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In applied mathematical analysis, "piecewise-regular" functions have been found to be consistent with many models of the human visual system, where images are perceived at a first stage as consisting of smooth regions separated by edges (as in a cartoon); [9] a cartoon-like function is a C 2 function, smooth except for the existence of ...
A function property holds piecewise for a function, if the function can be piecewise-defined in a way that the property holds for every subdomain. Examples of functions with such piecewise properties are: Piecewise constant function, also known as a step function; Piecewise linear function; Piecewise continuous function
A piecewise linear function is a function defined on a (possibly unbounded) interval of real numbers, such that there is a collection of intervals on each of which the function is an affine function. (Thus "piecewise linear" is actually defined to mean "piecewise affine ".)
Piecewise linear function, a function whose domain can be decomposed into pieces on which the function is linear; Piecewise linear manifold, a topological space formed by gluing together flat spaces; Piecewise linear homeomorphism, a topological equivalence between two piecewise linear manifolds; Piecewise linear cobordism, a cohomology theory
PDIFF serves to relate DIFF and PL, and it is equivalent to PL. PDIFF is mostly a technical point: smooth maps are not piecewise linear (unless linear), and piecewise linear maps are not smooth (unless globally linear) – the intersection is linear maps, or more precisely affine maps (because not based) – so they cannot directly be related: they are separate generalizations of the notion of ...
A valuation V is called piecewise-constant, if the corresponding value-density function v is a piecewise-constant function. In other words: there is a partition of the resource C into finitely many regions, C 1 ,..., C k , such that for each j in 1,..., k , the function v inside C j equals some constant U j .
For an infinite set of functions, the same notions may be defined using the infimum in place of the minimum, and the supremum in place of the maximum. [ 1 ] For continuous functions from a given class, the lower or upper envelope is a piecewise function whose pieces are from the same class.
Segmented regression, also known as piecewise regression or broken-stick regression, is a method in regression analysis in which the independent variable is partitioned into intervals and a separate line segment is fit to each interval. Segmented regression analysis can also be performed on multivariate data by partitioning the various ...