Resum+.Nous pr6sentons dans cet article des r6sultats de convergence des algorithmes asynchrones bas6s essentiellement sur la notion classique de contraction.Nous g6n6ralisons, en particulier, tousles r6sultats de convergence de ces algorithmes qui font l'hypoth6se de contraction en norme vectorielle qui r6cemment a 6t6 tr6s souvant utilis6e.Par ailleurs, l'hypoth6se de contraction en norme vectorielle peut se trouver difficile, voire impossible /t v6rifier pour certains probl6mes qui peuvent ~tre cependant abordds dans le cadre de la contraction classique que nous adoptons.
Summary.In this paper we present convergence results for the asynchronous algorithms based essentially on the notion of classical contraction.We generalize, in particular, all convergence results for those algorithms which are based on the vectorial norm hypothesis, in wide spread use recently.Certain problems, for which the vectorial norm hypothesis can be difficult or even impossible to verify, can nontheless be tackled within the scope of the classical contraction that we adopte.Subject classifications. AM S(MOS): 65H 10; C R: 5.15.
--ZusammenfassungAsynchronous Algorithms for Poisson's Equation with Nonlinear Boundary Conditions. Poisson's equation with nonlinear boundary conditions is discretized with the method of lines to obtain a system of second order differential equations with multi-point boundary conditions. This differential system is converted, using invariant imbedding for each one-dimensional problem, into a fixed point problem and then the asynchronous algorithms are applied.
AMS Subject Classifications: 65H 10, 65M20; CR: 5.15, 5.17Asynehrone Algoritlunen far die Poisson-Gleiehung mit nichtlinearen Randbedingungen. Die PoissonGleichung mit nichtlinearen Randbedingungen wird mittels der Linienmethode diskretisiert und ergibt ein System von gew6hnlichen Differentialgleichungen zweiter Ordnung mit Randbedingungen. Durch invariante Einbettung for jedes eindimensionale Problem wird dieses System in ein Fixpunktproblem verwandelt, auf das dann die asynchronen Algorithmen angewandt werden.
--ZusammenfassungOn Quartic Splines with Application to Quadratures. This paper presents a formulation and a study of an interpolatory quartic spline which interpolates the first and second derivatives of a given function. This formulation can be applied, in particular, to quadratures.
AMS Subject Classifications
R6sum6. Nous introduisons dans cet article deux classes d'algorithmes it6ratifs que nous appelons ~Algorithmes mixtes asynchrones)~ et nous en 6tudierons la convergence selon un ordre partiel. Ces algorithmes sont impl6mentables aussi bien sur les monoprocesseurs que sur les multiprocesseurs, et avec leur 6tude de convergence constituent une g6n6ralisation des algorithmes mixtes classiques ~Newton-relaxatiom).
Asynchronous Mixed Algorithms. Monotonic Convergence StudySummary. In this paper we introduce two classes of iterative algorithms which we call "Asynchronous mixed algorithms" and we study their convergence under partial ordering. These algorithms can be implemented just as well on monoprocessors as on multiprocessors, and, along with their convergence study, constitute a generalization of the mixed classical "Newton-relaxation" algorithms.
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