Applied iterative methods 应用迭代方法

This graduate-level text examines the practical use of iterative methods in solving large, sparse systems of linear algebraic equations and in resolving multidimensional boundary-value problems. Topics include polynomial acceleration of basic iterative methods, Chebyshev and conjugate gradient acceleration procedures applicable to partitioning the linear system into a “red/black” block form, more. 1981 ed. Includes 48 figures and 35 tables.

Preface
Acknowledgments
Notation
Chapter 1 Background on Linear Algebra and Related Topics
　1.1 Introduction
　1.2 Vectors and Matrices
　1.3 Eigenvalues and Eigenvectors
　1.4 Vector and Matrix Norms
　1.5 Partitioned Matrices
　1.6 The Generalized Dirichlet Problem
　1.7 The Model Problem
Chapter 2 Background on Basic Iterative Methods
　2.1 Introduction
　2.2 Convergence and Other Properties
　2.3 Examples of Basic Iterative Methods
　2.4 Comparison of Basic Methods
　2.5 Other Methods
Chapter 3 Polynomial Acceleration
　3.1 Introduction
　3.2 Polynomial Acceleration of Basic Iterative Methods
　3.3 Examples of Nonpolynomial Acceleration Methods
Chapter 4 Chebyshev Acceleration
　4.1 Introduction
　4.2 Optimal Chebyshev Acceleration
　4.3 Chebyshev Acceleration with Estimated Eigenvalue Bounds
　4.4 Sensitivity of the Rate of Convergence to the Estimated Eigenvalues
Chapter 5 An Adaptive Chebyshev Procedure Using Special Norms
　5.1 Introduction
　5.2 The Pseudoresidual Vector δ(n)
　5.3 Basic Assumptions
　5.4 Basic Adaptive Parameter and Stopping Relations
　5.5 An Overall Computational Algorithm
　5.6 Treatment of the W-Norm
　5.7 Numerical Results
Chapter 6 Adaptive Chebyshev Acceleration
　6.1 Introduction
　6.2 Eigenvector Convergence Theorems
　6.3 Adaptive Parameter and Stopping Procedures
　6.4 An Overall Computational Algorithm Using the 2-Norm
　6.5 The Estimation of the Smallest Eigenvalue uN
　6.6 Numerical Results
　6.7 Iterative Behavior When ME > u1
　6.8 Singular and Eigenvector Deficient Problems
Chapter 7 Conjugate Gradient Acceleration
　7.1 Introduction
　7.2 The Conjugate Gradient Method
　7.3 The Three-Term Form of the Conjugate Gradient Method
　7.4 Conjugate Gradient Acceleration
　7.5 Stopping Procedures
　7.6 Computational Procedures
　7.7 Numerical Results
Chapter 8　Special Methods for Red/Black Partitionings
Chapter 9 Adaptive Procedures for the Successive Overrelaxation Method
Chapter 10 The Use of Iterative Methods in the Solution of Partial Differential Equations
Chapter 11 Case Studies
Chapter 12 The Nonsymmetrizable Case
Appendix A Chebyshev Acceleration Subroutine
Appendix B CCSI Subroutine
Appendix C SOR Subroutine
Bibliography
Index