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Solving Least Squares Problems

Solving Least Squares Problems

Part of Classics in Applied Mathematics

  • Date Published: January 1987
  • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • format: Paperback
  • isbn: 9780898713565

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  • An accessible text for the study of numerical methods for solving least squares problems remains an essential part of a scientific software foundation. This book has served this purpose well. Numerical analysts, statisticians, and engineers have developed techniques and nomenclature for the least squares problems of their own discipline. This well-organized presentation of the basic material needed for the solution of least squares problems can unify this divergence of methods. Mathematicians, practising engineers, and scientists will welcome its return to print. The material covered includes Householder and Givens orthogonal transformations, the QR and SVD decompositions, equality constraints, solutions in nonnegative variables, banded problems, and updating methods for sequential estimation. Both the theory and practical algorithms are included. The easily understood explanations and the appendix providing a review of basic linear algebra make the book accessible for the non-specialist.

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    Product details

    • Date Published: January 1987
    • format: Paperback
    • isbn: 9780898713565
    • length: 350 pages
    • dimensions: 227 x 152 x 15 mm
    • weight: 0.469kg
    • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • Table of Contents

    Preface to the Classics Edition
    Preface
    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
    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.

  • Authors

    Charles L. Lawson, California Institute of Technology

    Richard J. Hanson, Rice University, Houston

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