Chapman and Hall/CRC
240 pages | 45 B/W Illus.
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.
"In Parallel Iterative Algorithms: From Sequential to Grid Computing, Bahi, Contassot-Vivier, and Couturier bring mathematical formalism to the study of parallel iterative solution techniques, creating a book that will be useful to those with a strong maths background who are making the transition into parallel scientific computing. … a great fit as a part of a graduate-level course on scientific computing in the math department, or for those already in scientific computing seeking to understand the key mathematical foundations of the analysis of iterative techniques. … The authors execute their mission well, making sure that they treat the mathematical theory of each method in just enough detail to be complete. … The combination of the theory and the implementation is valuable, and I found it illuminating to revisit algorithms I only knew at an implementation level from the mathematical perspective and to understand the reasons behind behaviors I had always taken as given. … a nice addition to your HPC bookshelf in that it brings a strong focus on mathematical formalism, which is often lacking in more computing-oriented approaches to numerical methods. … the book is loaded with citations, and readers looking for a different point of view or for more in depth material on a particular point will find a wealth of pointers to the literature."
—John West, HPCwire, February 2009
"On the whole, an interesting and useful book on an up-to-date topic."
– Gisbert Stoyan, in Zentralblatt Math, 2009
Sequential iterative algorithms
A classical illustration example
ITERATIVE ALGORITHMS AND APPLICATIONS TO NUMERICAL PROBLEMS
Systems of linear equations
Nonlinear equation systems
PARALLEL ARCHITECTURES AND ITERATIVE ALGORITHMS
Trends of used configurations
Classification of parallel iterative algorithms
Parallel linear iterative algorithms for linear systems
Nonlinear systems: parallel synchronous Newton-multisplitting algorithms
Advantages of asynchronous algorithms
Mathematical model and convergence results
Parallel asynchronous multisplitting algorithms
Coupling Newton and multisplitting algorithms
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
Sequences and sets