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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 Sublinear function ： ウィキペディア英語版 Sublinear function A sublinear function (or functional, as is more often used in functional analysis), in linear algebra and related areas of mathematics, is a function $f:\; V\; \backslash rightarrow\; \backslash mathbf$ on a vector space ''V'' over F, an ordered field (e.g. the real numbers $\backslash mathbb$), which satisfies :$f(\backslash gamma\; x\; )\; =\; \backslash gamma\; f\backslash left(\; x\backslash right)$  for any positive $\backslash gamma\backslash in$ \mathbf and any ''x'' ∈ ''V'' (''positive homogeneity''), :$f(x\; +\; y)\; \backslash le\; f(x)\; +\; f(y)$  for any ''x'', ''y'' ∈ ''V'' (subadditivity). In functional analysis the name Banach functional is used for sublinear function, especially when formulating Hahn–Banach theorem. In computer science, a function $f:\; \backslash mathbb\; \backslash rightarrow\; \backslash mathbb$ is called sublinear if $f(n)\; \backslash in\; o(n)$ in asymptotic notation (Notice the small $\backslash ,o$). Formally, $f(n)\; \backslash in\; o(n)$ if and only if, for any given $\backslash ,c\; >\; 0$, there exists an $\backslash ,n\_0$ such that : This means that for any linear function $g$, for sufficiently large input $f$ grows slower than $g$. == Examples == * Every (semi-)norm is a sublinear function. The opposite is not true, because (semi-)norms can have their domain vector space over any field (not necessarily ordered) and must have $\backslash mathbb$ as their codomain. 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「Sublinear 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.