Linear Least Squares Computations

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CRC Press, Feb 19, 1988 - Mathematics - 320 pages
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Presenting numerous algorithms in a simple algebraic form so that the reader can easily translate them into any computer language, this volume gives details of several methods for obtaining accurate least squares estimates. It explains how these estimates may be updated as new information becomes available and how to test linear hypotheses. Linear Least Squares Computations features many structured exercises that guide the reader through the available algorithms, plus a glossary of commonly used terms and a bibliography of supplementary reading ... collects "ancient" and modern results on linear least squares computations in a convenient single source ... develops the necessary matrix algebra in the context of multivariate statistics ... only makes peripheral use of concepts such as eigenvalues and partial differentiation ... interprets canonical forms employed in computation ... discusses many variants of the Gauss, Laplace-Schmidt, Givens, and Householder algorithms ... and uses an empirical approach for the appraisal of algorithms. Linear Least Squares Computations serves as an outstanding reference for industrial and applied mathematicians, statisticians, and econometricians, as well as a text for advanced undergraduate and graduate statistics, mathematics, and econometrics courses in computer programming, linear regression analysis, and applied statistics. Book jacket.
 

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Contents

THE GAUSS AND GAUSSJORDAN
1
THE CAUCHYBIENAYME LAPLACE
59
Procedures
69
Contents
81
GIVENSS PROCEDURE
97
UPDATING THE QU DECOMPOSITION
127
PSEUDORANDOM NUMBERS
141
THE STANDARD LINEAR MODEL
153
GENERALIZED LEAST SQUARES
185
Givens Transformations II
201
ITERATIVE SOLUTIONS OF LINEAR
217
CANONICAL EXPRESSIONS FOR THE LEAST
229
TRADITIONAL EXPRESSIONS FOR
245
Contents xiii
257
SUPPLEMENTARY READING
275
AUTHOR INDEX
283

CONDITION NUMBERS
167
Contents xi
173

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About the author (1988)

R. W. Farebrother is Senior Lecturer in Econometrics at the University of Manchester in England, where he has taught since 1971

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