Parallel Iterative Algorithms

Parallel Iterative Algorithms : From Sequential to Grid Computing

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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.
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Product details

  • Electronic book text | 240 pages
  • Taylor & Francis Ltd
  • Chapman & Hall/CRC
  • London, United Kingdom
  • 45 Illustrations, black and white
  • 1584888091
  • 9781584888093

Table of contents

INTRODUCTION ITERATIVE ALGORITHMS Basic theory Sequential iterative algorithms A classical illustration exampleITERATIVE ALGORITHMS AND APPLICATIONS TO NUMERICAL PROBLEMSSystems of linear equationsNonlinear equation systemsExercisesPARALLEL ARCHITECTURES AND ITERATIVE ALGORITHMS Historical context Parallel architectures Trends of used configurations Classification of parallel iterative algorithmsSYNCHRONOUS ITERATIONS Parallel linear iterative algorithms for linear systems Nonlinear systems: parallel synchronous Newton-multisplitting algorithms Preconditioning Implementation Convergence detectionExercisesASYNCHRONOUS ITERATIONSAdvantages of asynchronous algorithmsMathematical model and convergence results Convergence situations Parallel asynchronous multisplitting algorithms Coupling Newton and multisplitting algorithmsImplementation Convergence detection ExercisesPROGRAMMING ENVIRONMENTS AND EXPERIMENTAL RESULTS Implementation of AIAC algorithms with nondedicated environmentsTwo environments dedicated to asynchronous iterative algorithmsRatio 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 schemeAPPENDIX: DIAGONAL DOMINANCE AND IRREDUCIBLE MATRICESZ-matrices, M-matrices, and H-matricesPerron-Frobenius theorem Sequences and setsREFERENCESINDEX
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