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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 Sparse grid ： ウィキペディア英語版 Sparse grid Sparse grids are numerical techniques to represent, integrate or interpolate high dimensional functions. They were originally developed by the Russian mathematician Sergey A. Smolyak, a student of Lazar Lyusternik, and are based on a sparse tensor product construction. Computer algorithms for efficient implementations of such grids were later developed by Michael Griebel and Christoph Zenger. == Curse of dimensionality == The standard way of representing multidimensional functions are tensor or full grids. The number of basis functions or nodes (grid points) that have to be stored and processed depend exponentially on the number of dimensions. Even with today's computational power it is not possible to process functions with more than 4 or 5 dimensions. The curse of dimension is expressed in the order of the integration error that is made by a quadrature of level $l$, with $N\_$ points. The function has regularity $r$, i.e. is $r$ times differentiable. The number of dimensions is $d$. $|E\_l|\; =\; O(N\_l^\})$ 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「Sparse grid」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.