Iterative Solution of Large Linear Systems
eBook - PDF

Iterative Solution of Large Linear Systems

  1. 598 pages
  2. English
  3. PDF
  4. Only available on web
eBook - PDF

Iterative Solution of Large Linear Systems

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About This Book

Iterative Solution of Large Linear Systems describes the systematic development of a substantial portion of the theory of iterative methods for solving large linear systems, with emphasis on practical techniques. The focal point of the book is an analysis of the convergence properties of the successive overrelaxation (SOR) method as applied to a linear system where the matrix is "consistently ordered". Comprised of 18 chapters, this volume begins by showing how the solution of a certain partial differential equation by finite difference methods leads to a large linear system with a sparse matrix. The next chapter reviews matrix theory and the properties of matrices, as well as several theorems of matrix theory without proof. A number of iterative methods, including the SOR method, are then considered. Convergence theorems are also given for various iterative methods under certain assumptions on the matrix A of the system. Subsequent chapters deal with the eigenvalues of the SOR method for consistently ordered matrices; the optimum relaxation factor; nonstationary linear iterative methods; and semi-iterative methods. This book will be of interest to students and practitioners in the fields of computer science and applied mathematics.

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Information

Publisher
Academic Press
Year
2014
ISBN
9781483274133
Topic
Mathematics
Subtopic
Algebra
Index
Mathematics

Table of contents

  1. Front Cover
  2. Iterative Solution of Large Linear Systems
  3. Copyright Page
  4. Table of Contents
  5. Dedication
  6. Preface
  7. Acknowledgments
  8. Notation
  9. List of Fundamental Matrix Properties
  10. List of Iterative Methods
  11. Chapter 1. Introduction
  12. Chapter 2. Matrix Preliminaries
  13. Chapter 3. Linear Stationary Iterative Methods
  14. Chapter 4. Convergence of the Basic Iterative Methods
  15. Chapter 5. Eigenvalues of the SOR Method for Consistently Ordered Matrices
  16. Chapter 6. Determination of the Optimum Relaxation Factor
  17. Chapter 7. Norms of the SOR Method
  18. Chapter 8. The Modified SOR Method: Fixed Parameters
  19. Chapter 9. Nonstationary Linear Iterative Methods
  20. Chapter 10. The Modified SOR Method: Variable Parameters
  21. Chapter 11. Semi-Iterative Methods
  22. Chapter 12. Extensions of the SOR Theory: Stieltjes Matrices
  23. Chapter 13. Generalized Consistently Ordered Matrices
  24. Chapter 14. Group Iterative Methods
  25. Chapter 15. Symmetric SOR Method and Related Methods
  26. Chapter 16. Second-Degree Methods
  27. Chapter 17. Alternating Direction Implicit Methods
  28. Chapter 18. Selection of Iterative Method
  29. Bibliography
  30. Index