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)
 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 Englishspeaking 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
 Language

 eng
 lat
 eng
 Extent
 1 electronic text (xi, 241 p.)
 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
 Isbn
 9781611971248
 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
 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 Englishspeaking 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
 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
 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
 Bibliography note
 Includes bibliographical references (p. 237241)
 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=ebscotest&password=ebscotest
 Dimensions
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 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
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