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2014 | nr 12 (18) | 9--37
Tytuł artykułu

C.F. Gauss and the Method of Least Squares

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Gauss i metoda najmniejszych kwadratów
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EN
Abstrakty
Metodę najmniejszych kwadratów wprowadził Gauss, Helmert w pełni zakończył jej rozwój, Bessel zaś dokonał ważnych odkryć w astronomii i geodezji, był w tym jednak wyjątkowo niedbały. Gaussowski warunek o najmniejszej wariancji doprowadził do efektywnych estymatorów poszukiwanych nieznanych wielkości. W przypadku gdy błędy obserwacji mają rozkład normalny, estymatory są łącznie efektywne. Pamiętniki Gaussa z 1823 r. prościej prowadzą do zasady najmniejszych kwadratów, niż się powszechnie sądziło.(abstrakt oryginalny)
EN
Gauss introduced the MLSq and Helmert completed its development whereas Bessel made important discoveries in astronomy and geodesy but was often extremely inattentive. Gauss' final condition of least variance led to effective estimators of the unknowns sought, jointly effective in case of the normal distribution of the observational errors. Gauss' memoire of 1823 leads to the principle of least squares much easier than generally thought.(original abstract)
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Bibliografia
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