Contents

Chapters in this book

1. Frontmatter i
2. Contents vii
3. Preface xi
4. PART 1. Theory
5. Chapter 1. Introduction 3
6. Chapter 2. Orthogonal Polynomials 8
7. Chapter 3. Properties of Tridiagonal Matrices 24
8. Chapter 4. The Lanczos and Conjugate Gradient Algorithms 39
9. Chapter 5. Computation of the Jacobi Matrices 55
10. Chapter 6. Gauss Quadrature 84
11. Chapter 7. Bounds for Bilinear Forms u^Tƒ(A)v 112
12. Chapter 8. Extensions to Nonsymmetric Matrices 117
13. Chapter 9. Solving Secular Equations 122
14. PART 2. Applications
15. Chapter 10. Examples of Gauss Quadrature Rules 139
16. Chapter 11. Bounds and Estimates for Elements of Functions of Matrices 162
17. Chapter 12. Estimates of Norms of Errors in the Conjugate Gradient Algorithm 200
18. Chapter 13. Least Squares Problems 227
19. Chapter 14. Total Least Squares 256
20. Chapter 15. Discrete Ill-Posed Problems 280
21. Bibliography 335
22. Index 361