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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 Radially unbounded function ： ウィキペディア英語版 Radially unbounded function In mathematics, a radially unbounded function is a function $f:\; \backslash mathbb^n\; \backslash rightarrow\; \backslash mathbb$ for which :$\backslash |x\backslash |\; \backslash to\; \backslash infty\; \backslash Rightarrow\; f(x)\; \backslash to\; \backslash infty.\; \backslash ,$ Such functions are applied in control theory and required in optimization for determination of compact spaces. Notice that the norm used in the definition can be any norm defined on $\backslash mathbb^n$, and that the behavior of the function along the axes does not necessarily reveal that it is radially unbounded or not; i.e. to be radially unbounded the condition must be verified along any path that results in: :$\backslash |x\backslash |\; \backslash to\; \backslash infty\; \backslash ,$ For example, the functions :$\backslash \; f\_1(x)=\; (x\_1-x\_2)^2\; \backslash ,$ :$\backslash \; f\_2(x)=\; (x\_1^2+x\_2^2)/(1+x\_1^2+x\_2^2)+(x\_1-x\_2)^2\; \backslash ,$ are not radially unbounded since along the line $x\_1\; =\; x\_2$, the condition is not verified even though the second function is globally positive definite. ==References== 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「Radially unbounded function」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.