Linear Least Squares Computations

FAREBROTHER (Autor)

Buch | Hardcover

320 Seiten

1988
Crc Press Inc (Verlag)
978-0-8247-7661-9 (ISBN)

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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.

R.W. Farebrother

PREFACE, 1 THE GAUSS AND GAUSS-JORDAN METHODS: ASPECTS OF COMPUTER PROGRAMMING , 2 MATRIX ANALYSIS OF GAUSS’S METHOD: THE CHOLESKY AND DOOLITTLE DECOMPOSITIONS, 3 THE LINEAR ALGEBRAIC MODEL: THE METHOD OF AVERAGES AND THE METHOD OF LEAST SQUARES, 4 THE CAUCHY-BIENAYME, LAPLACE, AND SCHMIDT PROCEDURES, 5 HOUSEHOLDER’S PROCEDURE. 6 CrVENS’S PROCEDURE, 7 UPDATING THE QU DECOMPOSITION, 8 PSEUDO-RANDOM NUMBERS, 9 THE STANDARD LINEAR MODEL 10 CONDITION NUMBERS, 11 INSTRUMENTAL VARIABLE , 12 GENERALIZED LEAST SQUARES ESTIMATION, 13 ITERATIVE SOLUTIONS OF LINEAR AND NONLINEAR LEAST SQUARES PROBLEMS, 14 CANONICAL EXPRESSIONS FOR THE LEAST SQUARES ESTIMATORS AND TEST STATISTICS, 15 TRADITIONAL EXPRESSIONS FOR THE LEAST SQUARES UPDATING FORMULAS AND TEST STATISTICS, 16 LEAST SQUARES ESTIMATION SUBJECT TO LINEAR EQUALITY CONSTRAINTS SUPPLEMENTARY READING GLOSSARY OF MATRIX ALGEBRA AUTHOR INDEX SUBJECT INDEX

Erscheint lt. Verlag	19.2.1988
Reihe/Serie	Statistics: A Series of Textbooks and Monographs
Verlagsort	Bosa Roca
Sprache	englisch
Maße	156 x 234 mm
Gewicht	544 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
ISBN-10	0-8247-7661-5 / 0824776615
ISBN-13	978-0-8247-7661-9 / 9780824776619
Zustand	Neuware