翻訳と辞書 Words near each other ・ Polyorchis ・ Polyortha ・ Polyortha atroperla ・ Polyortha biezankoi ・ Polyortha bryographa ・ Polyortha bryometalla ・ Polyortha chiriquitana ・ Polyortha chlamydata ・ Polyortha clarkeana ・ Polyortha euchlorana ・ Polyortha evestigana ・ Polyortha glaucotes ・ Polynomial and rational function modeling ・ Polynomial arithmetic ・ Polynomial basis ・ Polynomial chaos ・ Polynomial code ・ Polynomial conjoint measurement ・ Polynomial decomposition ・ Polynomial delay ・ Polynomial Diophantine equation ・ Polynomial expansion ・ Polynomial function theorems for zeros ・ Polynomial greatest common divisor ・ Polynomial hierarchy ・ Polynomial identity ring ・ Polynomial interpolation ・ Polynomial kernel ・ Polynomial least squares ・ Polynomial lemniscate 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 Polynomial chaos ： ウィキペディア英語版 Polynomial chaos Polynomial chaos (PC), also called Wiener chaos expansion, is a non-sampling-based method to determine evolution of uncertainty in dynamical system, when there is probabilistic uncertainty in the system parameters. PC was first introduced by Norbert Wiener where Hermite polynomials were used to model stochastic processes with Gaussian random variables. It can be thought of as an extension of Volterra's theory of nonlinear functionals for stochastic systems. According to Cameron and Martin such an expansion converges in the $L\_2$ sense for any arbitrary stochastic process with finite second moment. This applies to most physical systems. == Generalized polynomial chaos == Xiu (in his PhD under Karniadakis at Brown University) generalized the result of Cameron–Martin to various continuous and discrete distributions using orthogonal polynomials from the so-called Askey-scheme and demonstrated $L\_2$ convergence in the corresponding Hilbert functional space. This is popularly known as the generalized polynomial chaos (gPC) framework. The gPC framework has been applied to applications including stochastic fluid dynamics, stochastic finite elements, solid mechanics, nonlinear estimation, the evaluation of finite word-length effects in non-linear fixed-point digital systems and probabilistic robust control. It has been demonstrated that gPC based methods are computationally superior to Monte-Carlo based methods in a number of applications . However, the method has a notable limitation. For large numbers of random variables, polynomial chaos becomes very computationally expensive and Monte-Carlo methods are typically more feasible . 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「Polynomial chaos」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.