عنوان

Solving least squares problems /

0898713560

9780898713565

b749356

Solving least squares problems /

[Book]

Charles L. Lawson, Richard J. Hanson.

Philadelphia :

SIAM,

©1995.

xii, 337 pages :

illustrations ;

23 cm.

Classics in applied mathematics ;

15

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

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

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 -- Appendixes: -- A. Basic linear algebra including projections -- B. Proof of global quadratic convergence of the QR algorithm -- C. Description and use of FORTRAN codes for solving problem LS -- D. Developments from 1974-1995.

0

Least squares-- Data processing.

Álgebra linear numérica.

Análise numérica.

ANALYSIS (MATHEMATICS)

DATA PROCESSING.

Least squares-- Data processing.

Least squares-- Data processing.

LEAST SQUARES.

Methode der kleinsten Quadrate

Mínimos quadrados.

Moindres carrés-- Informatique.

Numerical analysis.

Probabilités.

Lawson, Charles L.

Hanson, Richard J.,1938-

20201204091736.0

[Book]

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