Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgements
- Symbols
- Part I Numerical Linear Algebra
- 1 Linear Operators and Matrices
- 2 The Singular Value Decomposition
- 3 Systems of Linear Equations
- 4 Norms and Matrix Conditioning
- 5 Linear Least Squares Problem
- 6 Linear Iterative Methods
- 7 Variational and Krylov Subspace Methods
- 8 Eigenvalue Problems
- Part II Constructive Approximation Theory
- Part III Nonlinear Equations and Optimization
- Part IV Initial Value Problems for Ordinary Differential Equations
- Part V Boundary and Initial Boundary Value Problems
- Appendix A Linear Algebra Review
- Appendix B Basic Analysis Review
- Appendix C Banach Fixed Point Theorem
- Appendix D A (Petting) Zoo of Function Spaces
- References
- Index
6 - Linear Iterative Methods
from Part I - Numerical Linear Algebra
Published online by Cambridge University Press: 29 September 2022
Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgements
- Symbols
- Part I Numerical Linear Algebra
- 1 Linear Operators and Matrices
- 2 The Singular Value Decomposition
- 3 Systems of Linear Equations
- 4 Norms and Matrix Conditioning
- 5 Linear Least Squares Problem
- 6 Linear Iterative Methods
- 7 Variational and Krylov Subspace Methods
- 8 Eigenvalue Problems
- Part II Constructive Approximation Theory
- Part III Nonlinear Equations and Optimization
- Part IV Initial Value Problems for Ordinary Differential Equations
- Part V Boundary and Initial Boundary Value Problems
- Appendix A Linear Algebra Review
- Appendix B Basic Analysis Review
- Appendix C Banach Fixed Point Theorem
- Appendix D A (Petting) Zoo of Function Spaces
- References
- Index
Summary
We present the classical theory of linear iterative schemes for linear systems of equations: the Richardson, Jacobi, Gauss–Seidel, and relaxation methods are presented and analyzed. We introduce the Householder-John criterion for convergence of iterative schemes. The symmetrization and symmetric iterations are presented for the relaxation scheme. Some nonstationary methods, like minimal residuals, Chebyshev iterations, and minimal corrections are presented.
Keywords
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- Information
- Classical Numerical AnalysisA Comprehensive Course, pp. 121 - 155Publisher: Cambridge University PressPrint publication year: 2022