| Description |
1 online resource (xviii, 217 pages) : illustrations |
| Series |
Chapman & Hall/CRC numerical analysis and scientific computing |
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Chapman & Hall/CRC numerical analysis and scientific computing.
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| 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 |
| 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 describe |
| Bibliography |
Includes bibliographical references (pages 205-213) and index |
| Notes |
Print version record |
| Subject |
Parallel processing (Electronic computers)
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Parallel algorithms.
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Computational grids (Computer systems)
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Iterative methods (Mathematics)
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MATHEMATICS -- Numerical Analysis.
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Computational grids (Computer systems)
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Iterative methods (Mathematics)
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Parallel algorithms
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Parallel processing (Electronic computers)
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| Form |
Electronic book
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| Author |
Contassot-Vivier, Sylvain.
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Couturier, Raphaël.
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| ISBN |
1584888091 |
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9781584888093 |
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