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Theory of the combination of observations least subject to error : part one, part two, supplement = Theoria combinationis observationum erroribus minimus obnoxiae : pars prior, pars posterior, supplementum

Author: Carl Friedrich Gauss; G W Stewart; Society for Industrial and Applied Mathematics.
Publisher: Philadelphia, Pa. : Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), 1995.
Series: Classics in applied mathematics, 11.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
Summary:
In the 1820s Gauss published two memoirs on least squares, which contain his final, definitive treatment of the area along with a wealth of material on probability, statistics, numerical analysis, and geodesy. These memoirs, originally published in Latin with German Notices, have been inaccessible to the English-speaking community. Here for the first time they are collected in an English translation. For scholars  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
(DLC) 95006589
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Carl Friedrich Gauss; G W Stewart; Society for Industrial and Applied Mathematics.
ISBN: 9781611971248 1611971241
OCLC Number: 722473332
Notes: Title from title screen, viewed 04/05/2011.
Description: 1 electronic text (xi, 241 pages) : digital file.
Contents: Translator's introduction. Pars prior/Part one. Random and regular errors in observations. Regular errors excluded --
Their treatment --
General properties of random errors --
The distribution of the error --
The constant part or mean value of the error --
The mean square error as a measure of uncertainty --
Mean error, weight and precision --
Effect of removing the constant part --
Interpercentile ranges and probable error --
properties of the uniform, triangular, and normal distribution --
Inequalities relating the mean error and interpercentile ranges --
The fourth moments of the uniform, triangular, and normal distributions --
The distribution of a function of several errors --
The mean value of a function of several errors --
Some special cases --
Convergence of the estimate of the mean error --
The mean error of the estimate itself --
The mean error of the estimate for the mean value --
Combining errors with different weights --
Overdetermined systems of equations --
The problem of obtaining the unknowns as combinations of observations --
The principle of least squares --
The mean error of a function of quantities with errors --
The regression model --
The best combination for estimating the first unknown --
The weight of the estimate --
Estimates of the remaining unknowns and their weights --
Justification of the principle of least squares --
The case of a single unknown --
The arithmetic mean. Pars posterior/Part two. Existence of the least squares estimates. Relation between combinations for different unknowns --
A formula for the residual sum of squares --
Another formula for the residual sum of squares --
Four formulas for the residual sum of squares as a function of the unknowns --
Errors in the least squares estimates as functions of the errors in the observations --
Mean errors and correlations --
Linear functions of the unknowns --
Least squares with a linear constraint --
Review of Gaussian elimination --
Abbreviated computation of the weights of the unknowns --
Computational details --
Abbreviated computation of the weight of a linear function of the unknowns --
Updating the unknowns and their weights when a new observation is added to the system --
Updating the unknowns and their weights when the weight of an observation changes --
A bad formula for estimating the errors in the observations from the residual sum of squares --
The correct formula --
The mean error of the residual sum of squares --
Inequalities for the mean error of the residual sum of squares --
The case of the normal distribution. Supplementum/Supplement. Problems having constraints on the observations: reduction to an ordinary least squares problem. Functions of the observations, their mean errors --
Estimating a function of observations that are subject to constraints --
Characterization of permissible estimates --
The function that gives the most reliable estimate --
The value of the most reliable estimate --
Four formulas for the weight of the value of the estimate --
The case of more than one function --
The most reliable adjustments of the observations and their use in estimation --
Least squares characterization of the most reliable adjustment --
Difficulties in determining weights --
A better method --
Computational details --
Existence of the estimates --
Estimating the mean error in the observations --
Estimating the mean error in the observations, continued --
The mean error in the estimate --
Incomplete adjustment of observations --
Relation between complete and incomplete adjustments --
A block iterative method for adjusting observations --
The inverse of a symetric system is a symmetric --
Fundamentals of geodesy --
De Krayenhof's triangulation --
A triangulation from Hannover --
Determining weights in the Hannover triangulation. --
Anzeigen/Notices: Part one, part two, supplement --
Afterword. Gauss's schooldays --
Legendre and the priority controversy --
Beginnings: Mayer, Boscovich and Laplace --
Gauss and Laplace --
The theoria motus --
Laplace and the central limit theorem --
The Theoria Combinationis Observationum --
The precision of observations --
The combination of observations --
The inversion of linear systems --
Gaussian elimination and numerical linear algebra --
The generalized minimum variance theorem --
References.
Series Title: Classics in applied mathematics, 11.
Other Titles: Theoria combinationis observationum erroribus minimis obnoxiae.
Theoria combinationis observationum erroribus minimus obnoxiae
Responsibility: by Carl Friedrich Gauss ; translated by G.W. Stewart.
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Abstract:

English translation of Gauss' two memoirs which contain his final, definitive treatment of least squares and wealth of additional material.  Read more...

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