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**Parallel and distributed computation: numerical methods.**
*(English)*
Zbl 0743.65107

Prentice-Hall International Editions. Englewood Cliffs, NJ: Prentice-Hall International, Inc. xix, 715 p. (1989).

Parallel processing has confirmed its usefulness already by solving a number of important problems of numerical mathematics. From advent of parallel computers these have been used for a broad variety of large- sized and time demanding applications. Model numerical problems serve in benchmarks to test every new parallel computer system appearing on the market.

From a mathematical point of view, the monograph deals with analysis, design and implementation of parallel numerical algorithms. On a space of more than one hundred pages an adequate introductory knowledge about general aspects of parallel processing is given. The kernel of the book is structured into two main parts. The first part is devoted to synchronous algorithms while the second one is oriented towards methods which are based on the asynchronous execution principle.

There are five chapters which describe parallel synchronous algorithms. A detailed attention is paid to solving linear systems of equations with general and special matrices in the first chapter of them. The next chapter treats nonlinear problems. The synchronous part concludes chapters for the shortest path problem, dynamic programming and network flow analysis.

A class of totally asynchronous methods with some theoretical formulations is the subject of the first chapter in the asynchronous part of the book. The subsequent chapter is devoted to partially asynchronous algorithms, i.e. when some amount of synchronization is introduced in the algorithm. The final chapter of the monograph presents a design of an asynchronous network of processors for realization of a general type of parallel algorithms.

It is to recommend the book to those readers who deal seriously with solving numerical problems on advanced computers with parallel architecture. It is not just a “cooking book” containing algorithmic recipes but there can be found enough from the theory of parallel numerics itself.

From a mathematical point of view, the monograph deals with analysis, design and implementation of parallel numerical algorithms. On a space of more than one hundred pages an adequate introductory knowledge about general aspects of parallel processing is given. The kernel of the book is structured into two main parts. The first part is devoted to synchronous algorithms while the second one is oriented towards methods which are based on the asynchronous execution principle.

There are five chapters which describe parallel synchronous algorithms. A detailed attention is paid to solving linear systems of equations with general and special matrices in the first chapter of them. The next chapter treats nonlinear problems. The synchronous part concludes chapters for the shortest path problem, dynamic programming and network flow analysis.

A class of totally asynchronous methods with some theoretical formulations is the subject of the first chapter in the asynchronous part of the book. The subsequent chapter is devoted to partially asynchronous algorithms, i.e. when some amount of synchronization is introduced in the algorithm. The final chapter of the monograph presents a design of an asynchronous network of processors for realization of a general type of parallel algorithms.

It is to recommend the book to those readers who deal seriously with solving numerical problems on advanced computers with parallel architecture. It is not just a “cooking book” containing algorithmic recipes but there can be found enough from the theory of parallel numerics itself.

Reviewer: M.Vajterśic (Bratislava)

### MSC:

65Yxx | Computer aspects of numerical algorithms |

65-02 | Research exposition (monographs, survey articles) pertaining to numerical analysis |

68W15 | Distributed algorithms |

65F05 | Direct numerical methods for linear systems and matrix inversion |

65F10 | Iterative numerical methods for linear systems |

65H10 | Numerical computation of solutions to systems of equations |

65K05 | Numerical mathematical programming methods |

65K10 | Numerical optimization and variational techniques |