|
A sublinear function (or functional, as is more often used in functional analysis), in linear algebra and related areas of mathematics, is a function on a vector space ''V'' over F, an ordered field (e.g. the real numbers ), which satisfies : for any positive and any ''x'' ∈ ''V'' (''positive homogeneity''), : 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 is called sublinear if in asymptotic notation (Notice the small ). Formally, if and only if, for any given , there exists an such that : This means that for any linear function , for sufficiently large input grows slower than . == 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 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
|