Abstract
In the previous chapter we talked, in general, about the method of least squares and, in particular, the mathematical justification for selecting it over other criteria. In this chapter we consider practical methods for analyzing a least squares problem. Equations (4.4)–(4.8) present a brief derivation, by calculus, of the normal equations, still the most popular—but by no means only—way of solving least squares problems; in Section 5.4 we shall see that orthogonal transformations allow us to obtain a least squares solution without forming normal equations, a procedure that offers certain advantages but also suffers from some drawbacks, something that proponents of orthogonal transformations frequently overlook.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Branham, R.L., Jr. (1986). Is Robust Estimation Useful for Astronomical Data Reduction?, Quarterly J. Royal Astron. Soc., 27, p. 182.
Coleman, D., Holland, P., Kaden, N., Klema, V., and Peters, S.C. (1980). A System of Subroutines for Iteratively Reweighted Least Squares Computations, ACM Trans Math. Software, 6, p. 327.
Faddeeva, V.N. (1959). Computational Methods of Linear Algebra ( Dover, New York).
Forsythe, G., Malcolm, MA, and Moler, CB (1977). Computer Methods for Mathematical Computations (Prentice-Hall, Englewood Cliffs, N.J.).
Forsythe, G. and Moler, C.B. (1967). Computer Solution of Linear Algebraic Systems (Prentice-Hall, Englewood Cliffs, N.J.).
Givens, W. (1954). Numerical Computation of the Characteristic Values of a Real Symmetric Matrix, Oak Ridge Nat. Lab. Report ORNL—1574 ( Oak Ridge, Tenn.).
Golub, G.H. and Wilkinson, J.H. (1966). Note on the Iterative Refinement of Least Squares Solution, Numer. Math., 9, p. 139.
Hanson, R.J. (1973). Is the Fast Givens Transformation Really Fast?, ACM SIGNUM Newsletter, 8, p. 7.
Householder, A.S. (1958). Unitary Triangularization of a Nonsymmetric Matrix, J. ACM. 5, p. 339.
Jennings, L.S. and Osborne, M.R. (1974). A Direct Error Analysis for Least Squares, Numer. Math., 22, p. 325.
Lawson, C.L. and Hanson, R.J. (1974). Solving Least Squares Problems (Prentice-Hall, Englewood Cliffs, N.J.).
Wilkinson, J.H. (1965). The Algebraic Eigenvalue Problem ( Oxford University Press, Oxford).
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1990 Springer-Verlag New York Inc.
About this chapter
Cite this chapter
Branham, R.L. (1990). Linear Least Squares. In: Scientific Data Analysis. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3362-6_5
Download citation
DOI: https://doi.org/10.1007/978-1-4612-3362-6_5
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-7981-5
Online ISBN: 978-1-4612-3362-6
eBook Packages: Springer Book Archive