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 more

Product details

  • Hardback | 240 pages
  • 213.36 x 276.86 x 12.7mm | 453.59g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • 45 black & white illustrations
  • 1584888083
  • 9781584888086

About Jacques Mohcine Bahi

University of Franche-Comte, Belfort cedex, France University of Franche-Comte, Belfort cedex, France University of Franche-Comte, Belfort cedex, Franceshow more

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 INDEXshow more