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