Asynchronous parallel algorithms II

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.

Read this article from a comprehensive knowledge base, updated and supplemented with articles reviewed by scientific committees.

Read the article

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}^{*} + \partial Ψ (U^{}

You do not have access to this resource.

Exclusive to subscribers. 97% yet to be discovered!

You do not have access to this resource. Click here to request your free trial access!

Already subscribed? Log in!

KEYWORDS

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

Ongoing reading
Asynchronous parallel algorithms II

Mathematical framework

Article included in this offer

"Mathematics"

( 165 articles )

Complete knowledge base

Updated and enriched with articles validated by our scientific committees

Services

A set of exclusive tools to complement the resources

View offer details

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 asynchronous computation of fixed points....

You do not have access to this resource.

Exclusive to subscribers. 97% yet to be discovered!

You do not have access to this resource. Click here to request your free trial access!

Already subscribed? Log in!