• Thumbnail for Piecewise function
    mathematics, a piecewise function (also called a piecewise-defined function, a hybrid function, or a function defined by cases) is a function whose domain...
    10 KB (1,065 words) - 20:45, 18 July 2025
  • 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...
    10 KB (1,211 words) - 10:47, 27 May 2025
  • Thumbnail for Step function
    intervals. Informally speaking, a step function is a piecewise constant function having only finitely many pieces. A function f : R → R {\displaystyle f\colon...
    7 KB (947 words) - 18:31, 16 February 2025
  • Thumbnail for Heaviside step function
    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 ,...
    14 KB (2,157 words) - 11:06, 13 June 2025
  • Thumbnail for Spline (mathematics)
    In mathematics, a spline is a function defined piecewise by polynomials. In interpolating problems, spline interpolation is often preferred to polynomial...
    23 KB (3,784 words) - 15:53, 6 July 2025
  • Thumbnail for Sign function
    {\displaystyle \operatorname {sgn}(x)} . The signum function of a real number x {\displaystyle x} is a piecewise function which is defined as follows: sgn ⁡ x :=...
    16 KB (2,711 words) - 09:57, 3 June 2025
  • Thumbnail for Window function
    astronomy, inspired by the Planck distribution. It is defined as a piecewise function: w [ 0 ] = 0 , w [ n ] = ( 1 + exp ⁡ ( ε N n − ε N ε N − n ) ) − 1...
    74 KB (8,875 words) - 04:15, 25 June 2025
  • Thumbnail for Ramp function
    the ramp function. The ramp function (R(x) : R → R0+) may be defined analytically in several ways. Possible definitions are: A piecewise function: R ( x...
    7 KB (1,005 words) - 03:45, 8 August 2024
  • Thumbnail for Triangular function
    sometimes called the Bartlett window. The most common definition is as a piecewise function: tri ⁡ ( x ) = Λ ( x )   = def   max ( 1 − | x | , 0 ) = { 1 − | x...
    6 KB (998 words) - 12:23, 26 January 2025
  • Thumbnail for Domain of a function
    ∈ R : x ≠ 0 } {\displaystyle \{x\in \mathbb {R} :x\neq 0\}} . The piecewise function f {\displaystyle f} defined by f ( x ) = { 1 / x x ≠ 0 0 x = 0 , {\displaystyle...
    8 KB (962 words) - 11:47, 12 April 2025
  • mathematics, piecewise properties may be exemplified in: A function property holds piecewise for a function, if the function can be piecewise-defined in...
    799 bytes (121 words) - 14:23, 3 October 2024
  • Geometrically, the graph of the function must pass through the origin. Homogeneous function Nonlinear system Piecewise linear function Linear approximation Linear...
    5 KB (652 words) - 04:16, 25 February 2025
  • C=\{c_{i}:i\in \mathbb {N} \}} can be calculated. Consider for example the piecewise function f ( t ) = { 0 , if  t ∈ [ 0 , 1 ]  and rational, 1 , if  t ∈ [ 0 ...
    18 KB (2,872 words) - 23:25, 17 July 2025
  • Thumbnail for Cubic function
    is a piecewise cubic function. If the value of a function is known at several points, cubic interpolation consists in approximating the function by a...
    12 KB (1,746 words) - 17:57, 14 May 2025
  • 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...
    6 KB (749 words) - 03:12, 22 June 2025
  • Thumbnail for Desmos
    graph restriction, simultaneous graphing, piecewise function graphing, recursive function graphing, polar function graphing, two types of graphing grids –...
    13 KB (1,091 words) - 19:39, 12 July 2025
  • Archived from the original on 28 August 2019. Weisstein, Eric W. "Piecewise Function". mathworld.wolfram.com. Retrieved 2024-07-20. Steyer, Carly (7 July...
    49 KB (5,286 words) - 12:59, 21 July 2025
  • Thumbnail for Dirac delta function
    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...
    98 KB (14,418 words) - 05:48, 22 July 2025
  • Thumbnail for Analytic function
    everywhere analytic because it is not differentiable at 0. Piecewise defined functions (functions given by different formulae in different regions) are typically...
    15 KB (2,233 words) - 20:17, 16 July 2025
  • The Huber loss function describes the penalty incurred by an estimation procedure f. Huber (1964) defines the loss function piecewise by L δ ( a ) = {...
    8 KB (1,098 words) - 15:41, 14 May 2025
  • Thumbnail for Weierstrass function
    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...
    20 KB (2,430 words) - 04:26, 4 April 2025
  • 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...
    4 KB (446 words) - 00:07, 25 June 2025
  • to 1, but using simpler functions, especially piecewise linear functions or piecewise constant functions. These are preferred where speed of computation...
    2 KB (173 words) - 18:13, 26 June 2025
  • Thumbnail for B-spline
    a fundamental building block for all spline functions of that degree. A B-spline is defined as a piecewise polynomial of order n {\displaystyle n} , meaning...
    31 KB (5,735 words) - 15:03, 23 June 2025
  • modifiers apply (see above), with the point translation function being a piecewise function: a constant amount is given for scoreless hands, and the...
    12 KB (1,773 words) - 08:07, 22 May 2025
  • holomorphic functions linear functions piecewise linear functions continuous functions, compact open topology all functions, space of pointwise convergence...
    9 KB (1,225 words) - 11:21, 22 June 2025
  • Thumbnail for Hash function
    A hash function is any function that can be used to map data of arbitrary size to fixed-size values, though there are some hash functions that support...
    50 KB (7,455 words) - 07:54, 7 July 2025
  • Thumbnail for Lambert W function
    W function by piecewise minimax rational function approximation with variable transformation". doi:10.13140/RG.2.2.30264.37128. "Lambert W Functions -...
    79 KB (12,516 words) - 05:05, 21 July 2025
  • Equicontinuity (category Theory of continuous functions)
    Mathematical term Normal function – Function of ordinals in mathematics Piecewise – Function defined by multiple sub-functionsPages displaying short descriptions...
    25 KB (3,738 words) - 18:43, 4 July 2025
  • Thumbnail for Rec. 709
    analog-to-digital converters. Thus the standard opted for a piecewise function that combines a simple linear function V = a L {\displaystyle V=a\,L} for low light levels...
    32 KB (3,988 words) - 12:50, 23 June 2025