| Document Type
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BL
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| Record Number
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994986
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| Doc. No
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b749356
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| Main Entry
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Lawson, Charles L.
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| Title & Author
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Solving least squares problems /\ Charles L. Lawson, Richard J. Hanson.
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| Publication Statement
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Philadelphia :: SIAM,, ©1995.
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| Series Statement
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Classics in applied mathematics ;; 15
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| Page. NO
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xii, 337 pages :: illustrations ;; 23 cm.
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| ISBN
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0898713560
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: 9780898713565
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| Notes
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"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.
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| Bibliographies/Indexes
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Includes bibliographical references (pages 312-326) and index.
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| Contents
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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.
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| Subject
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Least squares-- Data processing.
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Álgebra linear numérica.
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Análise numérica.
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| Subject
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ANALYSIS (MATHEMATICS)
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DATA PROCESSING.
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Least squares-- Data processing.
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Least squares-- Data processing.
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LEAST SQUARES.
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Methode der kleinsten Quadrate
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Mínimos quadrados.
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Moindres carrés-- Informatique.
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Numerical analysis.
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Probabilités.
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| Dewey Classification
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511/.42
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| LC Classification
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QA275.L38 1995
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| NLM classification
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*65F20msc
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15A09msc
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31.76bcl
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62J05msc
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65-01msc
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65C99msc
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65D10msc
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65K05msc
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90C20msc
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SK 910rvk
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| Added Entry
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Hanson, Richard J.,1938-
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