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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 collage theorem ： ウィキペディア英語版 collage theorem In mathematics, the collage theorem characterises an iterated function system whose attractor is close, relative to the Hausdorff metric, to a given set. The IFS described is composed of contractions whose images, as a collage or union when mapping the given set, are arbitrarily close to the given set. It is typically used in fractal compression. == Statement of the theorem == Let $\backslash mathbb$ be a complete metric space. Suppose $L$ is a nonempty, compact subset of $\backslash mathbb$ and let $\backslash epsilon\; \backslash geq\; 0$ be given. Choose an iterated function system (IFS) $\backslash$ with contractivity factor , (The contractivity factor of the IFS is the maximum of the contractivity factors of the maps $w\_i$.) Suppose :$h\backslash left(\; L,\; \backslash bigcup\_^N\; w\_n\; (L)\; \backslash right)\; \backslash leq\; \backslash varepsilon,$ where $h(d)$ is the Hausdorff metric. Then :$h(L,A)\; \backslash leq\; \backslash frac$ where ''A'' is the attractor of the IFS. Equivalently, :$h(L,A)\; \backslash leq\; (1-s)^\; h\backslash left(L,\backslash cup\_^N\; w\_n(L)\backslash right)\; \backslash quad$, for all nonempty, compact subsets L of $\backslash mathbb$. Informally, If $L$ is close to being stabilized by the IFS, then $L$ is also close to being the attractor of the IFS. 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「collage theorem」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.