Solving Least Squares Problems

Table of Contents

Preface to the Classics Edition
Preface
1. Introduction
2. Analysis of the Least Squares Problem
3. Orthogonal Decomposition by Certain Elementary Orthogonal Transformations
4. Orthogonal Decomposition by Singular Value Decomposition
5. Perturbation Theorems for Singular Values
6. Bounds for the Condition Number of a Triangular Matrix
7. The Pseudoinverse
8. Perturbation Bounds for the Pseudoinverse
9. Perturbation Bounds for the Solution of Problem LS
10. Numerical Computations Using Elementary Orthogonal Transformations
11. Computing the Solution for the Overdetermined or Exactly Determined Full Rank Problem
12. Computation of the Covariance Matrix of the Solution Parameters
13. Computing the Solution for the Underdetermined Full Rank Problem
14. Computing the Solution for Problem LS with Possibly Deficient Pseudorank
15. Analysis of Computing Errors for Householder Transformations
16. Analysis of Computing Errors for the Problem LS
17. Analysis of Computing Errors for the Problem LS Using Mixed Precision Arithmetic
18. Computation of the Singular Value Decomposition and the Solution of Problem LS
19. Other Methods for Least Squares Problems
20. Linear Least Squares with Linear Equality Constraints Using a Basis of the Null Space
21. Linear Least Squares with Linear Equality Constraints by Direct Elimination
22. Linear Least Squares with Linear Equality Constraints by Weighting
23. Linear Least Squares with Linear Inequality Constraints
24. Modifying a QR Decomposition to Add or Remove Column Vectors
25. Practical Analysis of Least Squares Problems
26. Examples of Some Methods of Analyzing a Least Squares Problem
27. Modifying a QR Decomposition to Add or Remove Row Vectors with Application to Sequential Processing of Problems Having a Large or Banded Coefficient Matrix
Appendix A: Basic Linear Algebra Including Projections
Appendix B: Proof of Global Quadratic Convergence of the QR Algorithm
Appendix C: Description and Use of FORTRAN Codes for Solving Problem LS
Appendix D: Developments from 1974 to 1995
Bibliography
Index.