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In mathematics, Laplace's method, named after Pierre-Simon Laplace, is a technique used to approximate integrals of the form where is a twice-differentiable function, M is a large number, and the endpoints a and b could possibly be infinite. This technique was originally presented in .

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rdfs:label	Laplaceova metoda (cs) Methode von Laplace (de) Metodo di Laplace (it) Méthode de Laplace (fr) Laplace's method (en) 라플라스 방법 (ko) ラプラスの方法 (ja) Método de Laplace (pt) Метод Лапласа (ru) 拉普拉斯方法 (zh)
rdfs:comment	Laplaceova metoda je technika pro asymptotické aproximace Laplaceových integrálů, tedy přibližný výpočet integrálů ve tvaru Meze a mohou nabývat hodnot . Čím větší je tím je aproximace přesnější. Speciálním případem těchto integrálů je Laplaceova transformace. Metoda je pojmenována podle francouzského matematika Pierra-Simona Laplaceho, který ji publikoval v roce 1774. Zobecněním metody na komplexní čísla je . (cs) Die Methode von Laplace ist eine Technik, um Laplace-Integrale asymptotisch zu approximieren, das heißt Integrale der Form näherungsweise zu lösen. Dabei können und auch als gewählt werden. Je größer ist, desto besser funktioniert die Approximation. Ein Spezialfall dieser Integrale ist die Laplace-Transformation. Die Methode ist nach dem französischen Mathematiker Pierre-Simon Laplace benannt, der sie im Jahre 1774 publizierte. Eine Verallgemeinerung der Methode auf den komplexen Raum ist die (englisch Method of steepest descent). (de) En mathématiques, la méthode de Laplace, due à Pierre-Simon de Laplace, est une méthode pour l'évaluation numérique d'intégrales de la forme : où est une fonction deux fois dérivable, M est un grand nombre réel et les bornes a et b peuvent éventuellement être infinies. (fr) 数学においてラプラスの方法（らぷらすのほうほう、英: Laplace's method）とは、ピエール＝シモン・ラプラスにちなんだ積分の近似に用いられる方法。ここで f(x) は二回連続微分可能な関数、n は大きな数で、端点 a, b は有限でなくともよい。この方法はで初めて用いられた。 (ja) Nell'analisi matematica, il metodo di Laplace, il cui nome deriva da Pierre-Simon Laplace, è una tecnica usata per approssimare integrali nella forma dove è una qualunque funzione derivabile due volte, è un numero grande e gli estremi d'integrazione e possono essere anche infiniti. Questa tecnica fu per la prima volta presentata nell'articolo "Mémoir sur la probabilité des causes par évènemens" di Laplace del 1774. (it) 수학에서 라플라스 방법(영어: Laplace’s method)은 실변수 함수의 적분을 그 극대점 근처에서 근사하는 방법이다. (ko) Em matemática, o método de Laplace é uma técnica originalmente desenvolvida por Pierre-Simon Laplace (1774, p. 366-367) para aproximar integrais da forma onde é uma função duplamente diferenciável, M é um grande número, e os pontos finais da integral a e b podem estar no infinito. (pt) Метод Лапласа — метод, использующийся для приближённого вычисления интеграла вида где — некоторая дважды дифференцируемая функция, а — некоторое большое число. (ru) 在数学上，以皮埃尔-西蒙·拉普拉斯命名的拉普拉斯方法是用于得出下列积分形式的近似解的方法：其中的 ƒ(x) 是一個二次可微函数， M 是一個很大的數，而積分邊界點 a 與 b 則允許為無限大。此外，函數 ƒ(x) 在此積分範圍內的全域極大值所在處必須是唯一的並且不在邊界點上。則它的近似解可以寫為: 其中的 x0 為極大值所在處。這方法最早是拉普拉斯在 (1774, pp. 366–367) 所發表。(待考查) (zh) In mathematics, Laplace's method, named after Pierre-Simon Laplace, is a technique used to approximate integrals of the form where is a twice-differentiable function, M is a large number, and the endpoints a and b could possibly be infinite. This technique was originally presented in . (en)
differentFrom	Laplace's approximation Laplace smoothing
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dcterms:subject	Asymptotic analysis Perturbation theory
Wikipage page ID	642006 (xsd:integer)
Wikipage revision ID	1118128778 (xsd:integer)
Link from a Wikipage to another Wikipage	Bayesian statistics Volume element Derivative Integrated nested Laplace approximations Inverse Laplace transform Complex analysis Mathematics Maxima and minima Median Gaussian integral Neighbourhood (mathematics) Function (mathematics) Gamma function Gaussian function Stirling's approximation Combinatorics Partition function (quantum field theory) Stationary point Stationary phase approximation Tangent Asymptotic analysis Cauchy's integral formula Laplace's approximation Laplace principle (large deviations theory) Large deviations theory Line integral Normal distribution Normalizing constant Diffeomorphism Taylor's Theorem Taylor's theorem Big O notation Hessian matrix Pierre-Simon Laplace Positive-definite matrix Perturbation theory Infinitesimal Integer Integral Method of steepest descent Random matrices Maximum a posteriori estimation Meromorphic Riemann–Hilbert problem Taylor expansion Gaussian Matrix determinant Relative error Absolute error Perron formula Integrable model Complex sphere Morgan Kaufmann
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