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Algorithmes numériques et calcul haute performance - Chaire CADMOS

Chaire

Publications associées (333)

Numerical algorithms for solving the continuous-time algebraic Riccati matrix equation on a distributed memory parallel computer are considered. In particular, it is shown that the Schur method, based on computing the stable invariant subspace of a Hamilto ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2008

Blocked algorithms for the reduction to Hessenberg-triangular form revisited

Daniel Kressner, Bo Kågström

We present two variants of Moler and Stewart's algorithm for reducing a matrix pair to Hessenberg-triangular (HT) form with increased data locality in the access to the matrices. In one of these variants, a careful reorganization and accumulation of Givens ...

2008

Block variants of Hammarling's method for solving Lyapunov equations

Daniel Kressner

This article is concerned with the efficient numerical solution of the Lyapunov equation A(T) X + XA = -C with a stable matrix A and a symmetric positive semidefinite matrix C of possibly small rank. We discuss the efficient implementation of Hammarling's ...

Association for Computing Machinery2008

The effect of aggressive early deflation on the convergence of the QR algorithm

Daniel Kressner

Aggressive early deflation has proven to significantly enhance the convergence of the QR algorithm for computing the eigenvalues of a nonsymmetric matrix. One purpose of this paper is to point out that this deflation strategy is equivalent to extracting co ...

Society for Industrial and Applied Mathematics2008

Dictionary Identifiability from Few Training Samples

Rémi Gribonval, Karin Schnass

This article treats the problem of learning a dictionary providing sparse representations for a given signal class, via

ell^1

minimisation, or more precisely the problem of identifying a dictionary

dico

from a set of training samples

Y

knowing that $ ...

2008

Induced and coinduced Banach Lie-Poisson spaces and integrability

Tudor Ratiu

The Poisson induction and coinduction procedures are used to construct Banach Lie-Poisson spaces as well as related systems of integrals in involution. This general method applied to the Banach Lie-Poisson space of trace class operators leads to infinite H ...

2008

Numerical Mathematics

Alfio Quarteroni

Numerical mathematics is the branch of mathematics that proposes, develops, analyzes and applies methods from scientific computing to several fields including analysis, linear algebra, geometry, approximation theory, functional equations, optimization and ...

Springer2007

In this paper we propose a new structure for multiplication using optimal normal bases of type

2

. The multiplier uses an efficient linear transformation to convert the normal basis representations of elements of

F_{q^{n}}

to suitable polynomials of deg ...

2007

In this thesis, we deal with binet matrices, an extension of network matrices. The main result of this thesis is the following. A rational matrix A of size n×m can be tested for being binet in time O(n6m). If A is binet, our algorithm outputs a nonsingular ...

EPFL2007

Computing periodic deflating subspaces associated with a specified set of eigenvalues

Daniel Kressner, Bo Kågström

We present a direct method for reordering eigenvalues in the generalized periodic real Schur form of a regular K-cyclic matrix pair sequence (A k ,E k ). Following and generalizing existing approaches, reordering consists of consecutively computing the sol ...

2007

In this paper we propose a new structure for multiplication using optimal normal bases of type

2

. The multiplier uses an efficient linear transformation to convert the normal basis representations of elements of

F_{q^{n}}

to suitable polynomials of deg ...

2007

Dictionary Identifiability from Few Training Samples

Rémi Gribonval, Karin Schnass

This article treats the problem of learning a dictionary providing sparse representations for a given signal class, via

ell^1

minimisation, or more precisely the problem of identifying a dictionary

dico

from a set of training samples

Y

knowing that $ ...

2008