In mathematics, a piecewise-defined function (also called a piecewise function, a hybrid function, or definition by cases) is a function whose domain...

piecewise linear or segmented function is a real-valued function of a real variable, whose graph is composed of straight-line segments. A piecewise linear...

indicator functions of intervals. Informally speaking, a step function is a piecewise constant function having only finitely many pieces. A function f : R →...

In mathematics, a spline is a function defined piecewise by polynomials. In interpolating problems, spline interpolation is often preferred to polynomial...

A piecewise-constant valuation is a kind of a function that represents the utility of an agent over a continuous resource, such as land. It occurs when...

In mathematics, a piecewise linear manifold (PL manifold) is a topological manifold together with a piecewise linear structure on it. Such a structure...

Piecewise linear may refer to: Piecewise linear curve, a connected sequence of line segments Piecewise linear function, a function whose domain can be...

In mathematics, piecewise syndeticity is a notion of largeness of subsets of the natural numbers. A set S ⊂ N {\displaystyle S\subset \mathbb {N} } is...

On the other hand, some authors replace "piecewise linear" with "piecewise quadratic" or even "piecewise polynomial". The author might then say "higher...

In probability theory, a piecewise-deterministic Markov process (PDMP) is a process whose behaviour is governed by random jumps at points in time, but...

rising from 0 to 1, but using simpler functions, especially piecewise linear functions or piecewise constant functions. These are preferred where speed of...

Segmented regression, also known as piecewise regression or broken-stick regression, is a method in regression analysis in which the independent variable...

mathematics, triangulation describes the replacement of topological spaces by piecewise linear spaces, i.e. the choice of a homeomorphism in a suitable simplicial...

geometric topology, PDIFF, for piecewise differentiable, is the category of piecewise-smooth manifolds and piecewise-smooth maps between them. It properly...

function is called a spline. For instance, the natural cubic spline is piecewise cubic and twice continuously differentiable. Furthermore, its second derivative...

mean signal is piecewise constant. For this reason, step detection can be profitably viewed as the problem of recovering a piecewise constant signal...

that can be partitioned into exactly two monotone chains. The graphs of piecewise linear functions form monotone chains with respect to a horizontal line...

collapsible. Any n-dimensional PL manifold that is collapsible is in fact piecewise-linearly isomorphic to an n-ball. Discrete Morse theory Shelling (topology) –...

a , b ] → R 2 {\displaystyle \gamma :[a,b]\to \mathbb {R} ^{2}} be a piecewise smooth Jordan plane curve. The Jordan curve theorem implies that γ {\displaystyle...

In mathematics, a piecewise algebraic space is a generalization of a semialgebraic set, introduced by Maxim Kontsevich and Yan Soibelman. The motivation...

Coefficient ring: The definition is similar to cobordism, except that one uses piecewise linear or topological instead of smooth manifolds, either oriented or...

a set of data points (x0, y0), (x1, y1), ..., (xn, yn) is defined as piecewise linear, resulting from the concatenation of linear segment interpolants...

Simplifying a piecewise linear curve with the Douglas–Peucker algorithm....

with specialized computer programs or estimation techniques such as the piecewise-linear model. Circuit simulation software, such as HSPICE (an analog circuit...

Simplicial continuation, or piecewise linear continuation (Allgower and Georg), is a one-parameter continuation method which is well suited to small to...

+\lambda \nabla ^{2})f-\delta f{\bar {f}}dx} . By discretizing this onto piecewise-constant elements with our signal on the vertices we obtain ∑ i M i δ...

In mathematics, some functions or groups of functions are important enough to deserve their own names. This is a listing of articles which explain some...

In the context of artificial neural networks, the rectifier or ReLU (rectified linear unit) activation function is an activation function defined as the...

In statistics and information theory, a maximum entropy probability distribution has entropy that is at least as great as that of all other members of...

Figure 1, and x Z O H ( t ) {\displaystyle x_{\mathrm {ZOH} }(t)} is the piecewise-constant signal depicted in Figure 2. The equation above for the output...