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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 covering number ： ウィキペディア英語版 covering number In mathematics, the idea of a ''covering number'' is to count how many small spherical balls would be needed to completely cover (with overlap) a given space. There are two closely related concepts as well, the ''packing number'', which counts how many disjoint balls fit in a space, and the ''metric entropy'', which counts how many points fit in a space when constrained to lie at some fixed minimum distance apart. == Mathematical Definition == More precisely, consider a subset $K$ of a metric space $(X,d)$ and a parameter $\backslash varepsilon\; >\; 0$. Denote the ball of radius $\backslash varepsilon$ centered at the point $x\backslash in\; X$ by $B\_\backslash varepsilon(x)$. There are two notions of covering number, internal and external, along with the packing number and the metric entropy. * The packing number $N^\}\_\backslash varepsilon(K)$ is the fewest number of points $x\_i\; \backslash in\; K$ such that the balls $B\_\backslash varepsilon(x\_i)$ cover $K$. * The external covering number $N^\}\_\backslash varepsilon(K)$ is the largest number of points $x\_i\backslash in\; K$ such that the points are $\backslash varepsilon$-separated, i.e. $d(x\_i,x\_j)\backslash ge\; \backslash varepsilon$ for all $i\; \backslash neq\; j$. 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「covering number」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.