高性能計算機上的數值線性代數

《高性能計算機上的數值線性代數》是由清華大學出版社出版編著的實體書。主要講述數值線性代數在高性能計算機的表現及計算方法。

基本介紹

• 書名：高性能計算機上的數值線性代數
• 作者：JackJ.Dongarra
• ISBN：9787302244998
• 出版社：清華大學出版社

圖書信息

書名：Numerical Linear Algebra on High-Performance Computers（高性能計算機上的數值線性代數）

ISBN：9787302244998

作者：JackJ.Dongarra著

定價：49元

出版日期：2011-3-23

出版社：清華大學出版社

圖書簡介

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 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. we intend this book to be used by three groups of readers: graduate students, researchers working in computational science, and numerical analysts. as such, we hope this book can serve both as a reference and as a supplement to a teaching text on aspects of scientific computation.

the book is divided into five major parts: (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 systems of equations (chapter 6); (4) iterative solution of sparse systems of equations (chapters 7-9); and (5) iterative solution of sparse eigenvalue problems (chapters 10-11). any book that attempts to cover these topics must necessarily be somewhat out of date before it appears, because the area is in a state of flux. we have purposely avoided highly detailed descriptions of popular machines and have tried instead to focus on concepts as much as possible; nevertheless, to make the description more concrete, we do point to specific computers.

目錄

about the authors

preface

introduction

1 high-performance computing

1.1 trends in computer design

1.2 traditional computers and their limitations

1.3 parallelism within a single processor

1.3.1 multiple functional units

1.3.2 pipelining

1.3.3 overlapping

1.3.4 risc

1.3.5 vliw

1.3.6 vector instructions

1.3.7 chaining

1.3.8 memory-to-memory and register-to-register organizations

1.3.9 register set

1.3.10 stripmining

1.3.11 reconfigurable vector registers

1.3.12 memory organization

1.4 data organization

1.4.1 main memory

1.4.2 cache

1.4.3 local memory

1.5 memory management

1.6 parallelism through multiple pipes or multiple processors

1.7 message passing

1.8 virtual shared memory

1.8.1 routing

1.9 interconnection topology

1.9.1 crossbar switch

1.9.2 timeshared bus

1.9.3 ring connection

1.9.4 mesh connection

1.9.5 hypercube

1.9.6 multi-staged network

1.10 programming techniques

1.11 trends: network-based computing

2 overview of current high-performance computers

2.1 supercomputers

2.2 risc-based processors

2.3 parallel processors

……

3 implementation details and overhead

4 performance: analysis, modeling, and measurements

5 building blocks in linear algebra

6 direct solution of sparse linear systems

7 krylov subspaces: projection

8 iterative methods for linear systems

9 preconditioning and parallel preconditioning

10 linear eigenvalue problems ax=λχ

11 the generalized eigenproblem

bibliography

index