Investigating the Performance of Asynchronous Jacobi's Method for Solving Systems of Linear Equations

Bethune, Iain and Bull, J. Mark and Dingle, Nicholas J. and Higham, Nicholas J. (2011) Investigating the Performance of Asynchronous Jacobi's Method for Solving Systems of Linear Equations. [MIMS Preprint]

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Abstract

Ever-increasing core counts create the need to develop parallel algorithms that avoid closely-coupled execution across cores. In this paper we present two case studies investigating the performance of several parallel asynchronous implementations of Jacobi's method for solving systems of linear equations. Although conditions for the convergence of asynchronous Jacobi are well known, what drives its rate of convergence is less well understood. The first case study investigates the algorithm's performance when executed on large numbers of processors on a Cray XE6, while the second explores the effect of varying the number of synchronous and asynchronous processors. We observe that the performance of parallel asynchronous Jacobi is highly implementation, problem and architecture-dependent.

Item Type: MIMS Preprint
Uncontrolled Keywords: Asynchronous parallel algorithms, Jacobi's method, case studies
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theory
MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
MSC 2010, the AMS's Mathematics Subject Classification > 68 Computer science
Depositing User: Dr Nicholas Dingle
Date Deposited: 02 Dec 2011
Last Modified: 08 Nov 2017 18:18
URI: https://eprints.maths.manchester.ac.uk/id/eprint/1720

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