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Scientific Computing - An Introduction with Parallel Computing
von: Gene H. Golub, James M. Ortega
Elsevier Textbooks, 2014
ISBN: 9781483296043 , 453 Seiten
Format: PDF
Kopierschutz: DRM
Preis: 40,99 EUR
Front cover
1
Scientific Computing: An Introduction with Parallel Computing
4
Copyright Page
5
Table of Contents
8
Dedication
Dedication
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
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