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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 HOSVD based canonical form of TP functions and qLPV models ： ウィキペディア英語版 HOSVD-based canonical form of TP functions and qLPV models Based on the key idea of higher-order singular value decomposition (HOSVD) in tensor algebra Baranyi and Yam proposed the concept of HOSVD-based canonical form of TP functions and quasi-LPV system models. Szeidl et al. proved that the TP model transformation is capable of numerically reconstructing this canonical form. Related definitions (on TP functions, finite element TP functions, and TP models) can be found here. Details on the control theoretical background (i.e., the TP type polytopic Linear Parameter-Varying state-space model) can be found here. A free MATLAB implementation of the TP model transformation can be downloaded at () or at MATLAB Central (). ==Existence of the HOSVD based canonical form== Assume a given finite element TP function: ::$f(\backslash mathbf)=\backslash mathcal\backslash boxtimes\_^N\; \backslash mathbf\_n(x\_n),$ where $\backslash mathbf\backslash in\; \backslash Omega\; \backslash subset\; R^N$. Assume that, the weighting functions in $\backslash mathbf\_n(x\_n)$ are othonormal (or we transform to) for all $n=1\backslash ldots\; N$. Then, the execution of the HOSVD on the core tensor $\backslash mathcal$ leads to: ::$\backslash mathcal=\backslash mathcal\backslash boxtimes\_^N\; \backslash mathbf\_n$. Then, ::$f(\backslash mathbf)=\backslash mathcal\backslash boxtimes\_^N\; \backslash mathbf\_n(x\_n)=\backslash left(\backslash mathcal\backslash boxtimes\_^N\; \backslash mathbf\_n\backslash right)\backslash boxtimes\_^N\backslash mathbf\_n(x\_n),$ that is: ::$f(\backslash mathbf)=\backslash mathcal\backslash boxtimes\_^N\; \backslash left(\backslash mathbf\_n(x\_n)\backslash mathbf\_n\backslash right)\; =\; \backslash mathcal\backslash boxtimes\_^N\; \backslash mathbf\_n(x\_n),$ where weighting functions of $\backslash mathbf\_n(x\_n),$ are orthonormed (as both the $\backslash mathbf\_n(x\_n)$ and $\backslash mathbf\_n$ where orthonormed) and core tensor $\backslash mathcal$ contains the higher order singular values. 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「HOSVD-based canonical form of TP functions and qLPV models」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.