高性能计算机上的数值线性代数

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

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

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.