This is a classic book on least squares problems. It has been cited extensively. But it is written in 1970s. I think it is not good for self-learning or reference. The notations are very old and the structure should be refined.
Author(s): Charles L. Lawson, Richard J. Hanson
Series: Classics in Applied Mathematics
Publisher: Society for Industrial Mathematics
Year: 1987
Language: English
Pages: 352
Cover......Page 1
Front Matter
......Page 2
About Classics
......Page 3
Title
......Page 6
Table of Contents
......Page 8
Preface to the Classics Edition
......Page 12
Preface
......Page 14
1 Introduction
......Page 16
2 Analysis of the Least Squares Problem
......Page 20
3 Orthogonal Decomposition by Certain Elementary Orthogonal Transformations
......Page 24
4 Orthogonal Decomposition by Singular Value Decomposition
......Page 33
5 Perturbation Theorems for Singular Values
......Page 38
6 Bounds for the Condition Number of a Triangular Matrix
......Page 43
7 The Pseudoinverse
......Page 51
8 Perturbation Bounds for the Pseudoinverse
......Page 56
9 Perturbation Bounds for the Solution of Problem LS
......Page 64
10 Numerical Computations Using Elementary Orthogonal Transformations
......Page 68
11 Computing the Solution for the Overdetermined or Exactly Determined Full Rank Problem
......Page 78
12 Computation of the Covariance Matrix of the Solution Parameters
......Page 82
13 Computing the Solution for the Underdetermined Full Rank Problem
......Page 89
14 Computing the Solution for Problem LS With Possibly Deficient Pseudorank
......Page 92
15 Analysis of Computing Errors for Householder Transformations
......Page 98
16 Analysis of Computing Errors for the Problem LS
......Page 105
17 Analysis of Computing Errors for the Problem LS Using Mixed Precision Arithmetic
......Page 115
18 Computation of the Singular Value Decomposition and the Solution of Problem LS
......Page 122
19 Other Methods for Least Squares Problems
......Page 136
20 Linear Least Squares With Linear Equality Constraints Using A Basis of the Null Space
......Page 149
21 Linear Least Squares With Linear Equality Constraints by Direct Elimination
......Page 159
22 Linear Least Squares With Linear Equality Constraints by Weighing
......Page 163
23 Linear Least Squares With Linear Inequality Constraints
......Page 173
24 Modifying a QR Decomposition to Add or Remove Column Vectors
......Page 189
25 Practical Analysis of Least Squares Problems
......Page 195
26 Examples of Some Methods of Analyzing a Least Squares Problem
......Page 214
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
......Page 222
Appendix A Basic Linear Algebra Including Projections
......Page 248
Appendix B Proof of Global Quadratic Convergence of the QR Algorithm
......Page 255
Appendix C Description and Use of FORTRAN Codes for Solving Problem LS
......Page 263
Appendix D Developments from 1974 to 1995
......Page 299
Bibliography
......Page 327
Index
......Page 342
