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...

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

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...

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

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

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

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

{\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}...

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...

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...

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...

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

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

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...

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...

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...

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

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

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

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

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...

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...

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

sublinear in space (e.g., counting the distinct elements of a stream), different randomizations of the algorithm (say, with different hash functions)...

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...

implementation on SourceForge. One-way functions are necessary, but not known to be sufficient, for nontrivial (i.e., with sublinear communication) single database...

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...

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...

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

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...