稀疏线性系统的迭你方法(第二版)(影印版)

2.2 Finite Difference Methods
2.3 The Finite Element Method
2.4 Mesh Generation and Refinement
2.5 Finite Volume Method
Exercises
Notes and References
3 Sparse Matrices
3.1 Introduction
3.2 Graph Representations
3.3 Permutations and Reorderings
3.4 Storage Schemes
3.5 Basic Sparse Matrix Operations
3.6 Sparse Direct Solution Methods
3.7 Test Problems
Exercises
Notes and References
4 Basic Iterative Methods
4.1 Jacobi, Gauss-Seidel, and Successive Overrelaxation
4.2 Convergence
4.3 Alternating Direction Methods
Exercises
Notes and References
5 Projection Methods
5.1 Basic Definitions and Algorithms
5.2 General Theory
5.3 One-Dimensional Projection Processes
5.4 Additive and Multiplicative Processes
Exercises
Notes and References
6 Kryiov Subspace Methods, Part I
6.1 Introduction
6.2 Krylov Subspaces
6.3 Arnoldi's Method
6.4 Arnoldi's Method for Linear Systems
6.5 Generalized Minimal Residual Method
6.6 The Symmetric Lanczos Algorithm
6.7 The Conjugate Gradient Algorithm
6.8 The Conjugate Residual Method
6.9 Generalized Conjugate Residual, ORTHOMIN, and ORTHODIR
6.10 The Faber-Manteuffel Theorem
6.11 Convergence Analysis
6.12 Block Krylov Methods
Exercises
Notes and References
7 Kryiov Subspaee Methods, Part II
7.1 Lanczos Biorthogonalization
7.2 The Lanczos Algorithm for Linear Systems ..
7.3 The Biconjugate Gradient and Quasi-Minimal Residual Algorithms
7.4 Transpose-Free Variants
Exercises
Notes and References
8 Methods Related to the Normal Equations
8.1 The Normal Equations
8.2 Row Projection Methods
8.3 Conjugate Gradient and Normal Equations
8.4 Saddle-Point Problems
Exercises
Notes and References
9 Preconditioned Iterations
9.1 Introduction
9.2 Preconditioned Conjugate Gradient
9.3 Preconditioned Generalized Minimal Residual
9.4 Flexible Variants
9.5 Preconditioned Conjugate Gradient for the Normal Equations
9.6 The Concus, Golub, and Widlund Algorithm
Exercises
Notes and References
10 Preconditioning Techniques
10.1 Introduction
10.2 Jacobi, Successive Overrelaxation, and Symmetric Successive Overrelaxation Preconditioners
10.3 Incomplete LU Factorization Preconditioners
10.4 Threshold Strategies and Incomplete LU with Threshold
10.5 Approximate Inverse Preconditioners
10.6 Reordering for Incomplete LU
10.7 Block Preconditioners
10.8 Preconditioners for the Normal Equations
Exercises
Notes and References
11 Parallel Implementations
11.1 Introduction
11.2 Forms of Parallelism
11.3 Types of Parallel Architectures
11.4 Types of Operations
11.5 Matrix-by-Vector Products
11.6 Standard Preconditioning Operations
Exercises
Notes and References
12 Parallel Preconditioners
12.1 Introduction
12.2 Block Jacobi Preconditioners
12.3 Polynomial Preconditioners
12.4 Multicoloring
12.5 Multi-Elimination Incomplete LU
12.6 Distributed Incomplete LU and Symmetric Successive Overrelaxation
12.7 Other Techniques
Exercises
Notes and References
13 Multigrid Methods
13.1 Introduction
13.2 Matrices and Spectra of Model Problems
13.3 Intergrid Operations
13.4 Standard Multigrid Techniques
13.5 Analysis of the Two-Grid Cycle
13.6 Algebraic Multigrid
13.7 Multigrid versus Krylov Methods
Exercises
Notes and References
14 Domain Decomposition Methods
14.1 Introduction
14.2 Direct Solution and the Schur Complement
14.3 Schwarz Alternating Procedures
14.4 Schur Complement Approaches
14.5 Full Matrix Methods
14.6 Graph Partitioning
Exercises
Notes and References
Bibliography
Index ...