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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 → F {displaystyle f:V o mathbb {F} } on a vector space V over F {displaystyle mathbb {F} } an ordered field (e.g. the real numbers R {displaystyle mathbb {R} } ), which satisfies 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 → F {displaystyle f:V o mathbb {F} } on a vector space V over F {displaystyle mathbb {F} } an ordered field (e.g. the real numbers R {displaystyle mathbb {R} } ), which satisfies In functional analysis the name Banach functional is used for sublinear function, especially when formulating Hahn–Banach theorem. In computer science, a function f : Z + → R {displaystyle f:mathbb {Z} ^{+} o mathbb {R} } is called sublinear if f ( n ) ∈ o ( n ) {displaystyle f(n)in o(n)} in asymptotic notation (notice the small o {displaystyle o} ). Formally, f ( n ) ∈ o ( n ) {displaystyle f(n)in o(n)} if and only if, for any given c > 0 {displaystyle c>0} , there exists an n 0 {displaystyle n_{0}} such that This means that for any linear function g , {displaystyle g,} for sufficiently large input f {displaystyle f} grows slower than g . {displaystyle g.}

[ "Discrete mathematics", "Mathematical optimization", "Mathematical analysis", "Algebra", "Combinatorics", "sublinear algorithms", "sublinear time" ]
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