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    1. Naturvetenskap och teknik
    2. Matematik och naturvetenskap
    3. Matematik
    4. Matematisk statistik

    Theory of the Combination of Observations Least Subject to Errors

    Part One, Part Two, Supplement

    AvCarl Friedrich Gauss

    Häftad, Engelska, 1995

    Del i serien Classics in Applied Mathematics

    787 kr

    Beställningsvara. Skickas inom 5-8 vardagar. Fri frakt över 249 kr.

    Beskrivning

    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.

    Produktinformation

    • Utgivningsdatum:1995-04-30
    • Mått:151 x 228 x 13 mm
    • Vikt:502 g
    • Format:Häftad
    • Språk:Engelska
    • Serie:Classics in Applied Mathematics
    • Antal sidor:252
    • Förlag:Society for Industrial & Applied Mathematics,U.S.
    • ISBN:9780898713473
    • Översättare:G.W. Stewart, G. W. Stewart, G W Stewart

    Utforska kategorier

    • Matematisk statistik inom Naturvetenskap och teknik
    • Tillämpad matematik inom Naturvetenskap och teknik

    Innehållsförteckning

    • Translator's IntroductionPars Prior/Part One: Random and regular errors in observationsRegular errors excludedtheir treatmentGeneral properties of random errorsThe distribution of the errorThe constant part or mean value of the errorThe mean square error as a measure of uncertaintyMean error, weight and precisionEffect of removing the constant partInterpercentile ranges and probable errorproperties of the uniform, triangular, and normal distributionInequalities relating the mean error and interpercentile rangesThe fourth moments of the uniform, triangular, and normal distributionsThe distribution of a function of several errorsThe mean value of a function of several errorsSome special casesConvergence of the estimate of the mean errorthe mean error of the estimate itselfthe mean error of the estimate for the mean valueCombining errors with different weightsOverdetermined systems of equationsthe problem of obtaining the unknowns as combinations of observationsthe principle of least squaresThe mean error of a function of quantities with errorsThe regression modelThe best combination for estimating the first unknownThe weight of the estimateestimates of the remaining unknowns and their weightsjustification of the principle of least squaresThe case of a single unknownthe arithmetic mean. Pars Posterior/Part Two: Existence of the least squares estimatesRelation between combinations for different unknownsA formula for the residual sum of squaresAnother formula for the residual sum of squaresFour formulas for the residual sum of squares as a function of the unknownsErrors in the least squares estimates as functions of the errors in the observationsmean errors and correlationsLinear functions of the unknownsLeast squares with a linear cons traintReview of Gaussian eliminationAbbreviated computation of the weights of the unknownsComputational detailsA bbreviated computation of the weight of a linear function of the unknownsUpdating the unknowns and their weights when a new observation is added to the systemUpdating the unknowns and their weights when the weight of an observation change sA bad formula for estimating the errors in the observations from the residual sum of squaresThe correct formulaThe mean error of the residual sum of squaresInequalities for the mean error of the residual sum of squaresthe case of the normal distribution. Supplementum/Supplement: Problems having constraints on the observationsreduction to an ordinary least squares problemFunctions of the observationstheir mean errorsEstimating a function of observations that are subject to constraintsCharacterization of permissible estimatesThe function that gives the most reliable estimateThe value of the most reliable estimateFour formulas for the weight of the value of the estimateThe case of more than one functionThe most reliable adjustments of the observations and their use in estimationLeast squares characterization of the most reliable adjustmentDifficulties in determining weightsA better methodComputational detailsExistence of the estimatesEstimating the mean error in the observationsEstimating the mean error in the observations, continuedThe mean error in the estimateIncomplete adjustment of observationsRelation between complete and incomplete adjustmentsA block iterative method for adjusting observationsThe inverse of a symetric system is a symmetricFundamentals of geodesyDe Krayenhof's triangulationA triangulation from HannoverDetermining weights in the Hannover triangulation. Anzeigen/Notices. Part One. Part Two. Supplement. After word. Gauss's SchooldaysLegendre and the Priority ControversyBeginnings: Mayer, Boscovich and LaplaceGauss and LaplaceThe Theoria MotusLaplace and the Central Limit TheoremThe Theoria Combinationis ObservationumThe Precision of Observations