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...

of "piecewise". Terms like piecewise linear, piecewise smooth, piecewise continuous, and others are also very common. The meaning of a function being...

graph of the function must pass through the origin. Homogeneous function Nonlinear system Piecewise linear function Linear approximation Linear interpolation...

intervals. Informally speaking, a step function is a piecewise constant function having only finitely many pieces. A function f : R → R {\displaystyle f\colon...

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

an atlas, such that one can pass from chart to chart in it by piecewise linear functions. This is slightly stronger than the topological notion of a triangulation...

higher-dimensional piecewise linear functions (see second figure below). Many libraries and shading languages have a "lerp" helper-function (in GLSL known...

holomorphic functions linear functions piecewise linear functions continuous functions, compact open topology all functions, space of pointwise convergence...

chooses basis functions. We used piecewise linear basis functions in our discussion, but it is common to use piecewise polynomial basis functions. Separate...

they may also take the form of other nonlinear functions, piecewise linear functions, or step functions. They are also often monotonically increasing,...

Examples of functions with such piecewise properties are: Piecewise constant function, also known as a step function Piecewise linear function Piecewise continuous...

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

x_{j+1}=1} . A linear B-spline is the same as a continuous piecewise linear function f ( x ) {\displaystyle f(x)} , and this general triangle function is useful...

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...

and represented the function as 1. Taking the convention that H(0) = 1, the Heaviside function may be defined as: a piecewise function: H ( x ) := { 1 ,...

impulse response) so that each input impulse results in the correct piecewise linear function in the output. First-order hold is the hypothetical filter or...

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

numerical analysis, a piecewise linear approximation to the identity is desirable. This can be obtained by taking η1 to be a hat function. With this choice...

floor and ceiling functions). The first three are piecewise constant, changing abruptly at each data point, while the last six use linear interpolation between...

the extreme case of an asymmetric triangle wave. The equivalent piecewise linear functions x ( t ) = t − ⌊ t ⌋ {\displaystyle x(t)=t-\lfloor t\rfloor } x...

of approximately 0.44. It can be made more accurate by using a piecewise linear function of m {\displaystyle m} , or more crudely by adding a constant...

poorly designed hash functions can result in access times approaching linear in the number of items in the table. Hash functions can be designed to give...

(rectified linear unit) activation function is an activation function defined as the non-negative part of its argument, i.e., the ramp function: ReLU ⁡ (...

A linear congruential generator (LCG) is an algorithm that yields a sequence of pseudo-randomized numbers calculated with a discontinuous piecewise linear...

coordinate system. Then a polyhedral terrain is the image of a piecewise-linear function in x and y variables. The polyhedral terrain is a generalization...

It attempts to approximate the solution to some equation by piecewise linear functions, where the pieces are chosen concerning a sufficiently fine grid...

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

interpolate linearly between the points ( x i , y ^ i ) {\displaystyle (x_{i},{\hat {y}}_{i})} , as illustrated in the figure, yielding a continuous piecewise linear...

the cosine function can be replaced in the infinite series by a piecewise linear "zigzag" function. G. H. Hardy showed that the function of the above...

k<2^{n}.} These functions sn,k are continuous, piecewise linear, supported by the interval In,k that also supports ψn,k. The function sn,k is equal to 1...