Applied Iterative Methods (eBook)

Louis A. Hageman (Autor)

eBook Download: PDF

2014 | 1. Auflage
386 Seiten
Elsevier Science (Verlag)
9781483294377 (ISBN)

Infos

Applied Iterative Methods

Inhalt

Front Cover 1
Applied Iterative Methods 4
Copyright Page 5
Table of Contents 6
Preface 10
Acknowledgments 14
Notation 16
Chapter 1. 
22 
1.1 Introduction 22
1.2 Vectors and Matrices 23
1.3 Eigenvalues and Eigenvectors 24
1.4 Vector and Matrix Norms 28
1.5 Partitioned Matrices 30
1.6 The Generalized Dirichlet Problem 31
1.7 The Model Problem 35
Chapter 2. 
39 
2.1 Introduction 39
2.2 Convergence and Other Properties 40
2.3 Examples of Basic Iterative Methods 43
2.4 Comparison of Basic Methods 54
2.5 Other Methods 57
Chapter 3. 
60 
3.1 Introduction 60
3.2 Polynomial Acceleration of Basic Iterative Methods 60
3.3 Examples of Nonpolynomial Acceleration Methods 64
Chapter 4. 
66 
4.1 Introduction 66
4.2 Optimal Chebyshev Acceleration 67
4.3 Chebyshev Acceleration with Estimated Eigenvalue Bounds 72
4.4 Sensitivity of the Rate of Convergence to the Estimated Eigenvalues 76
Chapter 5. 
80 
5.1 Introduction 80
5.2 The Pseudoresidual Vector d(n) 82
5.3 Basic Assumptions 83
5.4 Basic Adaptive Parameter and Stopping Relations 85
5.5 An Overall Computational Algorithm 93
5.6 Treatment of the W-Norm 95
5.7 Numerical Results 100
Chapter 6. 
114 
6.1 Introduction 114
6.2 Eigenvector Convergence Theorems 116
6.3 Adaptive Parameter and Stopping Procedures 121
6.4 An Overall Computational Algorithm Using the 2-Norm 127
6.5 The Estimation of the Smallest Eigenvalue µN 133
6.6 Numerical Results 141
6.7 Iterative Behavior When ME > µ1
6.8 Singular and Eigenvector Deficient Problems 155
Chapter 7. 
159 
7.1 Introduction 159
7.2 The Conjugate Gradient Method 160
7.3 The Three-Term Form of the Conjugate Gradient Method 164
7.4 Conjugate Gradient Acceleration 166
7.5 Stopping Procedures 169
7.6 Computational Procedures 172
7.7 Numerical Results 177
Chapter 8. 
183 
8.1 Introduction 183
8.2 The RS-SI and RS-CG Methods 187
8.3 The CCSI and CCG Procedures 191
8.4 Numerical Results 210
8.5 Arithmetic and Storage Requirements 220
8.6 Combined (Hybrid) Chebyshev and Conjugate Gradient Iterations 222
8.7 Proofs 226
Chapter 9. 
230 
9.1 Introduction 230
9.2 Consistently Ordered Matrices and Related Matrices 232
9.3 The SOR Method 235
9.4 Eigenvector Convergence of the SOR Difference Vector 240
9.5 SOR Adaptive Parameter and Stopping Procedures 244
9.6 An Overall Computational Algorithm 249
9.7 The SOR Method for Problems with Red/Black Partitionings 255
9.8 Numerical Results 260
9.9 On the Relative Merits of Certain Partitionings and Certain Iterative 
267 
9.10 Proofs of Theorems and Discussion of the Strategy Condition (9-5.21) 274
Chapter 10. 
280 
10.1 Introduction 280
10.2 The Time-Independent Two-Dimensional Problem 283
10.3 The Time-Independent Three-Dimensional Problem 298
10.4 The Time-Dependent Problem 304
Chapter 11. 
308 
11.1 Introduction 308
11.2 The Two-Group Neutron Diffusion Problem 309
11.3 The Neutron Transport Equation in x-y Geometry 321
11.4 A Nonlinear Network Problem 339
Chapter 12. 
351 
12.1 Introduction 351
12.2 Chebyshev Acceleration 353
12.3 Generalized Conjugate Gradient Acceleration Procedures 360
12.4 Lanczos Acceleration 369
12.5 Acceleration Procedures for the GCW Method 372
12.6 An Example 375
Appendix A: 
378 
Appendix B: 
384 
Appendix C: 
389 
Bibliography 394
Index 402

Produkt-Details

• Erscheint lt. Verlag: 28.6.2014
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Technik
• ISBN-13: 9781483294377 / 9781483294377