Solving Least Squares Problems

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.