Formal proof for delayed finite field arithmetic using floating point operators (2008)
Boldo, Sylvie, Daumas, Marc, Giorgi, Pascal
Formal proof checkers such as Coq are capable of validating proofs of correction of algorithms for finite field arithmetics but they require extensive training from potential users. The delayed...
Formal proof for delayed finite field arithmetic using floating point operators (2008)
Boldo, Sylvie, Daumas, Marc, Giorgi, Pascal
Formal proof checkers such as Coq are capable of validating proofs of correction of algorithms for finite field arithmetics but they require extensive training from potential users. The delayed...
Dense Linear Algebra over Finite Fields: the FFLAS and FFPACK packages (2007)
Dumas, Jean-Guillaume, Gautier, Thierry, Giorgi, Pascal, Pernet, Clément
In the past two decades, some major efforts have been made to reduce exact (e.g. integer, rational, polynomial) linear algebra problems to matrix multiplication in order to provide algorithms with...
Dense Linear Algebra over Finite Fields: the FFLAS and FFPACK packages (2007)
Dumas, Jean-Guillaume, Gautier, Thierry, Giorgi, Pascal, Pernet, Clément
In the past two decades, some major efforts have been made to reduce exact (e.g. integer, rational, polynomial) linear algebra problems to matrix multiplication in order to provide algorithms with...
Formal proof for delayed finite field arithmetic using floating point operators (2007)
Formal proof checkers such as Coq are capable of validating proofs of correction of algorithms for finite field arithmetics but they require extensive training from potential users. The delayed...
Formal proof for delayed finite field arithmetic using floating point operators (2007)
Formal proof checkers such as Coq are capable of validating proofs of correction of algorithms for finite field arithmetics but they require extensive training from potential users. The delayed...
Parallel computation of the rank of large sparse matrices from algebraic K-theory (2007)
Dumas, Jean-Guillaume, Elbaz-Vincent, Philippe, Giorgi, Pascal, Urbanska, Anna
This paper deals with the computation of the rank and of some integer Smith forms of a series of sparse matrices arising in algebraic K-theory. The number of non zero entries in the considered...
Parallel computation of the rank of large sparse matrices from algebraic K-theory (2007)
Dumas, Jean-Guillaume, Elbaz-Vincent, Philippe, Giorgi, Pascal, Urbanska, Anna
This paper deals with the computation of the rank and of some integer Smith forms of a series of sparse matrices arising in algebraic K-theory. The number of non zero entries in the considered...
Parallel computation of the rank of large sparse matrices from algebraic K-theory (2007)
Dumas, Jean-Guillaume, Elbaz-Vincent, Philippe, Giorgi, Pascal, Urbanska, Anna
This paper deals with the computation of the rank and of some integer Smith forms of a series of sparse matrices arising in algebraic K-theory. The number of non zero entries in the considered...
Parallel computation of the rank of large sparse matrices from algebraic K-theory (2007)
Dumas, Jean-Guillaume, Elbaz-Vincent, Philippe, Giorgi, Pascal, Urbanska, Anna
This paper deals with the computation of the rank and of some integer Smith forms of a series of sparse matrices arising in algebraic K-theory. The number of non zero entries in the considered...
Subquadratic Binary Field Multiplier in Double Polynomial System (2007)
Giorgi, Pascal, Negre, Christophe, Plantard, Thomas
We propose a new space efficient operator to multiply elements lying in a binary field GF(2^k). Our approach is based on a novel system of representation called "Double Polynomial System" which set...
Subquadratic Binary Field Multiplier in Double Polynomial System (2007)
Giorgi, Pascal, Negre, Christophe, Plantard, Thomas
We propose a new space efficient operator to multiply elements lying in a binary field GF(2^k). Our approach is based on a novel system of representation called "Double Polynomial System" which set...
Proof checking for delayed finite field arithmetic using floating point operators (2007)
Formal proof checkers such as Coq, PVS and HOL light are capable of validating proofs on finite field arithmetics and their implementations but they require extensive training from potential users....
Formal proof for delayed finite field arithmetic using floating point operators (2007)
Boldo, Sylvie, Daumas, Marc, Giorgi, Pascal
Formal proof checkers such as Coq are capable of validating proofs of correction of algorithms for finite field arithmetics but they require extensive training from potential users. The delayed...
Faster Inversion and Other Black Box Matrix Computations Using Efficient Block Projections (2007)
Eberly, Wayne, Giesbrecht, Mark, Giorgi, Pascal, Storjohann, Arne, Villard, Gilles
Block projections have been used, in [Eberly et al. 2006], to obtain an efficient algorithm to find solutions for sparse systems of linear equations. A bound of softO(n^(2.5)) machine operations is...
Faster Inversion and Other Black Box Matrix Computations Using Efficient Block Projections (2007)
Eberly, Wayne, Giesbrecht, Mark, Giorgi, Pascal, Storjohann, Arne, Villard, Gilles
Block projections have been used, in [Eberly et al. 2006], to obtain an efficient algorithm to find solutions for sparse systems of linear equations. A bound of softO(n^(2.5)) machine operations is...
Faster Inversion and Other Black Box Matrix Computations Using Efficient Block Projections (2007)
Eberly, Wayne, Giesbrecht, Mark, Giorgi, Pascal, Storjohann, Arne, Villard, Gilles
Block projections have been used, in [Eberly et al. 2006], to obtain an efficient algorithm to find solutions for sparse systems of linear equations. A bound of softO(n^(2.5)) machine operations is...
Solving Sparse Integer Linear Systems (2006)
Eberly, Wayne, Giesbrecht, Mark, Giorgi, Pascal, Storjohann, Arne, Villard, Gilles
We propose a new algorithm to solve sparse linear systems of equations over the integers. This algorithm is based on a $p$-adic lifting technique combined with the use of block matrices with...
Solving Sparse Integer Linear Systems (2006)
Eberly, Wayne, Giesbrecht, Mark, Giorgi, Pascal, Storjohann, Arne, Villard, Gilles
We propose a new algorithm to solve sparse linear systems of equations over the integers. This algorithm is based on a $p$-adic lifting technique combined with the use of block matrices with...
Solving Sparse Integer Linear Systems (2006)
Eberly, Wayne, Giesbrecht, Mark, Giorgi, Pascal, Storjohann, Arne, Villard, Gilles
We propose a new algorithm to solve sparse linear systems of equations over the integers. This algorithm is based on a $p$-adic lifting technique combined with the use of block matrices with...
Solving Sparse Integer Linear Systems (2006)
Eberly, Wayne, Giesbrecht, Mark, Giorgi, Pascal, Storjohann, Arne, Villard, Gilles
We propose a new algorithm to solve sparse linear systems of equations over the integers. This algorithm is based on a $p$-adic lifting technique combined with the use of block matrices with...
Solving Sparse Integer Linear Systems (2006)
Eberly, Wayne, Giesbrecht, Mark, Giorgi, Pascal, Storjohann, Arne, Villard, Gilles
We propose a new algorithm to solve sparse linear systems of equations over the integers. This algorithm is based on a $p$-adic lifting technique combined with the use of block matrices with...
Dense Linear Algebra over Finite Fields: the FFLAS and FFPACK packages (2006)
Dumas, Jean-Guillaume, Gautier, Thierry, Giorgi, Pascal, Pernet, Clément
In the last past two decades, several efforts have been made to reduce exact linear algebra problems to matrix multiplication in order to provide algorithms with optimal asymptotic complexity. To...
Dense Linear Algebra over Finite Fields: the FFLAS and FFPACK packages (2006)
Dumas, Jean-Guillaume, Gautier, Thierry, Giorgi, Pascal, Pernet, Clément
In the past two decades, some major efforts have been made to reduce exact (e.g. integer, rational, polynomial) linear algebra problems to matrix multiplication in order to provide algorithms with...
Dense Linear Algebra over Finite Fields: the FFLAS and FFPACK packages (2006)
Dumas, Jean-Guillaume, Gautier, Thierry, Giorgi, Pascal, Pernet, Clément
In the last past two decades, several efforts have been made to reduce exact linear algebra problems to matrix multiplication in order to provide algorithms with optimal asymptotic complexity. To...
Dense Linear Algebra over Finite Fields: the FFLAS and FFPACK packages (2006)
Dumas, Jean-Guillaume, Gautier, Thierry, Giorgi, Pascal, Pernet, Clément
In the last past two decades, several efforts have been made to reduce exact linear algebra problems to matrix multiplication in order to provide algorithms with optimal asymptotic complexity. To...
On the Complexity of Polynomial Matrix Computations (2004)
Pascal Giorgi, Claude-pierre Jeannerod, Gilles Villard
We study the link between the complexity of polynomial matrix multiplication and the complexity of solving other basic linear algebra problems on polynomial matrices. By polynomial matrices we mean n...
On the Complexity of Polynomial Matrix Computations (2003)
Unite Mixte, Pascal Giorgi, Claude-pierre Jeannerod, Gilles Villard
We study the link between the complexity of polynomial matrix multiplication and the complexity of solving other basic linear algebra problems on polynomial matrices. By polynomial matrices we mean n...
On the Complexity of Polynomial Matrix Computations. (2003)
Giorgi, Pascal, Jeannerod, Claude-Pierre, Villard, Gilles
(eng) We study the link between the complexity of polynomial matrix multiplication and the complexity of solving other basic linear algebra problems on polynomial matrices. By polynomial matrices we...
LinBox: A Generic Library for Exact Linear Algebra. (2002)
Dumas, J.G., Gautier, T., Giesbrecht, M., Giorgi, Pascal, Hovinen, B., ...
(eng) LinBox is a high-performance generic software library for black box linear algebra over symbolic (exact) entry domains. The generic software methodology enables the user to instantiate the...