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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Discretization ： ウィキペディア英語版 Discretization In mathematics, discretization concerns the process of transferring continuous functions, models, and equations into discrete counterparts. This process is usually carried out as a first step toward making them suitable for numerical evaluation and implementation on digital computers. Processing on a digital computer requires another process called quantization. Dichotomization is the special case of discretization in which the number of discrete classes is 2, which can approximate a continuous variable as a binary variable (creating a dichotomy for modeling purposes). * Euler–Maruyama method * Zero-order hold Discretization is also related to discrete mathematics, and is an important component of granular computing. In this context, ''discretization'' may also refer to modification of variable or category ''granularity'', as when multiple discrete variables are aggregated or multiple discrete categories fused. Whenever continuous data is discretized, there is always some amount of discretization error. The goal is to reduce the amount to a level considered negligible for the modeling purposes at hand. == Discretization of linear state space models == Discretization is also concerned with the transformation of continuous differential equations into discrete difference equations, suitable for numerical computing. The following continuous-time state space model :$\backslash dot(t)\; +\; \backslash mathbf\; B\; \backslash mathbf(t)\; +\; \backslash mathbf(t)$ :$\backslash mathbf(t)\; =\; \backslash mathbf\; C\; \backslash mathbf(t)\; +\; \backslash mathbf\; D\; \backslash mathbf(t)\; +\; \backslash mathbf(t)$ where ''v'' and ''w'' are continuous zero-mean white noise sources with covariances :$\backslash mathbf(t)\; \backslash sim\; N(0,\backslash mathbf\; Q)$ :$\backslash mathbf(t)\; \backslash sim\; N(0,\backslash mathbf\; R)$ can be discretized, assuming zero-order hold for the input ''u'' and continuous integration for the noise ''v'', to :$\backslash mathbf()\; =\; \backslash mathbf\; A\_d\; \backslash mathbf()\; +\; \backslash mathbf\; B\_d\; \backslash mathbf()\; +\; \backslash mathbf()$ :$\backslash mathbf()\; =\; \backslash mathbf\; C\_d\; \backslash mathbf()\; +\; \backslash mathbf\; D\_d\; \backslash mathbf()\; +\; \backslash mathbf()$ with covariances :$\backslash mathbf()\; \backslash sim\; N(0,\backslash mathbf\; Q\_d)$ :$\backslash mathbf()\; \backslash sim\; N(0,\backslash mathbf\; R\_d)$ where :$\backslash mathbf\; A\_d\; =\; e^\; =\; \backslash mathcal^\backslash \_$ :$\backslash mathbf\; B\_d\; =\; \backslash left(\; \backslash int\_^e^d\backslash tau\; \backslash right)\; \backslash mathbf\; B\; =\; \backslash mathbf\; A^(\backslash mathbf\; A\_d\; -\; I)\backslash mathbf\; B$, if $\backslash mathbf\; A$ is nonsingular :$\backslash mathbf\; C\_d\; =\; \backslash mathbf\; C$ :$\backslash mathbf\; D\_d\; =\; \backslash mathbf\; D$ :$\backslash mathbf\; Q\_d\; =\; \backslash int\_^\; e^\; \backslash mathbf\; Q\; e^\; d\backslash tau$ :$\backslash mathbf\; R\_d\; =\; \backslash frac\; \backslash mathbf\; R$ and $T$ is the sample time, although $\backslash mathbf\; A^T$ is the transposed matrix of $\backslash mathbf\; A$. A clever trick to compute ''A''''d'' and ''B''''d'' in one step is by utilizing the following property:〔Raymond DeCarlo: ''Linear Systems: A State Variable Approach with Numerical Implementation'', Prentice Hall, NJ, 1989〕 : \mathbf & \mathbf \end T} = \begin \mathbf} \\ \mathbf & \mathbf \end and then having :$\backslash mathbf\; A\_d\; =\; \backslash mathbf\; M\_$ :$\backslash mathbf\; B\_d\; =\; \backslash mathbf\; M\_$ 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「Discretization」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.