Solving Least Square Problems

Preface to the Classics Edition Preface Chapter 1: Introduction Chapter 2: Analysis of the Least Squares Problem Chapter 3: Orthogonal Decomposition by Certain Elementary Orthogonal Transformations Chapter 4: Orthogonal Decomposition by Singular Value Decomposition Chapter 5: Perturbation Theorems for Singular Values Chapter 6: Bounds for the Condition Number of a Triangular Matrix Chapter 7: The Pseudoinverse Chapter 8: Perturbation Bounds for the Pseudoinverse Chapter 9: Perturbation Bounds for the Solution of Problem LS Chapter 10: Numerical Computations Using Elementary Orthogonal Transformations Chapter 11: Computing the Solution for the Overdetermined or Exactly Determined Full Rank Problem Chapter 12: Computation of the Covariance Matrix of the Solution Parameters Chapter 13: Computing the Solution for the Underdetermined Full Rank Problem Chapter 14: Computing the Solution for Problem LS with Possibly Deficient Pseudorank Chapter 15: Analysis of Computing Errors for Householder Transformations Chapter 16: Analysis of Computing Errors for the Problem LS Chapter 17: Analysis of Computing Errors for the Problem LS Using Mixed Precision Arithmetic Chapter 18: Computation of the Singular Value Decomposition and the Solution of Problem LS Chapter 19: Other Methods for Least Squares Problems Chapter 20: Linear Least Squares with Linear Equality Constraints Using a Basis of the Null Space Chapter 21: Linear Least Squares with Linear Equality Constraints by Direct Elimination Chapter 22: Linear Least Squares with Linear Equality Constraints by Weighting Chapter 23: Linear Least Squares with Linear Inequality Constraints Chapter 24: Modifying a QR Decomposition to Add or Remove Column Vectors Chapter 25: Practical Analysis of Least Squares Problems Chapter 26: Examples of Some Methods of Analyzing a Least Squares Problem Chapter 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.