Q-adic Transform revisited (2008)
We present an algorithm to perform a simultaneous modular reduction of several residues. This algorithm is applied fast modular polynomial multiplication. The idea is to convert the $X$-adic...
Q-adic Transform revisited (2008)
We present an algorithm to perform a simultaneous modular reduction of several residues. This algorithm is applied fast modular polynomial multiplication. The idea is to convert the $X$-adic...
Q-adic Transform revisited (2008)
We present an algorithm to perform a simultaneous modular reduction of several residues. This algorithm is applied fast modular polynomial multiplication. The idea is to convert the $X$-adic...
Q-adic Transform revisited (2008)
We present an algorithm to perform a simultaneous modular reduction of several residues. This algorithm is applied fast modular polynomial multiplication. The idea is to convert the $X$-adic...
Caractérisation des Quenines et leur représentation spirale (2008)
Les nombres de Raymond Queneau sont les entiers n pour lesquels la quenine (permutation spirale envoyant tout nombre pair sur sa moiti et tout nombre impair sur son opposé ajouté à n) est d'ordre...
Caractérisation des Quenines et leur représentation spirale (2008)
Les nombres de Raymond Queneau sont les entiers n pour lesquels la quenine (permutation spirale envoyant tout nombre pair sur sa moiti et tout nombre impair sur son opposé ajouté à n) est d'ordre...
Compressed Modular Matrix Multiplication (2008)
Dumas, Jean-Guillaume, Fousse, Laurent, Salvy, Bruno
We propose to store several integers modulo a small prime into a single machine word. Modular addition is performed by addition and possibly subtraction of a word containing several times the modulo....
Compressed Modular Matrix Multiplication (2008)
Dumas, Jean-Guillaume, Fousse, Laurent, Salvy, Bruno
We propose to store several integers modulo a small prime into a single machine word. Modular addition is performed by addition and possibly subtraction of a word containing several times the modulo....
Compressed Modular Matrix Multiplication (2008)
Dumas, Jean-Guillaume, Fousse, Laurent, Salvy, Bruno
We propose to store several integers modulo a small prime into a single machine word. Modular addition is performed by addition and possibly subtraction of a word containing several times the modulo....
Compressed Modular Matrix Multiplication (2008)
Dumas, Jean-Guillaume, Fousse, Laurent, Salvy, Bruno
We propose to store several integers modulo a small prime into a single machine word. Modular addition is performed by addition and possibly subtraction of a word containing several times the modulo....
Compressed Modular Matrix Multiplication (2008)
Dumas, Jean-Guillaume, Fousse, Laurent, Salvy, Bruno
We propose to store several integers modulo a small prime into a single machine word. Modular addition is performed by addition and possibly subtraction of a word containing several times the modulo....
Q-adic Transform revisited (2008)
We present an algorithm to perform fast modular polynomial multiplication. The idea is to convert the $X$-adic representation of modular polynomials, with $X$ an indeterminate, to a $q$-adic...
Q-adic Transform revisited (2008)
We present an algorithm to perform fast modular polynomial multiplication. The idea is to convert the $X$-adic representation of modular polynomials, with $X$ an indeterminate, to a $q$-adic...
An hybrid system approach to nonlinear optimal control problems (2008)
Dumas, Jean-Guillaume, Rondepierre, Aude
We consider a nonlinear ordinary differential equation and want to control its behavior so that it reaches a target by minimizing a cost function. Our approach is to use hybrid systems to solve this...
An hybrid system approach to nonlinear optimal control problems (2008)
Dumas, Jean-Guillaume, Rondepierre, Aude
We consider a nonlinear ordinary differential equation and want to control its behavior so that it reaches a target by minimizing a cost function. Our approach is to use hybrid systems to solve this...
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...
Sequential products in effect categories (2007)
Dumas, Jean-Guillaume, Duval, Dominique, Reynaud, Jean-Claude
A new categorical framework is provided for dealing with multiple arguments in a programming language with effects, for example in a language with imperative features. Like related frameworks...
An introspective algorithm for the integer determinant (2007)
Dumas, Jean-Guillaume, Urbanska, Anna
We present an algorithm computing the determinant of an integer matrix A. The algorithm is introspective in the sense that it uses several distinct algorithms that run in a concurrent manner. During...
Bounds on the coefficients of the characteristic and minimal polynomials (2007)
This note presents absolute bounds on the size of the coefficients of the characteristic and minimal polynomials depending on the size of the coefficients of the associated matrix. Moreover, we...
Caractérisation des Quenines et leur représentation spirale (2007)
Les nombres de Raymond Queneau sont les entiers n pour lesquels la quenine (permutation spirale envoyant tout nombre pair sur sa moiti et tout nombre impair sur son opposé ajouté à n) est d'ordre...
Memory efficient scheduling of Strassen-Winograd's matrix multiplication algorithm (2007)
Dumas, Jean-Guillaume, Pernet, Clément, Zhou, Wei
Strassen's algorithm was the first sub-cubic algorithm for matrix multiplication. Its improvement by Winograd led to a highly practicable algorithm. In this report, we propose new schedules of the...
An introspective algorithm for the integer determinant (2007)
Dumas, Jean-Guillaume, Urbanska, Anna
We present an algorithm computing the determinant of an integer matrix A. The algorithm is introspective in the sense that it uses several distinct algorithms that run in a concurrent manner. During...
Bounds on the coefficients of the characteristic and minimal polynomials (2007)
This note presents absolute bounds on the size of the coefficients of the characteristic and minimal polynomials depending on the size of the coefficients of the associated matrix. Moreover, we...
Caractérisation des Quenines et leur représentation spirale (2007)
Les nombres de Raymond Queneau sont les entiers n pour lesquels la quenine (permutation spirale envoyant tout nombre pair sur sa moiti et tout nombre impair sur son opposé ajouté à n) est d'ordre...
Memory efficient scheduling of Strassen-Winograd's matrix multiplication algorithm (2007)
Dumas, Jean-Guillaume, Pernet, Clément, Zhou, Wei
Strassen's algorithm was the first sub-cubic algorithm for matrix multiplication. Its improvement by Winograd led to a highly practicable algorithm. In this report, we propose new schedules of the...
Sequential products in effect categories (2007)
Dumas, Jean-Guillaume, Duval, Dominique, Reynaud, Jean-Claude
A new categorical framework is provided for dealing with multiple arguments in a programming language with effects, for example in a language with imperative features. Like related frameworks...
Q-adic Transform revisited (2007)
We present an algorithm to perform a simultaneous modular reduction of several residues. This algorithm is applied fast modular polynomial multiplication. The idea is to convert the $X$-adic...
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...
Towards a diagrammatic modeling of the LinBox C++ linear algebra library (2006)
Dumas, Jean-Guillaume, Duval, Dominique
We propose a new diagrammatic modeling language, DML. The paradigm used is that of the category theory and in particular of the pushout tool. We show that most of the object-oriented structures can...
Towards a diagrammatic modeling of the LinBox C++ linear algebra library (2006)
Dumas, Jean-Guillaume, Duval, Dominique
We propose a new diagrammatic modeling language, DML. The paradigm used is that of the category theory and in particular of the pushout tool. We show that most of the object-oriented structures can...
Efficient Computation of the Characteristic Polynomial (2005)
Dumas, Jean-Guillaume, Pernet, Clément, Wan, Zhendong
This article deals with the computation of the characteristic polynomial of dense matrices over small finite fields and over the integers. We first present two algorithms for the finite fields: one...
Efficient Computation of the Characteristic Polynomial (2005)
Dumas, Jean-Guillaume, Pernet, Clément, Wan, Zhendong
This article deals with the computation of the characteristic polynomial of dense matrices over small finite fields and over the integers. We first present two algorithms for the finite fields: one...
Efficient polynomial time algorithms computing industrial-strength primitive roots (2004)
Dubrois, Jacques, Dumas, Jean-Guillaume
E. Bach, following an idea of T. Itoh, has shown how to build a small set of numbers modulo a prime p such that at least one element of this set is a generator of...
Efficient polynomial time algorithms computing industrial-strength primitive roots (2004)
Dubrois, Jacques, Dumas, Jean-Guillaume
E. Bach, following an idea of T. Itoh, has shown how to build a small set of numbers modulo a prime p such that at least one element of this set is a generator of...
Efficient dot product over word-size finite fields (2004)
We want to achieve efficiency for the exact computation of the dot product of two vectors over word-size finite fields. We therefore compare the practical behaviors of a wide range of implementation...
Efficient dot product over word-size finite fields (2004)
We want to achieve efficiency for the exact computation of the dot product of two vectors over word-size finite fields. We therefore compare the practical behaviors of a wide range of implementation...
Depuis quelques années, l'extension de l'utilisation de l'informatique dans tous les domaines de recherche scientifique et technique se traduit par un besoin croissant de puissance de calcul. Il est...
Depuis quelques années, l'extension de l'utilisation de l'informatique dans tous les domaines de recherche scientifique et technique se traduit par un besoin croissant de puissance de calcul. Il est...
Depuis quelques années, l'extension de l'utilisation de l'informatique dans tous les domaines de recherche scientifique et technique se traduit par un besoin croissant de puissance de calcul. Il est...
Depuis quelques années, l'extension de l'utilisation de l'informatique dans tous les domaines de recherche scientifique et technique se traduit par un besoin croissant de puissance de calcul. Il est...