Parallel Asynchronous Algorithms II. Implementation

Overview

ABSTRACT

This article is devoted to the implementation of asynchronous parallel iterative algorithms. We will first discuss the implementation of stopping tests both from a computational approach and from a numerical analysis approach using in the latter case either the contraction property or the partial ordering convergence one and also the nested sets. After recalling some notions concerning the architecture of multiprocessor machines, the implementation principle of these asynchronous parallel iterative methods will be discussed, in particular for the sub-domain methods ; load balancing for these algorithms will be also discussed.

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AUTHORS

Pierre SPITERI : Professor Emeritus - University of Toulouse, INP-ENSEEIHT – IRIT, Toulouse, France
Jean-Claude MIELLOU : Honorary Professor - University of Bourgogne Franche-Comté, Department of Mathematics, Besançon, France

INTRODUCTION

In a first article [AF 1 385] we considered the solution of two types of pseudo-linear problem. The first is a univocal problem of the type

{AU}^{*} + Φ (U *) = G

^( 1 )

where A is a matrix of dimension $M \in ℕ$ , set of natural numbers, G and U are vectors of dimension M and

U \to Φ (U) est une application continue croissante

^( 2 )

The second type of problem is multi-voiced because its solution U is subject to inequality constraints of the type

U_{\min} \leq U * ou bien U_{\min} \leq U * \leq U_{\max} ou bien U * \leq U_{\max}

^( 3 )

in this case we need to solve the following multi-voice problem

{AU}^{}

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KEYWORDS

multiprocessor architecture | message passing interface | termination of algorithms | sub-domain methods

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Parallel Asynchronous Algorithms II. Implementation

Mathematical framework

Bibliography

(1) - ORTEGA (J.M.), RHEINBOLDT (W.C.) - Iterative Solution of Nonlinear Equations in Several Variables. - Computer Science and Applied Mathematics. New-York: Academic Press (1970).
(2) - BERTSEKAS (D.) - Distributed...

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