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Something roughly the same as something else
An approximation is anything that is intentionally similar but not exactly equal to something else. The word approximation is derived from Latin approximatus
Approximation
Approximation for factorials
mathematics, Stirling's approximation (or Stirling's formula) is an asymptotic approximation for factorials. It is a good approximation, leading to accurate
Stirling's_approximation
Topics referred to by the same term
Rational approximation may refer to: Diophantine approximation, the approximation of real numbers by rational numbers Padé approximation, the approximation of
Rational_approximation
Small angle approximation in geometric optics
In geometric optics, the paraxial approximation is a small-angle approximation used in Gaussian optics and ray tracing of light through an optical system
Paraxial_approximation
Expressions for approximation accuracy
quantitative disciplines, order of approximation refers to formal or informal expressions for how accurate an approximation is in terms of the number of parameters
Order_of_approximation
Varying methods used to calculate pi
Approximations for the mathematical constant pi (π) in the history of mathematics reached an accuracy within 0.04% of the true value before the beginning
Approximations_of_pi
Mathematical method that minimizes maximum error
A minimax approximation algorithm (or L∞ approximation or uniform approximation) is a method to find an approximation of a mathematical function that
Minimax approximation algorithm
Minimax_approximation_algorithm
Class of algorithms that find approximate solutions to optimization problems
In computer science and operations research, approximation algorithms are efficient algorithms that find approximate solutions to optimization problems
Approximation_algorithm
In mathematics the Korovkin approximation is a convergence statement in which the approximation of a function is given by a certain sequence of functions
Korovkin_approximation
In models of radiative transfer, the two-stream approximation is a discrete ordinate approximation in which radiation propagating along only two discrete
Two-stream_approximation
Rational-number approximation of a real number
In number theory, the study of Diophantine approximation deals with the approximation of real numbers by rational numbers. It is named after Diophantus
Diophantine_approximation
Property of artificial neural networks
In the field of machine learning, the universal approximation theorems (UATs) state that neural networks with a certain structure can, in principle, approximate
Universal approximation theorem
Universal_approximation_theorem
Law of physics
Wien's approximation (also sometimes called Wien's law or the Wien distribution law) is a law of physics used to describe the spectrum of thermal radiation
Wien_approximation
Solution method for linear differential equations
In mathematical physics, the WKB approximation or WKB method is a technique for finding approximate solutions to linear differential equations with spatially
WKB_approximation
Assumption that motions of nuclei and electrons can be separated
quantum chemistry and molecular physics, the Born–Oppenheimer (BO) approximation is the assumption that the wave functions of atomic nucleus and electrons
Born–Oppenheimer approximation
Born–Oppenheimer_approximation
Approximation of a function by its tangent line at a point
In mathematics, a linear approximation is an approximation of a general function using a linear function (more precisely, an affine function). They are
Linear_approximation
Topics referred to by the same term
Boussinesq approximation may refer to several modelling concepts – as introduced by Joseph Valentin Boussinesq (1842–1929), a French mathematician and
Boussinesq_approximation
Mathematical concept
The approximation error in a given data value represents the significant discrepancy that arises when an exact, true value is compared against some approximation
Approximation_error
Theory of getting acceptably close inexact mathematical calculations
In mathematics, approximation theory is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterizing
Approximation_theory
In algebraic group theory, approximation theorems are an extension of the Chinese remainder theorem to algebraic groups G over global fields k. Eichler
Approximation in algebraic groups
Approximation_in_algebraic_groups
Fitness approximation aims to approximate the objective or fitness functions in evolutionary optimization by building up machine learning models based
Fitness_approximation
In computer science, hardness of approximation is a field that studies the algorithmic complexity of finding near-optimal solutions to optimization problems
Hardness_of_approximation
Method to calculate trajectory calculations for spacecraft
In astrodynamics, the patched conic approximation or patched two-body approximation is a method to simplify trajectory calculations for spacecraft in
Patched_conic_approximation
Topics referred to by the same term
successive approximation are a category of strategies in pure and applied mathematics. Successive approximation also may refer to: Successive approximation ADC
Successive_approximation
Probability distribution
for N much larger than n, the binomial distribution remains a good approximation, and is widely used. If the random variable X follows the binomial distribution
Binomial_distribution
Scattering theory
scattering theory and in particular in quantum mechanics, the Born approximation consists of taking the incident field in place of the total field as
Born_approximation
Rayleigh–Gans approximation, also known as Rayleigh–Gans–Debye approximation and Rayleigh–Gans–Born approximation, is an approximate solution to light
Rayleigh–Gans_approximation
Technique in numerical linear algebra
In mathematics, low-rank approximation refers to the process of approximating a given matrix by a matrix of lower rank. More precisely, it is a minimization
Low-rank_approximation
Approximating an arbitrary function with a well-behaved one
In general, a function approximation problem asks us to select a function that closely matches ("approximates") a function in a task-specific way.[better source needed]
Function_approximation
matrix approximation is a set of three matrices C, U and R that, when multiplied together, closely approximate a given matrix. A CUR approximation can be
CUR_matrix_approximation
Simplification of the basic trigonometric functions
can be calculated with reasonable accuracy by the following simple approximations: sin θ ≈ tan θ ≈ θ , cos θ ≈ 1 − 1 2 θ 2 ≈ 1 , {\displaystyle
Small-angle_approximation
Approximation of powers of some binomials
The binomial approximation is useful for approximately calculating powers of sums of 1 and a small number x. It states that ( 1 + x ) α ≈ 1 + α x . {\displaystyle
Binomial_approximation
Simplification for simulating fluids under natural convection
In fluid dynamics, the Boussinesq approximation (pronounced [businɛsk], named for Joseph Valentin Boussinesq) is used in the field of buoyancy-driven
Boussinesq approximation (buoyancy)
Boussinesq_approximation_(buoyancy)
Theoretical physics method in wave scattering equations
In theoretical physics, the eikonal approximation (Greek εἰκών for likeness, icon or image) is an approximative method useful in wave scattering equations
Eikonal_approximation
Analytical expression in statistics
Laplace's approximation or the quadratic approximation (QUAP) provides an analytical expression for a posterior probability distribution by fitting a Gaussian
Laplace's_approximation
Equations that keep static form even if quantities vary in time
Quasistatic approximation(s) refers to different domains and different meanings. In the most common acceptance, quasistatic approximation refers to equations
Quasistatic_approximation
Method in cosmology and astrophysics
Zeldovich approximation is a method in cosmology and astrophysics for describing the nonlinear evolution of the large-scale structure of the universe
Zeldovich_approximation
Product of numbers from 1 to n
the late 18th and early 19th centuries. Stirling's approximation provides an accurate approximation to the factorial of large numbers, showing that it
Factorial
Topics referred to by the same term
Weak approximation may refer to: Weak approximation theorem, an extension of the Chinese remainder theorem to algebraic groups over global fields Weak
Weak_approximation
Numerical method for calculating the gamma function
In mathematics, Spouge's approximation is a formula for computing an approximation of the gamma function. It was named after John L. Spouge, who defined
Spouge's_approximation
In probability theory, the Komlós–Major–Tusnády approximation (also known as the KMT approximation, the KMT embedding, or the Hungarian embedding) refers
Komlós–Major–Tusnády approximation
Komlós–Major–Tusnády_approximation
Family of iterative methods
Stochastic approximation methods are a family of iterative methods typically used for root-finding problems or for optimization problems. The recursive
Stochastic_approximation
Approximation of a function by a polynomial
In calculus, Taylor's theorem gives an approximation of a k-times differentiable function around a given point by a polynomial of degree k, called the
Taylor's_theorem
Vecchia approximation is a Gaussian processes approximation technique originally developed by Aldo Vecchia, a statistician at United States Geological
Vecchia_approximation
Mathematical approximation of a function
called the nth Taylor polynomial of the function. Taylor polynomials are approximations of a function, which become generally more accurate as n increases.
Taylor_series
Type of algorithm
A parameterized approximation algorithm is a type of algorithm that aims to find approximate solutions to NP-hard optimization problems in polynomial
Parameterized approximation algorithm
Parameterized_approximation_algorithm
Number, approximately 3.14
widely used historical approximations of the constant. Each approximation generated in this way is a best rational approximation; that is, each is closer
Pi
Model used in atom optics and magnetic resonance
The rotating-wave approximation is an approximation used in atom optics and magnetic resonance. In this approximation, terms in a Hamiltonian that oscillate
Rotating-wave_approximation
Computational quantum mechanical modelling method to investigate electronic structure
accurate for calculations in quantum chemistry until the 1990s, when the approximations used in the theory were greatly refined to better model the exchange
Density_functional_theory
1969 result in deformation theory
In mathematics, the Artin approximation theorem is a fundamental result of Michael Artin (1969) in deformation theory which implies that formal power
Artin_approximation_theorem
Sigmoid shape special function
the desired interval of approximation. Another approximation is given by Sergei Winitzki using his "global Padé approximations": erf ( x ) ≈ sgn x
Error_function
'Best' approximation of a function by a rational function of given order
In mathematics, a Padé approximant is the "best" approximation of a function near a specific point by a rational function of given order. Under this technique
Padé_approximant
Topics referred to by the same term
In mathematics, an approximation to the identity refers to a sequence or net that converges to the identity in some algebra. Specifically, it can mean:
Approximation_to_the_identity
The quasi-harmonic approximation is a phonon-based model of solid-state physics used to describe volume-dependent thermal effects, such as the thermal
Quasi-harmonic_approximation
Matrix decomposition
polar decomposition, and is a common means for implementing low-rank approximation for matrices. Specifically, the singular value decomposition of an m×n
Singular_value_decomposition
Superstrong approximation is a generalisation of strong approximation in algebraic groups G, to provide spectral gap results. The spectrum in question
Superstrong_approximation
Concept in number theory
number theory, Dirichlet's theorem on Diophantine approximation, also called Dirichlet's approximation theorem, states that for any real numbers α {\displaystyle
Dirichlet's approximation theorem
Dirichlet's_approximation_theorem
Root-finding algorithm
the number 0x5F3759DF, which is a floating-point representation of an approximation of 2 127 {\textstyle {\sqrt {2^{127}}}} . This results in an initial
Fast_inverse_square_root
Algorithm for transforming one optimization problem into another
computational complexity theory, especially the study of approximation algorithms, an approximation-preserving reduction is an algorithm for transforming
Approximation-preserving reduction
Approximation-preserving_reduction
Approximation method in statistics
refined iteratively, that is, the values are obtained by successive approximation: βjk+1=βjk+Δβj, where a superscript k is an iteration number, and the
Least_squares
Annual mathematical celebration on March 14
pi include Pi Approximation Day on July 22 (22/7 in the day/month format), an approximation of π; and June 28 (6.28), an approximation of 2π or τ (tau)
Pi_Day
Numerical method for calculating the gamma function
In mathematics, the Lanczos approximation is a method for computing the gamma function numerically, published by Cornelius Lanczos in 1964. It is a practical
Lanczos_approximation
Approximation in many-body systems
The GW approximation is a method used to calculate the self-energy of a many-body system of electrons. The approximation is that the expansion of the
GW_approximation
Algorithms for calculating square roots
these algorithms typically construct a series of increasingly accurate approximations. Most square root computation methods are iterative: after choosing
Square_root_algorithms
Unrelated vertices in graphs
may be approximated to within any approximation ratio c < 1 in polynomial time; similar polynomial-time approximation schemes exist in any family of graphs
Independent set (graph theory)
Independent_set_(graph_theory)
The coherent potential approximation (CPA) is a method, in theoretical physics, of finding the averaged Green's function of an inhomogeneous (or disordered)
Coherent potential approximation
Coherent_potential_approximation
Type of analog-to-digital converter
A successive-approximation ADC (or SAR ADC) is a type of analog-to-digital converter (ADC) that digitizes each sample from a continuous analog waveform
Successive-approximation_ADC
Complexity class of approximable problems
allow polynomial-time approximation algorithms with approximation ratio bounded by a constant (or constant-factor approximation algorithms for short)
APX
Approximations in density functional theory
Local-density approximations (LDA) are a class of approximations to the exchange–correlation (XC) energy functional in density functional theory (DFT)
Local-density_approximation
Approximation technique in integral calculus
In mathematics, a Riemann sum is a certain kind of approximation of an integral by a finite sum. It is named after nineteenth century German mathematician
Riemann_sum
Substituting rare characters with more common characters
A typographic approximation is a replacement of an element of the writing system (usually a glyph) with another glyph or glyphs. The replacement may be
Typographic_approximation
Problem in graph theory
polynomial-time approximation scheme (PTAS), arbitrarily close to the optimal solution, for it, unless P = NP. Thus, every known polynomial-time approximation algorithm
Maximum_cut
Approximation in quantum chemistry
The Born–Huang approximation is an approximation closely related to the Born–Oppenheimer approximation. It takes into account diagonal nonadiabatic effects
Born–Huang_approximation
Method of approximating the properties of a composite material
In materials science, effective medium approximations (EMA) or effective medium theory (EMT) pertain to analytical or theoretical modeling that describes
Effective medium approximations
Effective_medium_approximations
Approach to finding numerical solutions of ordinary differential equations
y_{n+1}=y_{n}+hf(t_{n},y_{n}).} The value of y n {\displaystyle y_{n}} is an approximation of the solution at time t n {\displaystyle t_{n}} , i.e., y n ≈ y (
Euler_method
Lighting formula in 3D computer graphics
In 3D computer graphics, Schlick's approximation, named after Christophe Schlick, is a formula for approximating the contribution of the Fresnel factor
Schlick's_approximation
NP-hard problem in combinatorial optimization
optimal. It was one of the first approximation algorithms, and was in part responsible for drawing attention to approximation algorithms as a practical approach
Travelling_salesman_problem
Concept in mathematics
Sparse approximation (also known as sparse representation) theory deals with sparse solutions for systems of linear equations. Techniques for finding
Sparse_approximation
Algorithm for finding zeros of functions
Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes) of a real-valued function. The most basic version
Newton's_method
approximation was introduced in 1935 by John G. Kirkwood as a means of representing a discrete probability distribution. The Kirkwood approximation for
Kirkwood_approximation
Continuous mappings can be approximated by ones that are piecewise simple
In mathematics, the simplicial approximation theorem is a foundational result for algebraic topology, guaranteeing that continuous mappings can be (by
Simplicial approximation theorem
Simplicial_approximation_theorem
Method in theoretical optics
physics, slowly varying envelope approximation (SVEA, sometimes also called slowly varying asymmetric approximation or SVAA) is the assumption that the
Slowly varying envelope approximation
Slowly_varying_envelope_approximation
Approximation whereby the Coriolis parameter, f, is set to vary linearly in space
fluid dynamics, an approximation whereby the Coriolis parameter, f, is set to vary linearly in space is called a beta plane approximation. On a rotating sphere
Beta_plane
Unsolved problem in computational complexity theory
unique game. It has broad applications in the theory of hardness of approximation. If the UGC is true and P ≠ NP, then for many important problems there
Unique_games_conjecture
Statistical approximation method
The saddlepoint approximation method, initially proposed by Daniels (1954) is a specific example of the mathematical saddlepoint technique applied to
Saddlepoint approximation method
Saddlepoint_approximation_method
Shape approximation
The muffin-tin approximation is a shape approximation of the potential well in a crystal lattice. It is most commonly employed in quantum mechanical simulations
Muffin-tin_approximation
Problem in combinatorial optimization
algorithm using dynamic programming. There is a fully polynomial-time approximation scheme, which uses the pseudo-polynomial time algorithm as a subroutine
Knapsack_problem
Heuristic used in simulations of ions passing through solids
In condensed-matter physics, the binary collision approximation (BCA) is a heuristic used to more efficiently simulate the penetration depth and defect
Binary collision approximation
Binary_collision_approximation
Number in base-10 numeral system
digits after the decimal separator, for example, that "3.14 is the approximation of π to two decimals" or "two decimal places." The numbers that may
Decimal
perimeter of an ellipse. Throughout history, a large number of closed-form approximations and expressions in terms of integrals or series have been given for
Perimeter_of_an_ellipse
Decomposition of periodic functions
while forming the associated trigonometric series (or its various approximations) is called synthesis. A Fourier series can be written in several equivalent
Fourier_series
Numerical approximation algorithm
improving approximate solutions for a class of problems, in which the i-th approximation (called an "iterate") is derived from the previous ones. A specific
Iterative_method
Software packages using DDA
calculating scattering and absorption of light using Discrete dipole approximation (DDA). Most of the software applies to arbitrary-shaped inhomogeneous
Discrete dipole approximation codes
Discrete_dipole_approximation_codes
related fields, relaxation is a modeling strategy. A relaxation is an approximation of a difficult problem by a nearby problem that is easier to solve.
Relaxation_(approximation)
Class of numerical techniques
n and the original function. Following is the process to derive an approximation for the first derivative of the function f by first truncating the Taylor
Finite_difference_method
Mathematical concept
specifically functional analysis, a Banach space is said to have the approximation property (AP) if every compact operator is a limit of finite-rank operators
Approximation_property
Simplification that approximates the electron–electron interaction in crystals as null
In condensed matter physics, the independent electron approximation is a simplification used in complex systems, consisting of many electrons, that approximates
Independent electron approximation
Independent_electron_approximation
Methods of calculating definite integrals
from the approximation. An important part of the analysis of any numerical integration method is to study the behavior of the approximation error as a
Numerical_integration
Discrete analog of a derivative
differences (or the associated difference quotients) are often used as approximations of derivatives, such as in numerical differentiation. The difference
Finite_difference
Mathematical theorem in the study of analysis
In mathematical analysis, the Weierstrass approximation theorem states that every continuous function defined on a closed interval [a, b] can be uniformly
Stone–Weierstrass_theorem
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