Bahi / Contassot-Vivier / Couturier Parallel Iterative Algorithms

From Sequential to Grid Computing
Erscheinungsjahr 2007
ISBN: 978-1-58488-809-3
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 240 Seiten

Reihe: Chapman & Hall/CRC Numerical Analysis and Scientific Computing Series

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.

Zielgruppe

Computer scientists, applied mathematicians, and engineers; undergraduate and beginning graduate students in parallel algorithm courses.

Autoren/Hrsg.

Bahi, Jacques Mohcine

Contassot-Vivier, Sylvain

Couturier, Raphael

Fachgebiete

• Mathematik | Informatik EDV | Informatik Informatik Künstliche Intelligenz

Inhaltsverzeichnis

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