Scientific Computing (eBook)

An Introduction with Parallel Computing

Gene H. Golub, James M. Ortega (Autoren)

eBook Download: PDF

2014 | 1. Auflage
442 Seiten
Elsevier Science (Verlag)
978-1-4832-9604-3 (ISBN)

Infos

This book introduces the basic concepts of parallel and vector computing in the context of an introduction to numerical methods. It contains chapters on parallel and vector matrix multiplication and solution of linear systems by direct and iterative methods. It is suitable for advanced undergraduate and beginning graduate courses in computer science, applied mathematics, and engineering. Ideally, students will have access to a parallel or Vector computer, but the material can be studied profitably in any case. - Gives a modern overview of scientific computing including parallel an vector computation - Introduces numerical methods for both ordinary and partial differential equations - Has considerable discussion of both direct and iterative methods for linear systems of equations, including parallel and vector algorithms - Covers most of the main topics for a first course in numerical methods and can serve as a text for this course

Inhalt

Front cover 1
Scientific Computing: An Introduction with Parallel Computing 4
Copyright Page 5
Table of Contents 8
Dedication 
6 
Preface 10
Chapter 1. The World of Scientific Computing 12
1.1 What Is Scientific Computing? 12
1.2 Mathematical Modeling 14
1.3 The Process of Numerical Solution 17
1.4 The Computational Environment 22
Chapter 2. Linear Algebra 26
2.1 Matrices and Vectors 26
2.2 Eigenvalues and Canonical Forms 39
2.3 Norms 50
Chapter 3. Parallel and Vector Computing 60
3.1 Parallel and Vector Computers 60
3.2 Basic Concepts of Parallel Computing 73
3.3 Matrix Multiplication 82
Chapter 4. Polynomial Approximation 102
4.1 Taylor Series, Interpolation and Splines 102
4.2 Least Squares Approximation 117
4.3 Application to Root-Finding 128
Chapter 5. Continuous Problems Solved Discretely 148
5.1 Numerical Integration 148
5.2 Initial Value Problems 161
5.3 Boundary Value Problems 184
5.4 Space and Time 202
5.5 The Curse of Dimensionality 213
Chapter 6. Direct Solution of Linear Equations 226
6.1 Gaussian Elimination 226
6.2 Errors in Gaussian Elimination 247
6.3 Other Factorizations 268
Chapter 7. Parallel Direct Methods 286
7.1 Basic Methods 286
7.2 Other Organizations of Factorization 305
7.3 Banded and Tridiagonal Systems 313
Chapter 8. Iterative Methods 332
8.1 Relaxation-Type Methods 332
8.2 Parallel and Vector Implementations 344
8.3 The Multigrid Method 364
Chapter 9. Conjugate Gradient-Type Methods 382
9.1 The Conjugate Gradient Method 382
9.2 Preconditioning 392
9.3 Nonsymmetric and Nonlinear Problems 408
Bibliography 424
Author Index 440
Subject Index 446

Produkt-Details

• Erscheint lt. Verlag: 28.6.2014
• Sprache: englisch
• Themenwelt: Informatik ► Software Entwicklung ► User Interfaces (HCI)
• Themenwelt: Mathematik / Informatik ► Informatik ► Theorie / Studium
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Naturwissenschaften
• ISBN-10: 1-4832-9604-0 / 1483296040
• ISBN-13: 978-1-4832-9604-3 / 9781483296043