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...

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...

norm-preserving version with the dominated extension version that uses sublinear functions. Whereas Helly's proof used mathematical induction, Hahn and Banach...

being nonnegative stands in contrast to other classes of functions, such as sublinear functions and real linear functionals, that do allow negative values...

descriptions of redirect targets Seminorm – Mathematical function Sublinear function – Type of function in linear algebra Knapp, A.W. (2005). Basic Real Analysis...

type of sublinear time algorithm is closely related to property testing and statistics. Other settings where algorithms can run in sublinear time include:...

in the definition of a sublinear function. Minkowski functionals are exactly those non-negative extended real-valued functions with this property. Real...

Hahn–Banach 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...

{\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}...

measure Subadditivity – Property of some mathematical functions Sublinear function – Type of function in linear algebra M. Marcus, H. Minc (1992). A survey...

continuous, or sublinear (in the sense of growth). Actually, the existence of such special moduli of continuity for a uniformly continuous function is always...

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...

1991, 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...

p:X\to \mathbb {R} } is a seminorm if and only if it is a balanced sublinear function. Absolutely convex set – Convex and balanced set Absorbing set – Set...

everywhere for functions in L 1 {\displaystyle L^{1}} . This theorem of G. H. Hardy and J. E. Littlewood states that M is bounded as a sublinear operator from...

setsPages displaying short descriptions of redirect targets Sublinear function – Type of function in linear algebra Solovay, Robert M. (1970), "A model of...

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...

superlinearly (i.e., faster than linearly). A sequence is said to converge sublinearly (i.e., slower than linearly) if it converges and lim k → ∞ | x k + 1...

linear or sublinear function with respect to frequency variables. A simple example for such phase derivative profiles is the inverse tangent function. Consider...

descriptions of redirect targets Seminorm – Mathematical function Sublinear function – Type of function in linear algebra Uniform space – Topological space...

{\displaystyle g_{n}<p_{n}\epsilon } . Hoheisel (1930) was the first to show a sublinear dependence; that there exists a constant θ < 1 such that π ( x + x θ )...

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...

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...

nearly 50 terms for five decimals and nearly 120 for six. Both converge sublinearly to π. On the other hand: π = 4 1 + 1 2 3 + 2 2 5 + 3 2 7 + ⋱ = 4 − 1...

important operators, such as the Hardy-Littlewood maximal operator, are only sublinear. This is not a hindrance to applying real interpolation methods, but complex...

Sublinear Wang transform of the cumulative distribution function A Wang transform of the cumulative distribution function is an increasing function g...

is correct. Leibniz's formula converges extremely slowly: it exhibits sublinear convergence. Calculating π to 10 correct decimal places using direct summation...

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...

2022). Bannai, Hideo; Holub, Jan (eds.). Longest Palindromic Substring in Sublinear Time. Combinatorial Pattern Matching. Leibniz International Proceedings...

∞. Another famous example is the Hardy–Littlewood maximal function, which is only sublinear operator rather than linear. While L p {\displaystyle L^{p}}...