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Original Articles

A method for the approximation of distributions

Pages 121-142 | Published online: 19 Mar 2007
 

Abstract

Le but de cet article est l‘étude d‘une méthode d‘approximation de distributions par des combinaisons linéaires de masses de Dirac. La valeur des coefficients de cette combinaison lineaire est dérminée explidtement, en utilisant des suites de fonctions tendant vers la mesure de Dirac. Nous pr£sentons d‘abord le principe de la méthode puis quelques résultats théoriques de convergence. Enfin, nous donnons des résultats numériques d‘approximation de distributions et nous appliquons la méthode à la résolution numerique d'equations integrates singulieres.

The object of this article is to study a method of approximation of distributions by linear combinations of Dirac masses. The value of the coefficients of this linear combination is explicitly determined by using sequences of functions tending towards the Dirac measure. First, we present the principle of the method, then some theoretical results of convergence. Finally, we give numerical results of approximation of distributions and we apply the method to the numerical solution of singular integral equations.

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