In linear algebra, a sublinear function (or functional as is more often used in functional analysis), also called a quasi-seminorm or a Banach functional...
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Hahn–Banach theorem (section For nonlinear functions)
norm-preserving version with the dominated extension version that uses sublinear functions. Whereas Helly's proof used mathematical induction, Hahn and Banach...
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seminorm is a type of function called a sublinear function. A map p : X → R {\displaystyle p:X\to \mathbb {R} } is called a sublinear function if it is subadditive...
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Minkowski functional (redirect from Minkowski's function)
being nonnegative stands in contrast to other classes of functions, such as sublinear functions and real linear functionals, that do allow negative values...
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in the definition of a sublinear function. Minkowski functionals are exactly those non-negative extended real-valued functions with this property. Real...
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every seminorm is a sublinear function and thus satisfies all properties of the latter. In particular, every norm is a convex function. The concept of unit...
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Superadditivity (redirect from Superadditive function)
measure Subadditivity – Property of some mathematical functions Sublinear function – Type of function in linear algebra M. Marcus, H. Minc (1992). A survey...
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Banach space (redirect from Banach function space)
{\displaystyle f:X\to \mathbb {R} } is a subadditive function (such as a norm, a sublinear function, or real linear functional), then f {\displaystyle f}...
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theorem: — If p : V → R {\displaystyle p:V\to \mathbb {R} } is a sublinear function, and φ : U → R {\displaystyle \varphi :U\to \mathbb {R} } is a linear...
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Th. 3.2) — If p : X → R {\displaystyle p:X\to \mathbb {R} } is a sublinear function, and f : M → R {\displaystyle f:M\to \mathbb {R} } is a linear functional...
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Balanced set (redirect from Balanced function)
p:X\to \mathbb {R} } is a seminorm if and only if it is a balanced sublinear function. Absolutely convex set – convex and balanced setPages displaying wikidata...
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in planar graphs) may be solved in time that is exponential in a sublinear function of the input size parameter n, significantly faster than a brute-force...
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Time complexity (redirect from Sublinear time)
type of sublinear time algorithm is closely related to property testing and statistics. Other settings where algorithms can run in sublinear time include:...
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continuous, or sublinear (in the sense of growth). Actually, the existence of such special moduli of continuity for a uniformly continuous function is always...
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Riesz extension theorem. Let V be a linear space, and let N be a sublinear function on V. Let φ be a functional on a subspace U ⊂ V that is dominated...
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Rate of convergence (redirect from Sublinear convergence)
\right\}} converges sublinearly and logarithmically. A similar situation exists for discretization methods designed to approximate a function y = f ( x ) {\displaystyle...
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homogenousPages displaying wikidata descriptions as a fallback Sublinear function – Type of function in linear algebra Uniform space – Topological space with...
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Sublinear Wang transform of the cumulative distribution function A Wang transform of the cumulative distribution function is an increasing function g...
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Discontinuous linear map (redirect from Discontinuous linear function)
setsPages displaying short descriptions of redirect targets Sublinear function – Type of function in linear algebra Solovay, Robert M. (1970), "A model of...
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linear or sublinear function with respect to frequency variables. A simple example for such phase derivative profiles is the inverse tangent function. Consider...
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states that M is bounded as a sublinear operator from Lp(Rd) to itself for p > 1. That is, if f ∈ Lp(Rd) then the maximal function Mf is weak L1-bounded and...
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Selection algorithm (section Sublinear data structures)
it may be possible to perform selection in an amount of time that is sublinear in the number of values. As a simple case of this, for data already sorted...
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is correct. Leibniz's formula converges extremely slowly: it exhibits sublinear convergence. Calculating π to 10 correct decimal places using direct summation...
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∞. Another famous example is the Hardy–Littlewood maximal function, which is only sublinear operator rather than linear. While L p {\displaystyle L^{p}}...
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2022). Bannai, Hideo; Holub, Jan (eds.). Longest Palindromic Substring in Sublinear Time. Combinatorial Pattern Matching. Leibniz International Proceedings...
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sublinear in space (e.g., counting the distinct elements of a stream), different randomizations of the algorithm (say, with different hash functions)...
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implementation on SourceForge. One-way functions are necessary, but not known to be sufficient, for nontrivial (i.e., with sublinear communication) single database...
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actually a majority. This second pass is needed, as it is not possible for a sublinear-space algorithm to determine whether there exists a majority element in...
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differently and therefore sized differently: a count–min sketch typically has a sublinear number of cells, related to the desired approximation quality of the sketch...
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Fourier. 62 (5): 1601–1626. doi:10.5802/aif.2731. Nikolski, N. (2014). "Sublinear dimension growth in the Kreiss Matrix Theorem". St. Petersburg Math. J...
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