| Preface | p. ix |
| Acknowledgments | p. xiii |
| Notation | p. xv |
| Background on Linear Algebra and Related Topics | |
| Introduction | p. 1 |
| Vectors and Matrices | p. 2 |
| Eigenvalues and Eigenvectors | p. 3 |
| Vector and Matrix Norms | p. 7 |
| Partitioned Matrices | p. 9 |
| The Generalized Dirichlet Problem | p. 10 |
| The Model Problem | p. 14 |
| Background on Basic Iterative Methods | |
| Introduction | p. 18 |
| Convergence and Other Properties | p. 19 |
| Examples of Basic Iterative Methods | p. 22 |
| Comparison of Basic Methods | p. 33 |
| Other Methods | p. 36 |
| Polynomial Acceleration | |
| Introduction | p. 39 |
| Polynomial Acceleration of Basic Iterative Methods | p. 39 |
| Examples of Nonpolynomial Acceleration Methods | p. 43 |
| Chebyshev Acceleration | |
| Introduction | p. 45 |
| Optimal Chebyshev Acceleration | p. 46 |
| Chebyshev Acceleration with Estimated Eigenvalue Bounds | p. 51 |
| Sensitivity of the Rate of Convergence to the Estimated Eigenvalues | p. 55 |
| An Adaptive Chebyshev Procedure Using Special Norms | |
| Introduction | p. 59 |
| The Pseudoresidual Vector [delta superscript (n)] | p. 61 |
| Basic Assumptions | p. 62 |
| Basic Adaptive Parameter and Stopping Relations | p. 64 |
| An Overall Computational Algorithm | p. 72 |
| Treatment of the W-Norm | p. 74 |
| Numerical Results | p. 79 |
| Adaptive Chebyshev Acceleration | |
| Introduction | p. 93 |
| Eigenvector Convergence Theorems | p. 95 |
| Adaptive Parameter and Stopping Procedures | p. 100 |
| An Overall Computational Algorithm Using the 2-Norm | p. 106 |
| The Estimation of the Smallest Eigenvalue [mu subscript N] | p. 112 |
| Numerical Results | p. 120 |
| Iterative Behavior When M[subscript E greater than sign mu subscript 1] | p. 131 |
| Singular and Eigenvector Deficient Problems | p. 134 |
| Conjugate Gradient Acceleration | |
| Introduction | p. 138 |
| The Conjugate Gradient Method | p. 139 |
| The Three-Term Form of the Conjugate Gradient Method | p. 143 |
| Conjugate Gradient Acceleration | p. 145 |
| Stopping Procedures | p. 148 |
| Computational Procedures | p. 151 |
| Numerical Results | p. 156 |
| Special Methods for Red/Black Partitionings | |
| Introduction | p. 162 |
| The RS-SI and RS-CG Methods | p. 166 |
| The CCSI and CCG Procedures | p. 170 |
| Numerical Results | p. 189 |
| Arithmetic and Storage Requirements | p. 199 |
| Combined (Hybrid) Chebyshev and Conjugate Gradient Iterations | p. 201 |
| Proofs | p. 205 |
| Adaptive Procedures for the Successive Overrelaxation Method | |
| Introduction | p. 209 |
| Consistently Ordered Matrices and Related Matrices | p. 211 |
| The SOR Method | p. 214 |
| Eigenvector Convergence of the SOR Difference Vector | p. 219 |
| SOR Adaptive Parameter and Stopping Procedures | p. 223 |
| An Overall Computational Algorithm | p. 228 |
| The SOR Method for Problems with Red/Black Partitionings | p. 234 |
| Numerical Results | p. 239 |
| On the Relative Merits of Certain Partitionings and Certain Iterative Procedures | p. 246 |
| Proofs of Theorems and Discussion of the Strategy Condition (9-5.21) | p. 253 |
| The Use of Iterative Methods in the Solution of Partial Differential Equations | |
| Introduction | p. 259 |
| The Time-Independent Two-Dimensional Problem | p. 262 |
| The Time-Independent Three-Dimensional Problem | p. 277 |
| The Time-Dependent Problem | p. 283 |
| Case Studies | |
| Introduction | p. 287 |
| The Two-Group Neutron Diffusion Problem | p. 288 |
| The Neutron Transport Equation in x-y Geometry | p. 300 |
| A Nonlinear Network Problem | p. 318 |
| The Nonsymmetrizable Case | |
| Introduction | p. 330 |
| Chebyshev Acceleration | p. 332 |
| Generalized Conjugate Gradient Acceleration Procedures | p. 339 |
| Lanczos Acceleration | p. 348 |
| Acceleration Procedures for the GCW Method | p. 351 |
| An Example | p. 354 |
| Chebyshev Acceleration Subroutine | p. 357 |
| CCSI Subroutine | p. 363 |
| SOR Subroutine | p. 368 |
| Bibliography | p. 373 |
| Index | p. 381 |
| Table of Contents provided by Ingram. All Rights Reserved. |
