended abstract. Zbl 1288.68294
Novocin, Andrew; Stehlé, Damien; Villard, Gilles |
|
2011
|
H-LLL: using Householder inside LLL. Zbl 1237.65041
Morel, Ivan; Stehlé, Damien; Villard, Gilles |
|
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 |
|
2007
|
Certification of the QR factor \(R\) and of lattice basis reducedness. Zbl 1190.65059
Villard, Gilles |
|
2007
|
Normal forms for general polynomial matrices. Zbl 1128.15005
Beckermann, Bernhard; Labahn, George; Villard, Gilles |
|
2006
|
Solving sparse rational linear systems. Zbl 1356.65118
Eberly, Wayne; Giesbrecht, Mark; Giorgi, Pascal; Storjohann, Arne; Villard, Gilles |
|
2006
|
Asymptotically fast polynomial matrix algorithms for multivariable systems. Zbl 1133.93319
Jeannerod, C.-P.; Villard, G. |
|
2006
|
Computing the rank and a small nullspace basis of a polynomial matrix. Zbl 1360.68957
Storjohann, Arne; Villard, Gilles |
|
2005
|
Essentially optimal computation of the inverse of generic polynomial matrices. Zbl 1101.68956
Jeannerod, Claude-Pierre; Villard, Gilles |
|
2005
|
On the complexity of computing determinants. Zbl 1061.68185
Kaltofen, Erich; Villard, Gilles |
|
2004
|
Computing the sign or the value of the determinant of an integer matrix, a complexity survey. Zbl 1037.65044
Kaltofen, Erich; Villard, Gilles |
|
2004
|
Matrix rank certification. Zbl 1038.65038
Saunders, B. David; Storjohann, Arne; Villard, Gilles |
|
2004
|
A rank theorem for Vandermonde matrices. Zbl 1059.15002
Koiran, Pascal; Portier, Natacha; Villard, Gilles |
|
2004
|
On the complexity of polynomial matrix computations. Zbl 1072.68708
Giorgi, Pascal; Jeannerod, Claude-Pierre; Villard, Gilles |
|
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 |
|
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. |
|
2002
|
On efficient sparse integer matrix Smith normal form computations. Zbl 1050.65044
Dumas, Jean-Guillaume; Saunders, B. David; Villard, Gilles |
|
2001
|
On the complexity of computing determinants. (Extended abstract). Zbl 1012.65505
Kaltofen, Erich; Villard, Gilles |
|
2001
|
Computing the Frobenius normal form of a sparse matrix. Zbl 0976.65042
Villard, Gilles |
|
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 |
|
2000
|
Processor efficient parallel solution of linear systems of equations. Zbl 0954.68024
Villard, Gilles |
|
2000
|
Block solution of sparse linear systems over \(\text{GF}(q)\): the singular case. Zbl 1097.65525
Villard, Gilles |
|
1998
|
Further analysis of Coppersmith’s block Wiedemann algorithm for the solution of sparse linear systems. (Extended abstract). Zbl 0917.65041
Villard, G. |
|
1997
|
Fast parallel algorithms for matrix reduction to normal forms. Zbl 0905.65054
Villard, Gilles |
|
1997
|
Computing Popov and Hermite forms of polynomial matrices. Zbl 0914.65045
Villard, G. |
|
1996
|
An algorithm for the reduction of linear DAE. Zbl 0915.65078
Quéré, M. P.; Villard, G. |
|
1995
|
Generalized subresultants for computing the Smith normal form of polynomial matrices. Zbl 0851.68048
Villard, Gilles |
|
1995
|
Fast parallel computation of the Smith normal form of polynomial matrices. Zbl 0978.65501
Villard, Gilles |
|
1994
|
Parallel algorithms: analysis and design.
(Algorithmes parallèles: analyse et conception.) Zbl 0855.68037
|
|
1994
|
Computation of the Smith normal form of polynomial matrices. Zbl 0964.65507
Villard, Gilles |
|
1993
|
Parallel lattice basis reduction. Zbl 0921.11075
Villard, Gilles |
|
1992
|
Data allocation strategies for the Gauss and Jordan algorithms on a ring of processors. Zbl 0681.65015
Robert, Yves; Tourancheau, Bernard; Villard, Gilles |
|
1989
|