Solving linear systems on vector and shared memory computers.

*(English)*Zbl 0770.65009
Miscellaneous Titles in Applied Mathematics. 23. Philadelphia, PA: SIAM, Society for Industrial and Applied Mathematics. xii, 256 p. (1990).

The purpose of this book is to unify and document in one place many of the techniques and much of the current understanding about solving systems of linear equations on vector and shared-memory parallel computers. This book is not a textbook, but it is meant to provide a fast entrance to the world of vector and parallel processing for these linear algebra applications. This book is intended for use by three groups of readers: graduate students, researchers working in computational science, and numerical analysts. As such, it can serve both as a reference and as a supplement to a teaching text on aspects of scientific computation.

The book is divided into four sections: (1) introduction to terms and concepts, including an overview of the state of the art for high- performance computers and a discussion of performance evaluation (Chapters 1-4); (2) direct solution of dense matrix problems (Chapter 5); (3) direct solution of sparse matrix problems (Chapter 6); (4) iterative solution of sparse matrix problems (Chapter 7). Highly detailed descriptions of popular machines are avoided. Instead the authors focus on concepts as much as possible; nevertheless, to make the description more concrete, specific computers are pointed to.

Rather than include a floppy disk containing the software described in the book, the authors have included a pointer to netlib. The software included in netlib is in the public domain and can be used freely. With netlib up-to-date software is available at all times. A directory in netlib called ddsv contains the software, and Appendix A of this book discusses what is available and how to make a request from netlib.

This book only touches on topics relating to massively parallel SIMD computers and distributed-memory machines, partly because the authors’ experience lies in shared-memory architectures and partly because the areas of massively parallel and distributed-memory computing are still rapidly changing.

There are five appendices on the topics: Acquiring Mathematical Software; Glossary; Information on Various High-Performance Computers; Level 1, 2, and 3 BLAS Quick Reference; and Operations Counts for Various BLAS and Decompositions.

The book is divided into four sections: (1) introduction to terms and concepts, including an overview of the state of the art for high- performance computers and a discussion of performance evaluation (Chapters 1-4); (2) direct solution of dense matrix problems (Chapter 5); (3) direct solution of sparse matrix problems (Chapter 6); (4) iterative solution of sparse matrix problems (Chapter 7). Highly detailed descriptions of popular machines are avoided. Instead the authors focus on concepts as much as possible; nevertheless, to make the description more concrete, specific computers are pointed to.

Rather than include a floppy disk containing the software described in the book, the authors have included a pointer to netlib. The software included in netlib is in the public domain and can be used freely. With netlib up-to-date software is available at all times. A directory in netlib called ddsv contains the software, and Appendix A of this book discusses what is available and how to make a request from netlib.

This book only touches on topics relating to massively parallel SIMD computers and distributed-memory machines, partly because the authors’ experience lies in shared-memory architectures and partly because the areas of massively parallel and distributed-memory computing are still rapidly changing.

There are five appendices on the topics: Acquiring Mathematical Software; Glossary; Information on Various High-Performance Computers; Level 1, 2, and 3 BLAS Quick Reference; and Operations Counts for Various BLAS and Decompositions.

Reviewer: I.N.Katz (St.Louis)

##### MSC:

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

65F10 | Iterative numerical methods for linear systems |

65Y05 | Parallel numerical computation |

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

65Y10 | Numerical algorithms for specific classes of architectures |

15-04 | Software, source code, etc. for problems pertaining to linear algebra |

68W15 | Distributed algorithms |