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, on a vector space is a real-valued function with only some of the properties of a seminorm. Unlike seminorms, a sublinear function does not have to be nonnegative-valued and also does not have to be absolutely homogeneous. Seminorms are themselves abstractions of the more well known notion of norms, where a seminorm has all the defining properties of a norm except that it is not required to map non-zero vectors to non-zero values.
In functional analysis the name Banach functional is sometimes used, reflecting that they are most commonly used when applying a general formulation of the Hahn–Banach theorem.
The notion of a sublinear function was introduced by Stefan Banach when he proved his version of the Hahn-Banach theorem.[1]
There is also a different notion in computer science, described below, that also goes by the name "sublinear function."
^Narici & Beckenstein 2011, pp. 177–220.
and 23 Related for: Sublinear function information
In linear algebra, a sublinearfunction (or functional as is more often used in functional analysis), also called a quasi-seminorm or a Banach functional...
being nonnegative stands in contrast to other classes of functions, such as sublinearfunctions and real linear functionals, that do allow negative values...
seminorm is a type of function called a sublinearfunction. A map p : X → R {\displaystyle p:X\to \mathbb {R} } is called a sublinearfunction if it is subadditive...
in the definition of a sublinearfunction. Minkowski functionals are exactly those non-negative extended real-valued functions with this property. Real...
{\displaystyle f:X\to \mathbb {R} } is a subadditive function (such as a norm, a sublinearfunction, or real linear functional), then f {\displaystyle f}...
theorem: — If p : V → R {\displaystyle p:V\to \mathbb {R} } is a sublinearfunction, and φ : U → R {\displaystyle \varphi :U\to \mathbb {R} } is a linear...
measure Subadditivity – Property of some mathematical functionsSublinearfunction – Type of function in linear algebra M. Marcus, H. Minc (1992). A survey...
in planar graphs) may be solved in time that is exponential in a sublinearfunction of the input size parameter n, significantly faster than a brute-force...
type of sublinear time algorithm is closely related to property testing and statistics. Other settings where algorithms can run in sublinear time include:...
continuous, or sublinear (in the sense of growth). Actually, the existence of such special moduli of continuity for a uniformly continuous function is always...
Th. 3.2) — If p : X → R {\displaystyle p:X\to \mathbb {R} } is a sublinearfunction, 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 sublinearfunction. Absolutely convex set – convex and balanced setPages displaying wikidata...
\right\}} converges sublinearly and logarithmically. A similar situation exists for discretization methods designed to approximate a function y = f ( x ) {\displaystyle...
Sublinear Wang transform of the cumulative distribution function A Wang transform of the cumulative distribution function is an increasing function g...
homogenousPages displaying wikidata descriptions as a fallback Sublinearfunction – Type of function in linear algebra Uniform space – Topological space with...
setsPages displaying short descriptions of redirect targets Sublinearfunction – Type of function in linear algebra Solovay, Robert M. (1970), "A model of...
linear or sublinearfunction with respect to frequency variables. A simple example for such phase derivative profiles is the inverse tangent function. Consider...
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)...
implementation on SourceForge. One-way functions are necessary, but not known to be sufficient, for nontrivial (i.e., with sublinear communication) single database...
security. Rubinfeld has also made important contributions to the study of sublinear algorithms, which are algorithms that do not need to process the entire...
Global Information