Algorithmes mixtes asynchrones. Etude de convergence monotone

Abstract

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.

A new class of asynchronous iterative algorithms with order intervals

“…Miellou [25] has given a sufficient condition of convergence for asynchronous iterations under partial ordering. Other contributions are due to El Tarazi [16], Miellou [27], El Baz (see [10], [12], and [13]), Frommer (see [18] and [19]). Reference is also made to Cousot [9] for a study related to the proof of programs using fixed point techniques.…”

Convergence versus Divergence Behaviors of Asynchronous Iterations, and Their Applications in Concrete Situations

“…In the same vein, various convergence results for asynchronous iterations applied to fixed point problem solving have been obtained [9]. One of the most remarkable results is related to the contraction of the function, and is stated as follows [12]: This result has been extended to fixed point applications with relaxation parameter [15,20], asynchronous iterative algorithms with memory in a context of classical contraction [20], and partial order [21]. Other classic results can be found in [14,22].…”