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 interested in comparisons the book includes the original text and the English translation on facing pages. More generally the book will be of interest to statisticians, numerical analysts, and other scientists who are interested in what Gauss did and how he set about doing it. An Afterword by the translator, G. W. Stewart, places Gauss's contributions in historical perspective.
Reihe
Sprache
Verlagsort
Zielgruppe
Produkt-Hinweis
Broschur/Paperback
Klebebindung
Maße
Höhe: 228 mm
Breite: 152 mm
Dicke: 14 mm
Gewicht
ISBN-13
978-0-89871-347-3 (9780898713473)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
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 cons traint
Review of Gaussian elimination
Abbreviated computation of the weights of the unknowns
Computational details
A bbreviated 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 change s
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. After word. 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
