Efficient Computation of Fourier Transforms on Compact Groups.
Embedding and a priori wavelet-adaptivity for Dirichlet problems
Embedding and a priori wavelet-adaptivity for Dirichlet problems
The accuracy of the domain embedding method from [A. Rieder, Modél. Math. Anal. Numér.32 (1998) 405-431] for the solution of Dirichlet problems suffers under a coarse boundary approximation. To overcome this drawback the method is furnished with an a priori (static) strategy for an adaptive approximation space refinement near the boundary. This is done by selecting suitable wavelet subspaces. Error estimates and numerical experiments validate the proposed adaptive scheme. In contrast to similar,...
Encryption schemes using finite frames and Hadamard arrays.
Error bound of certain Gaussian quadrature rules for trigonometric polynomials
Essai d'application de la méthode spectroscopique de Lanczos pour la recherche des valeurs propres des matrices
Etude de la vitesse de convergence de l'algorithme en cascade dans la construction des ondelettes d'Ingrid Daubechies.
The aim of this paper is the study of the convergence of algorithms involved in the resolution of two scale equations. They are fixed point algorithms, often called cascade algorithms, which are used in the construction of wavelets. We study their speed of convergence in Lebesgue and Besov spaces, and show that the quality of the convergence depends on two independent factors. The first one, as we could foresee, is the regularity of the scaling function which is the solution of the equation. The...
Évolution d'une singularité de type cusp dans une poche de tourbillon
Évolution d'une singularité de type cusp dans une poche de tourbillon.
We investigate the evolution of singularities in the boundary of a vortex patch for two-dimensional incompressible Euler equations. We are particularly interested in cusp-like singularities which, according to numerical simulations, are stable. In this paper, we first prove that, unlike the case of a corner-like singularity, the cusp-like singularity generates a lipschitzian velocity. We then state a global result of persistence of conormal regularity with respect to vector fields vanishing at a...
Exact Kronecker constants of Hadamard sets
A set S of integers is called ε-Kronecker if every function on S of modulus one can be approximated uniformly to within ε by a character. The least such ε is called the ε-Kronecker constant, κ(S). The angular Kronecker constant is the unique real number α(S) ∈ [0,1/2] such that κ(S) = |exp(2πiα(S)) - 1|. We show that for integers m > 1 and d ≥ 1, and α1,m,m²,... = 1/(2m).
Existence of solutions to nonlinear advection-diffusion equation applied to Burgers' equation using Sinc methods
This paper has two objectives. First, we prove the existence of solutions to the general advection-diffusion equation subject to a reasonably smooth initial condition. We investigate the behavior of the solution of these problems for large values of time. Secondly, a numerical scheme using the Sinc-Galerkin method is developed to approximate the solution of a simple model of turbulence, which is a special case of the advection-diffusion equation, known as Burgers' equation. The approximate solution...
Exploring the fractal parameters of urban growth and form with wave-spectrum analysis.