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Topics referred to by the same term
Function value may refer to: In mathematics, the value of a function when applied to an argument. In computer science, a closure. This disambiguation page
Function_value
Mapping arbitrary data to fixed-size values
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
Hash_function
Distance from zero to a number
the absolute value function is idempotent (meaning that the absolute value of any absolute value is itself). The absolute value function of a real number
Absolute_value
Notion in mathematics
as values. The value of a function, given the value(s) assigned to its argument(s), is the quantity assumed by the function for these argument values. For
Value_(mathematics)
Concept in economics and decision theory
the same utility value. Individual and social utility can be construed as the value of a utility function and a social welfare function, respectively. When
Utility
Association of one output to each input
possible applications of the concept. A function is often denoted by a letter such as f, g or h. The value of a function f at an element x of its domain (that
Function_(mathematics)
Constants of the mathematical zeta function
partial sums would grow indefinitely large. The zeta function values listed below include function values at the negative even numbers ( s = − 2 , − 4 {\displaystyle
Particular values of the Riemann zeta function
Particular_values_of_the_Riemann_zeta_function
Maximized objective function of an optimization problem
The value function of an optimization problem gives the value attained by the objective function at a solution, while only depending on the parameters
Value_function
Function used as a performance test problem for optimization algorithms
x_{0}=(-3,-4)} . The solution with the function value 10 − 10 {\displaystyle 10^{-10}} can be found after 325 function evaluations. Using the Nelder–Mead
Rosenbrock_function
Description of continuous random distribution
probability density function (PDF), density function, or simply density of an absolutely continuous random variable, is a function whose value at any given point
Probability_density_function
Continuous function on an interval takes on every value between its values at the ends
mathematical analysis, the intermediate value theorem states that if f {\displaystyle f} is a continuous function whose domain contains the interval [a
Intermediate_value_theorem
Point where function's value is zero
sometimes called a root) of a real-, complex-, or generally vector-valued function f {\displaystyle f} , is a member x {\displaystyle x} of the domain
Zero_of_a_function
Mathematical function with no sudden changes
mathematics, a continuous function is a function such that a small variation of its argument induces at most a small variation of its value. This implies there
Continuous_function
Function valued in a vector space; typically a real or complex one
A vector-valued function, also referred to as a vector function, is a mathematical function of one or more variables whose range is a set of multidimensional
Vector-valued_function
Mathematical function, denoted exp(x) or e^x
mathematics, the exponential function is the unique real function which maps zero to one and has a derivative everywhere equal to its value. It is denoted e x
Exponential_function
Mathematical function with convex lower level sets
In mathematics, a quasiconvex function is a real-valued function defined on a convex subset of a real vector space, such that for any real number y, the
Quasiconvex_function
Point to which functions converge in analysis
the concept of limit: roughly, a function is continuous if all of its limits agree with the values of the function. The concept of limit also appears
Limit_of_a_function
Mathematical function having a characteristic S-shaped curve or sigmoid curve
values of x) and the ogee curve (used in the spillway of some dams). Sigmoid functions have domain of all real numbers, with return (response) value commonly
Sigmoid_function
Mathematical function that outputs real values
In mathematics, a real-valued function is a function whose values are real numbers. In other words, it is a function that assigns a real number to each
Real-valued_function
Generalized mathematical function
a multivalued function, multiple-valued function, many-valued function, or multifunction, is a function that has two or more values in its range for
Multivalued_function
Average value of a random variable
function given by a function f {\displaystyle f} on the real number line. This means that the probability of X {\displaystyle X} taking on any value in
Expected_value
S-shaped curve
{\displaystyle L} is the carrying capacity, the supremum of the values of the function; k {\displaystyle k} is the logistic growth rate, the steepness
Logistic_function
All derivatives have the intermediate value property
theorem states that the derivative of any real-valued function of a real variable has the intermediate value property, that is, that the image of an interval
Darboux's_theorem_(analysis)
Negative of a convex function
In mathematics, a concave function is one for which the function value at any convex combination of elements in the domain is greater than or equal to
Concave_function
Sigmoid shape special function
applications, the function argument is a real number, in which case the function value is also real. In some older texts, the error function is defined without
Error_function
Theorem in mathematics
and real analysis, the mean value theorem (or Lagrange's mean value theorem) is a theorem about differentiable functions, roughly stating that the average
Mean_value_theorem
Function that returns its argument unchanged
an identity function, also called an identity relation, identity map or identity transformation, is a function that always returns the value that was used
Identity_function
Branch of mathematics studying functions of a complex variable
known as the theory of functions of a complex variable, is the branch of mathematical analysis that studies complex-valued functions of one or more complex
Complex_analysis
Special mathematical function defined as sin(x)/x
both cases, the value of the function at the removable singularity at zero is understood to be the limit value 1. The sinc function is then analytic
Sinc_function
Concept in game theory
coalition (set of players) S {\displaystyle S} , we define the payoff or value function v ( S ) {\displaystyle v(S)} as the total sum of payoffs that the members
Shapley_value
Mathematical constants
The gamma function is an important special function in mathematics. Its particular values can be expressed in closed form for integer, half-integer, and
Particular values of the gamma function
Particular_values_of_the_gamma_function
Function returning one of only two values
In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually {true, false}, {0,1} or {−1
Boolean_function
Mathematical relation assigning a probability event to a cost
decision theory, a loss function or cost function (sometimes also called an error function) is a function that maps an event or values of one or more variables
Loss_function
Probability that random variable X is less than or equal to x
cumulative distribution function (CDF) of a real-valued random variable X {\displaystyle X} , or just distribution function of X {\displaystyle X} ,
Cumulative distribution function
Cumulative_distribution_function
Extension of the factorial function
integral of the first kind is the beta function.) The relationship to the factorial can be shown by induction. The value Γ ( 1 ) {\displaystyle \Gamma (1)}
Gamma_function
Real function with secant line between points above the graph itself
mathematics, a real-valued function is called convex if the line segment between any two distinct points on the graph of the function lies above or on the
Convex_function
Function returning minus 1, zero or plus 1
In mathematics, the sign function or signum function (from signum, Latin for "sign") is a function that has the value −1, +1 or 0 according to whether
Sign_function
Counterexample to the converse of the intermediate value theorem
13 function is a mathematical function created by British mathematician John H. Conway as a counterexample to the converse of the intermediate value theorem
Conway's_base_13_function
mathematics, proto-value functions (PVFs) are automatically learned basis functions that are useful in approximating task-specific value functions, providing
Proto-value_function
Function whose values are sets (mathematics)
A set-valued function, also called a correspondence or set-valued relation, is a mathematical function that maps elements from one set, the domain of the
Set-valued_function
Function used as a performance test problem for optimization algorithms
f(𝐱)=0. The maximum function value for xi∈[−5.12,5.12] is located at 𝐱=(±4.52299366...,...,±4.52299366...): Here are all the values at 0.5 interval listed
Rastrigin_function
Smooth approximation of one-hot arg max
one-hot version of the arg max function: the function whose vector component values are all zero, except that it has a value of 1 corresponding to the location
Softmax_function
Program function without side effects
In computer programming, a pure function is a function that has the following properties: the function return values are identical for identical arguments
Pure_function
On finding a repeating loop in a sequence
iterated function values. For any function f that maps a finite set S to itself, and any initial value x0 in S, the sequence of iterated function values x0
Cycle_detection
Indicator function of positive numbers
function, or the unit step function, usually denoted by H or θ (but sometimes u, 1 or 𝟙), is a step function named after Oliver Heaviside, the value
Heaviside_step_function
Hash function that is suitable for use in cryptography
level of a cryptographic hash function has been defined using the following properties: Pre-image resistance Given a hash value h, it should be difficult
Cryptographic_hash_function
Uniform restraint of the change in functions
positive real number δ {\displaystyle \delta } such that function values over any function domain interval of the size δ {\displaystyle \delta } are
Uniform_continuity
Extension of cubic spline interpolation
different interpolation artifacts, depending on the b and c values chosen. Suppose the function values f {\displaystyle f} and the derivatives f x {\displaystyle
Bicubic_interpolation
Largest and smallest value taken by a function at a given point
analysis, the maximum and minimum of a function are, respectively, the greatest and least value taken by the function. Known generically as extrema, they
Maximum_and_minimum
Subfield of number theory
In mathematics, the study of special values of L-functions is a subfield of number theory devoted to generalising formulae such as the Leibniz formula
Special_values_of_L-functions
Functions in mathematics
convergent sequence of harmonic functions is still harmonic. This is true because every continuous function satisfying the mean value property is harmonic. Consider
Harmonic_function
Instantaneous rate of change (mathematics)
to change of a function's output with respect to its input. The derivative of a function of a single variable at a chosen input value, when it exists
Derivative
Function with a multiplicative scaling behaviour
the function's arguments is multiplied by the same scalar, then the function's value is multiplied by some power of this scalar; the power is called the
Homogeneous_function
Properties of mathematical relationships
also referred to as being a "linear function", and the relationship between the argument and the function value may be referred to as a "linear relationship"
Linearity
Programming language evaluation rules
kind of value that is passed to the function for each parameter (the binding strategy) and whether to evaluate the parameters of a function call, and
Evaluation_strategy
Study of mathematical algorithms for optimization problems
minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. The generalization
Mathematical_optimization
Linear combination of indicator functions of real intervals
also a step function. As such, the step functions form an algebra over the real numbers. A step function takes only a finite number of values. If the intervals
Step_function
Mathematical functions having established names and notations
functions. Before electronic computation, the importance of a special function was affirmed by the laborious computation of extended tables of values
Special_functions
Mathematical function, inverse of an exponential function
tends to be a multi-valued function. For example, the complex logarithm is the multi-valued inverse of the complex exponential function. Similarly, the discrete
Logarithm
Mathematical concept
example, consider the real-valued function of a real variable given by f(x) = 5x − 7. One can think of f as the function which multiplies its input by
Inverse_function
number of asymptotic values attained by a non-constant entire function of order ρ on curves going outwards toward infinite absolute value is less than or equal
Denjoy–Carleman–Ahlfors theorem
Denjoy–Carleman–Ahlfors_theorem
Algorithms in numerical analysis
from a function fitted to the function-values and derivative-values at a preceding set of points to extrapolate ("anticipate") this function's value at a
Predictor–corrector_method
Operation in calculus
antiderivative of the function to be integrated. Let f be a continuous real-valued function defined on a closed interval [a, b]. Let F be the function defined, for
Integral
Type of mathematical function
mathematics, a constant function is a function whose (output) value is the same for every input value. As a real-valued function of a real-valued argument, a constant
Constant_function
Mathematical functions
hyperbolic functions, prefixed with arc- or ar- or with a superscript −1 (for example arcsinh, arsinh, or sinh−1). For a given value of a hyperbolic function, the
Inverse_hyperbolic_functions
Concept in theoretical computer science
It is extremely hard to prove values for the busy beaver function (and the max shift function). Every known exact value of S(n) was proven by enumerating
Busy_beaver
Matrix of partial derivatives of a vector-valued function
calculus, the Jacobian matrix (/dʒəˈkoʊbiən/, /dʒɪ-, jɪ-/) of a vector-valued function of several variables is the matrix of all its first-order partial derivatives
Jacobian matrix and determinant
Jacobian_matrix_and_determinant
Function used in signal processing
statistics, a window function (also known as an apodization function or tapering function) is a mathematical function that is zero-valued outside of some chosen
Window_function
Number taken as representative of a list of numbers
frequency of each value is relevant (such as where a histogram, bar chart, or probability density function is being referenced), or to find a value that represents
Average
Logarithm to the base of the mathematical constant e
logarithm function, if considered as a real-valued function of a positive real variable, is the inverse function of the exponential function, leading to
Natural_logarithm
Type of problem involving ODEs or PDEs
finding the harmonic functions (solutions to Laplace's equation); the solution was given by the Dirichlet's principle. Boundary value problems are similar
Boundary_value_problem
Discrete-variable probability distribution
exactly equal to some value. The PMF is often the primary means of defining a discrete probability distribution, and such functions exist for either scalar
Probability_mass_function
Function in logic
In logic, a truth function is a function that accepts truth values as input and produces a unique truth value as output. In other words: the input and
Truth_function
Concept in probability theory and statistics
theory and statistics, the moment generating function of a real-valued random variable is a generating function that provides an alternative specification
Moment_generating_function
Specific values of a multivalued function
branch that takes a real value for small positive values of the variable. A principal value is the value at a point of the function defined by the principal
Principal_value
Distance from origin of tangent hyperplanes
support function of a compact nonempty convex set is real valued and continuous, but if the set is closed and unbounded, its support function is extended
Support_function
Public-key cryptographic pseudorandom function
The owner of the secret key can compute the function value as well as an associated proof for any input value. Everyone else, using the proof and the associated
Verifiable_random_function
Function that is continuous everywhere but differentiable nowhere
mathematics, the Weierstrass function, named after its discoverer, Karl Weierstrass, is an example of a real-valued function that is continuous everywhere
Weierstrass function (nowhere-differentiable function)
Weierstrass_function_(nowhere-differentiable_function)
Distribution function associated with the empirical measure of a sample
cumulative distribution function is a step function that jumps up by 1/n at each of the n data points. Its value at any specified value of the measured variable
Empirical distribution function
Empirical_distribution_function
Algorithm for finding a zero of a function
continuous function for which one knows two values with opposite signs. The method consists of repeatedly bisecting the interval defined by these values, then
Bisection_method
Method for estimating new data within known data points
the values of a function for a limited number of values of the independent variable. It is often required to interpolate; that is, estimate the value of
Interpolation
Engineering analysis that maximizes function-to-cost ratio
Value engineering (VE) is a systematic analysis of the functions of various components and materials to lower the cost of goods, products and services
Value_engineering
Family of higher-order functions
return value. Fold is also termed as reduce, accumulate, aggregate, compress, or inject. Typically, a fold is presented with a combining function, a top
Fold_(higher-order_function)
Philosophical concept
value and utility derived from the function and the primary use of the object. For example, the buyer of a Rolls-Royce limousine might partly value the
Sign_value
Analytic function in mathematics
zeta function that many mathematicians consider the most important unsolved problem in pure mathematics. The values of the Riemann zeta function at even
Riemann_zeta_function
image of functions. Injective function: has a distinct value for each distinct input. Also called an injection or, sometimes, one-to-one function. In other
List_of_types_of_functions
Function that derives secret keys from a secret value
cryptography, a key derivation function (KDF) is an algorithm that derives one or more secret keys from a secret value, such as a master key, a password
Key_derivation_function
Generalized function whose value is zero everywhere except at zero
continuous function f. The implication is that the Fourier series of any continuous function is Cesàro summable to the value of the function at every point
Dirac_delta_function
Gradient of the likelihood function
the gradient of the log-likelihood function with respect to the parameter vector. Evaluated at a particular value of the parameter vector, the score indicates
Informant_function
In mathematics, an integer-valued function is a function whose values are integers. In other words, it is a function that assigns an integer to each member
Integer-valued_function
Nearest integers from a number
the floor function for negative numbers. For an integer n, ⌊n⌋ = ⌈n⌉ = n. Although floor(x + 1) and ceil(x) are equal for non-integer values of x, and
Floor_and_ceiling_functions
Function defined by multiple sub-functions
mathematics, a piecewise function (also called a piecewise-defined function, a hybrid function, or a function defined by cases) is a function whose domain is partitioned
Piecewise_function
Function that attains finitely many values
analysis, a simple function is a real (or complex)-valued function over a subset of the real line, similar to a step function. Simple functions are sufficiently
Simple_function
Fundamental trigonometric functions
sine and cosine functions are denoted as sin(θ) and cos(θ). The definitions of sine and cosine have been extended to any real value in terms of the
Sine_and_cosine
Polynomial function of degree two
In mathematics, a quadratic function of a single variable is a function of the form f ( x ) = a x 2 + b x + c {\displaystyle f(x)=ax^{2}+bx+c} with
Quadratic_function
Function that outputs either true or false
A Boolean-valued function (sometimes called a predicate or a proposition) is a function of the type f : X → B, where X is an arbitrary set and where B
Boolean-valued_function
Mathematical function whose derivative exists
or complex function of a single variable is differentiable if its derivative exists at each point in its domain. For real-valued functions of a real variable
Differentiable_function
Mathematical function defined piecewise by polynomials
In this case, a spline is a piecewise polynomial function. This function, call it S, takes values from an interval [a,b] and maps them to R , {\displaystyle
Spline_(mathematics)
Evaluation of a function on its argument
mathematics, function application (or evaluation) is the act of taking a function and an input from its domain to obtain the corresponding value from its
Function_application
Mathematical transform that expresses a function of time as a function of frequency
complex valued function of frequency. The term Fourier transform refers to both the mathematical operation and to this complex-valued function. When a
Fourier_transform
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