Hook, James and Dingle, Nick
(2013)
*Performance Analysis of Asynchronous Parallel Jacobi.*
[MIMS Preprint]

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## Abstract

The directed acyclic graph (DAG) associated with a parallel al- gorithm captures the order in which separate local computations are completed and how their outputs are subsequently used in further com- putations. Unlike in a synchronous parallel algorithm the DAG asso- ciated with an asynchronous parallel algorithm is not predetermined. Instead it is a product of the asynchronous timing dynamics of the machine and, as such, it is best thought of as a pseudorandom vari- able. In this paper we present a new tighter bound on the rate of convergence of asynchronous parallel Jacobi (APJ), which is based on statistical properties of the DAG and is valid for systems which satisfy a standard sufficient condition for convergence. We also describe an experiment in which we make a precise log of the calculations taking place during an implementation of APJ on a distributed memory multicore machine, which enables us to reconstruct and study the DAG. We demonstrate that our bound provides a good approximation of the true rate of convergence in these examples and show how problems in the algorithmâ��s implementation can affect the asynchronous timing dynamics and in turn the rate of convergence of the algorithm.

Item Type: | MIMS Preprint |
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Uncontrolled Keywords: | Asynchronous parallel Jacobi, chaotic iterations, parallel algorithm performance |

Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 37 Dynamical systems and ergodic theory MSC 2010, the AMS's Mathematics Subject Classification > 60 Probability theory and stochastic processes MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis MSC 2010, the AMS's Mathematics Subject Classification > 68 Computer science |

Depositing User: | Mr James Hook |

Date Deposited: | 29 Oct 2013 |

Last Modified: | 08 Nov 2017 18:18 |

URI: | https://eprints.maths.manchester.ac.uk/id/eprint/2036 |

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