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The Resource 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, by Carl Friedrich Gauss ; translated by G.W. Stewart, (electronic resource)

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, by Carl Friedrich Gauss ; translated by G.W. Stewart, (electronic resource)

Label
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
Title
Theory of the combination of observations least subject to error
Title remainder
part one, part two, supplement = Theoria combinationis observationum erroribus minimus obnoxiae : pars prior, pars posterior, supplementum
Statement of responsibility
by Carl Friedrich Gauss ; translated by G.W. Stewart
Title variation
Theoria combinationis observationum erroribus minimus obnoxiae
Creator
Contributor
Subject
Language
  • eng
  • lat
  • eng
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 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
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Additional physical form
Also available in print version.
Cataloging source
CaBNVSL
Index
no index present
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Series statement
Classics in applied mathematics
Series volume
11
Target audience
adult
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, by Carl Friedrich Gauss ; translated by G.W. Stewart, (electronic resource)
Label
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, by Carl Friedrich Gauss ; translated by G.W. Stewart, (electronic resource)
Link
http://libproxy.rpi.edu/login?url=http://epubs.siam.org/ebooks/siam/classics_in_applied_mathematics/cl11
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Bibliography note
Includes bibliographical references (p. 237-241)
Color
black and white
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
http://library.link/vocab/cover_art
https://contentcafe2.btol.com/ContentCafe/Jacket.aspx?Return=1&Type=S&Value=9781611971248&userID=ebsco-test&password=ebsco-test
Dimensions
unknown
http://library.link/vocab/discovery_link
{'f': 'http://opac.lib.rpi.edu/record=b3128811'}
Extent
1 electronic text (xi, 241 p.)
File format
multiple file formats
Form of item
online
Governing access note
Restricted to subscribers or individual electronic text purchasers
Isbn
9781611971248
Isbn Type
(electronic bk.)
Other physical details
digital file.
Publisher number
CL11
Reformatting quality
access
Specific material designation
remote
System details
  • Mode of access: World Wide Web
  • System requirements: Adobe Acrobat Reader

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