Search results
Results from the WOW.Com Content Network
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
The map PL to PDiff, while not an equality – not every piecewise smooth function is piecewise linear – is an equivalence: one can go backwards by linearize pieces. Thus it can for some purposes be inverted, or considered an isomorphism, which gives a map Diff → PDiff → PL . {\displaystyle {\text{Diff}}\to {\text{PDiff}}\to {\text{PL}}.}
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 ...
Simple functions that lie directly underneath a given function f can be constructed by partitioning the range of f into a finite number of layers. The intersection of the graph of f with a layer identifies a set of intervals in the domain of f , which, taken together, is defined to be the preimage of the lower bound of that layer, under the ...