Linear Least Squares Computations

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CRC Press, Feb 19, 1988 - Mathematics - 320 pages
Presenting numerous algorithms in a simple algebraic form so that the reader can easilytranslate them into any computer language, this volume gives details of several methodsfor obtaining accurate least squares estimates. It explains how these estimates may beupdated as new information becomes available and how to test linear hypotheses.Linear Least Squares Computations features many structured exercises that guidethe reader through the available algorithms, plus a glossary of commonly used terms anda bibliography of supplementary reading ... collects "ancient" and modem results onlinear least squares computations in a convenient single source . . . develops the necessarymatrix algebra in the context of multivariate statistics . .. only makes peripheral use ofconcepts such as eigenvalues and partial differentiation .. . interprets canonical formsemployed in computation ... discusses many variants of the Gauss, Laplace-Schmidt, Givens, and Householder algorithms ... and uses an empirical approach for the appraisalof algorithms.Linear Least Squares Computations serves as an outstanding reference forindustrial and applied mathematicians, statisticians, and econometricians, as well as atext for advanced undergraduate and graduate statistics, mathematics, and econometricscourses in computer programming, linear regression analysis, and applied statistics
 

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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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