Solving least squares problems / Charles L. Lawson, Richard J. Hanson.

Format:

Book

Author/Creator:

Lawson, Charles L.

Contributor:

Hanson, Richard J., 1938-

Society for Industrial and Applied Mathematics.

Series:

Classics in applied mathematics ; 15.

Classics in applied mathematics ; 15

Language:

English

Subjects (All):

Least squares--Data processing.

Least squares.

Physical Description:

1 online resource (xii, 337 p. ) ill. ;

Place of Publication:

Philadelphia, Pa. : Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), 1995.

Language Note:

English

System Details:

Mode of access: World Wide Web.

System requirements: Adobe Acrobat Reader.

Contents:

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.

Notes:

"This SIAM edition is an unabridged, revised republication of the work first published by Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1974"--T.p. verso.

Includes bibliographical references (p. 312-326) and index.

Title from title screen, viewed 04/05/2011.

ISBN:

1-61197-121-7

Publisher Number:

CL15 SIAM