翻訳と辞書 Words near each other ・ Laplace Island (Antarctica) ・ Laplace Island (Western Australia) ・ Laplace limit ・ Laplace no Ma ・ Laplace number ・ Laplace operator ・ Laplace operators in differential geometry ・ Laplace plane ・ Laplace pressure ・ Laplace principle (large deviations theory) ・ Laplace transform ・ Laplace transform applied to differential equations ・ Laplace's demon ・ Laplace's equation ・ Laplace's law ・ Laplace's method ・ LaPlace, Louisiana ・ Laplace-P ・ LaplacesDemon ・ Laplace–Beltrami operator ・ Laplace–Carson transform ・ Laplace–Runge–Lenz vector ・ Laplace–Stieltjes transform ・ Laplacian matrix ・ Laplacian of the indicator ・ Laplacian smoothing ・ Laplae District ・ Laplanche ・ LaPlanche Street ・ Lapland Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Laplace's method ： ウィキペディア英語版 Laplace's method See also: Additive smoothing (Laplace smoothing) a method of smoothing of a statistical estimator In mathematics, Laplace's method, named after Pierre-Simon Laplace, is a technique used to approximate integrals of the form :$\backslash int\_a^b\backslash !\; e^\; \backslash ,\; dx$ where ''ƒ''(''x'') is some twice-differentiable function, ''M'' is a large number, and the integral endpoints ''a'' and ''b'' could possibly be infinite. This technique was originally presented in Laplace (1774, pp. 366–367). ==The idea of Laplace's method== Assume that the function ''ƒ''(''x'') has a unique global maximum at ''x''0. Then, the value ''ƒ''(''x''0) will be larger than other values ''ƒ''(''x''). If we multiply this function by a large number ''M'', the ratio between ''Mƒ''(''x''0) and ''Mƒ''(''x'') will stay the same (since ''Mƒ''(''x''0)/''Mƒ''(''x'') = ''ƒ''(''x''0)/''ƒ''(''x'')), but it will grow exponentially in the function (see figure) :$e^.\; \backslash ,$ Thus, significant contributions to the integral of this function will come only from points ''x'' in a neighborhood of ''x''0, which can then be estimated. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Laplace's method」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.