An Introduction to Parallel and Vector Scientific Computation

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Paperback | 14 August 2006

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306 Pages

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In this text, students of applied mathematics, science and engineering are introduced to fundamental ways of thinking about the broad context of parallelism. The authors begin by giving the reader a deeper understanding of the issues through a general examination of timing, data dependencies, and communication. These ideas are implemented with respect to shared memory, parallel and vector processing, and distributed memory cluster computing. Threads, OpenMP, and MPI are covered, along with code examples in Fortran, C, and Java. The principles of parallel computation are applied throughout as the authors cover traditional topics in a first course in scientific computing. Building on the fundamentals of floating point representation and numerical error, a thorough treatment of numerical linear algebra and eigenvector/eigenvalue problems is provided. By studying how these algorithms parallelize, the reader is able to explore parallelism inherent in other computations, such as Monte Carlo methods.

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'... in spite of the clear need to present these concepts to a much broader technical audience, there is a perplexing dearth of training material and textbooks in the field, particularly at the introductory level. ... it is indeed refreshing to see the publication of the book An Introduction to Parallel and Vector Scientific Computing, written by Ronald W. Shonkwiler and Lew Lefton, both of the Georgia institute of Technology. They have taken the bull by the horns and produced a book that appears to be entirely satisfactory as an introductory textbook for use in such a course.' Scientific Programming

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Preface	p. xi
Machines and Computation	p. 1
Introduction - The Nature of High-Performance Computation	p. 3
Computing Hardware Has Undergone Vast Improvement	p. 4
SIMD-Vector Computers	p. 9
MIMD - True, Coarse-Grain Parallel Computers	p. 14
Classification of Distributed Memory Computers	p. 16
Amdahl's Law and Profiling	p. 20
Exercises	p. 23
Theoretical Considerations - Complexity	p. 27
Directed Acyclic Graph Representation	p. 27
Some Basic Complexity Calculations	p. 33
Data Dependencies	p. 37
Programming Aids	p. 41
Exercises	p. 41
Machine Implementations	p. 44
Early Underpinnings of Parallelization - Multiple Processes	p. 45
Threads Programming	p. 50
Java Threads	p. 56
SGI Threads and OpenMP	p. 63
MPI	p. 67
Vector Parallelization on the Cray	p. 80
Quantum Computation	p. 89
Exercises	p. 97
Linear Systems	p. 101
Building Blocks - Floating Point Numbers and Basic Linear Algebra	p. 103
Floating Point Numbers and Numerical Error	p. 104
Round-off Error Propagation	p. 110
Basic Matrix Arithmetic	p. 113
Operations with Banded Matrices	p. 120
Exercises	p. 124
Direct Methods for Linear Systems and LU Decomposition	p. 126
Triangular Systems	p. 126
Gaussian Elimination	p. 134
ijk-Forms for LU Decomposition	p. 150
Bordering Algorithm for LU Decomposition	p. 155
Algorithm for Matrix Inversion in log[superscript 2] n Time	p. 156
Exercises	p. 158
Direct Methods for Systems with Special Structure	p. 162
Tridiagonal Systems - Thompson's Algorithm	p. 162
Tridiagonal Systems - Odd-Even Reduction	p. 163
Symmetric Systems - Cholesky Decomposition	p. 166
Exercises	p. 170
Error Analysis and QR Decomposition	p. 172
Error and Residual - Matrix Norms	p. 172
Givens Rotations	p. 180
Exercises	p. 184
Iterative Methods for Linear Systems	p. 186
Jacobi Iteration or the Method of Simultaneous Displacements	p. 186
Gauss-Seidel Iteration or the Method of Successive Displacements	p. 189
Fixed-Point Iteration	p. 191
Relaxation Methods	p. 193
Application to Poisson's Equation	p. 194
Parallelizing Gauss-Seidel Iteration	p. 198
Conjugate Gradient Method	p. 200
Exercises	p. 204
Finding Eigenvalues and Eigenvectors	p. 206
Eigenvalues and Eigenvectors	p. 206
The Power Method	p. 209
Jordan Cannonical Form	p. 210
Extensions of the Power Method	p. 215
Parallelization of the Power Method	p. 217
The QR Method for Eigenvalues	p. 217
Householder Transformations	p. 221
Hessenberg Form	p. 226
Exercises	p. 227
Monte Carlo Methods	p. 231
Monte Carlo Simulation	p. 233
Quadrature (Numerical Integration)	p. 233
Exercises	p. 242
Monte Carlo Optimization	p. 244
Monte Carlo Methods for Optimization	p. 244
IIP Parallel Search	p. 249
Simulated Annealing	p. 251
Genetic Algorithms	p. 255
Iterated Improvement Plus Random Restart	p. 258
Exercises	p. 262
Programming Examples	p. 265
MPI Examples	p. 267
Send a Message Sequentially to All Processors (C)	p. 267
Send and Receive Messages (Fortran)	p. 268
Fork Example	p. 270
Polynomial Evaluation(C)	p. 270
Lan Example	p. 275
Distributed Execution on a LAN(C)	p. 275
Threads Example	p. 280
Dynamic Scheduling(C)	p. 280
SGI Example	p. 282
Backsub.f(Fortran)	p. 282
References	p. 285
Index	p. 286
Table of Contents provided by Ingram. All Rights Reserved.

An Introduction to Parallel and Vector Scientific Computation

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