Parallel Iterative Algorithms

by Jacques Mohcine Bahi; Sylvain Contassot-Vivier; Raphael Couturier

• ISBN13: 9781584888093
• ISBN10: 1584888091
• Format: Nonspecific Binding
• Copyright: 2007-11-28
• Publisher: Taylor & Francis

Summary

Focusing on grid computing and asynchronism, Parallel Iterative Algorithms explores the theoretical and practical aspects of parallel numerical algorithms. Each chapter contains a theoretical discussion of the topic, an algorithmic section that fully details implementation examples and specific algorithms, and an evaluation of the advantages and drawbacks of the algorithms. Several exercises also appear at the end of most chapters. The first two chapters introduce the general features of sequential iterative algorithms and their applications to numerical problems. The book then describes different kinds of parallel systems and parallel iterative algorithms. It goes on to address both linear and nonlinear parallel synchronous and asynchronous iterative algorithms for numerical computation, with an emphasis on the multisplitting approach. The final chapter discusses the features required for efficient implementation of asynchronous iterative algorithms. Providing the theoretical and practical knowledge needed to design and implement efficient parallel iterative algorithms, this book illustrates how to apply these algorithms to solve linear and nonlinear numerical problems in parallel environments, including local, distant, homogeneous, and heterogeneous clusters.

Table of Contents

Introduction

Iterative Algorithms

Basic theory

Sequential iterative algorithms

A classical illustration example

Iterative Algorithms And Applications To Numerical Problems

Systems of linear equations

Nonlinear equation systems

Exercises

Parallel Architectures And Iterative Algorithms

Historical context

Parallel architectures

Trends of used configurations

Classification of parallel iterative algorithms

Synchronous Iterations

Parallel linear iterative algorithms for linear systems

Nonlinear systems: parallel synchronous Newton-multisplitting algorithms

Preconditioning

Implementation

Convergence detection

Exercises

Asynchronous Iterations

Advantages of asynchronous algorithms

Mathematical model and convergence results

Convergence situations

Parallel asynchronous multisplitting algorithms

Coupling Newton and multisplitting algorithms

Implementation

Convergence detection

Exercises

Programming Environments And Experimental Results

Implementation of AIAC algorithms with nondedicated environments

Two environments dedicated to asynchronous iterative algorithms

Ratio between computation time and communication time

Experiments in the context of linear systems

Experiments in the context of partial differential equations using a finite difference scheme

Appendix: Diagonal Dominance And Irreducible Matrices Z-matrices, M-matrices, and H-matrices Perron-Frobenius theorem Sequences and sets

References

Index

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