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Conversion of continuous functions into discrete counterparts
discretization error. The goal is to reduce the amount to a level considered negligible for the modeling purposes at hand. The terms discretization and
Discretization
Topics referred to by the same term
discrete in Wiktionary, the free dictionary. Discrete may refer to: Discrete particle or quantum in physics, for example in quantum theory Discrete device
Discrete
Quantization error in numerical analysis
lattice. Discretization error can usually be reduced by using a more finely spaced lattice, with an increased computational cost. Discretization error is
Discretization_error
Mathematical technique
(CAE) simulations, which require discretizing the governing equations in both space and time. Temporal discretization involves the integration of every
Temporal_discretization
machine learning, discretization refers to the process of converting or partitioning continuous attributes, features or variables to discretized or nominal
Discretization of continuous features
Discretization_of_continuous_features
Study of discrete mathematical structures
use recurrence relation. Discretization concerns the process of transferring continuous models and equations into discrete counterparts, often for the
Discrete_mathematics
Problem of inverting exponentiation in groups
number x {\displaystyle x} such that b x = a {\displaystyle b^{x}=a} . The discrete logarithm is an analogous concept in group theory. In any group G {\displaystyle
Discrete_logarithm
Numerical method for solving physical or engineering problems
Examples of discretization strategies are the h-version, p-version, hp-version, x-FEM, isogeometric analysis, etc. Each discretization strategy has certain
Finite_element_method
Branch of mathematical optimization
the variables used in a discrete optimization problem are restricted to be discrete variables—that is, to assume only a discrete set of values, such as
Discrete_optimization
Area of mathematics
appropriate discretization suited to your purpose (the so-called "game" of DDG). Integrable discretization is a systematic discretization based on integrable
Discrete differential geometry
Discrete_differential_geometry
Frameworks for modeling variables that evolve over time
portion of it. Aliasing Bernoulli process Digital data Discrete calculus Discrete system Discretization Normalized frequency Nyquist–Shannon sampling theorem
Discrete time and continuous time
Discrete_time_and_continuous_time
102002 Discrete Calculus, Grady, Leo J., Polimeni, Jonathan R., 2010 Hirani Thesis on Discrete Exterior Calculus A Primal-to-Primal Discretization of Exterior
Discrete_exterior_calculus
Discretization of the Navier–Stokes equations of fluid dynamics is a reformulation of the equations in such a way that they can be applied to computational
Discretization of Navier–Stokes equations
Discretization_of_Navier–Stokes_equations
System with a countable number of states
In theoretical computer science, a discrete system is a system with a countable number of states. Discrete systems may be contrasted with continuous systems
Discrete_system
Discrete (i.e., incremental) version of infinitesimal calculus
Discrete calculus is used for modeling either directly or indirectly as a discretization of infinitesimal calculus in every branch of the physical sciences,
Discrete_calculus
Types of numerical variables in mathematics
Discrete modelling Discrete series representation Discrete space Discrete spectrum Discrete time and continuous time Discretization Interpolation Principal
Continuous or discrete variable
Continuous_or_discrete_variable
Discrete device in an electronic system
An electronic component is any basic discrete electronic device or physical entity part of an electronic system used to affect electrons or their associated
Electronic_component
Function in discrete mathematics
the function means discretizing its frequency spectrum and discretization means periodic summation of the spectrum, the discretized and periodically summed
Discrete_Fourier_transform
Programmable machine that processes data
CSIRAC, EDVAC, UNIVAC I, IBM 701, IBM 702, IBM 650, Z22 Third generation (discrete transistors and SSI, MSI, LSI integrated circuits) Mainframes IBM 7090
Computer
mathematics, a sequence of discrete orthogonal polynomials is a sequence of polynomials that are pairwise orthogonal with respect to a discrete measure. Examples
Discrete orthogonal polynomials
Discrete_orthogonal_polynomials
Series in digital signal processing
function of the discrete variable, i.e. a discrete sequence. A Fourier series, by nature, has a discrete set of components with a discrete set of coefficients
Discrete_Fourier_series
Branch of geometry that studies combinatorial properties and constructive methods
Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric
Discrete_geometry
Speed of convergence of a mathematical sequence
In practical applications, when one discretization method gives a desired accuracy with a larger discretization scale parameter than another it will
Rate_of_convergence
Discrete analog of a derivative
This is often a problem because it amounts to changing the interval of discretization. The problem may be remedied substituting the average of δ n [ f ] (
Finite_difference
Finite difference equation
discretize the 2-dimensional Poisson equation (assuming a uniform spatial discretization, Δ x = Δ y {\displaystyle \Delta x=\Delta y} ) on an m × n grid gives
Discrete_Poisson_equation
Choice between two or more discrete alternatives
In economics, discrete choice models, or qualitative choice models, describe, explain, and predict choices between two or more discrete alternatives,
Discrete_choice
Category whose only morphisms are the identity morphisms
In mathematics, in the field of category theory, a discrete category is a category whose only morphisms are the identity morphisms: homC(X, X) = {idX}
Discrete_category
Electrical circuit with active components
can be moved from one place to another. Circuits can be constructed of discrete components connected by individual pieces of wire, but today it is much
Electronic_circuit
Type of simulation
A discrete-event simulation (DES) models the operation of a system as a (discrete) sequence of events in time. Each event occurs at a particular instant
Discrete-event_simulation
Type of topological space
In topology, a discrete space is a particularly simple example of a topological space or similar structure, one in which the points form a discontinuous
Discrete_space
Discrete modelling is the discrete analogue of continuous modelling. In discrete modelling, formulae are fit to discrete data—data that could potentially
Discrete_modelling
Probability distribution on equally likely outcomes
In probability theory and statistics, the discrete uniform distribution is a symmetric probability distribution wherein each of some finite whole number
Discrete_uniform_distribution
Type of group representation for locally compact groups
In mathematics, a discrete series representation is an irreducible unitary representation of a locally compact topological group G that is a subrepresentation
Discrete series representation
Discrete_series_representation
Annual ACM-SIAM Symposium on Discrete Algorithms (SODA) is an academic conference in the fields of algorithm design and discrete mathematics. It is considered
Symposium on Discrete Algorithms
Symposium_on_Discrete_Algorithms
Fourier analysis technique applied to sequences
mathematics, the discrete-time Fourier transform (DTFT) is a form of Fourier analysis that is applicable to a sequence of discrete values. The DTFT is
Discrete-time Fourier transform
Discrete-time_Fourier_transform
Fourier-related mathematical transform
A discrete Hartley transform (DHT) is a Fourier-related transform of discrete, periodic data similar to the discrete Fourier transform (DFT), with analogous
Discrete_Hartley_transform
Reconstruction of binary images from a small number of their projections
Discrete tomography focuses on the problem of reconstruction of binary images (or finite subsets of the integer lattice) from a small number of their projections
Discrete_tomography
Method in Itô calculus
respectively, and W t {\displaystyle W_{t}} is the Wiener process. As discrete approximations of continuous processes are typically assessed through comparison
Euler–Maruyama_method
Symmetry describing non-continuous changes in a system
geometry, a discrete symmetry is a symmetry that describes non-continuous changes in a system. For example, a square possesses discrete rotational symmetry
Discrete_symmetry
called a discrete measure (in respect to the Lebesgue measure) if it is concentrated on an at most countable set. The support need not be a discrete set.
Discrete_measure
Theory in psychology
Discrete emotion theory is the claim that there is a small number of core emotions. For example, Silvan Tomkins (1962, 1963) concluded that there are nine
Discrete_emotion_theory
Simple polynomial map exhibiting chaotic behavior
number of individuals K . The logistic map can also be derived from the discretization of the logistic equation for continuous-time population models. The
Logistic_map
Branch of mathematics
Continuous time Fourier series (CTFS) Discrete time Fourier transform (DTFT) Discrete time Fourier series (DTFS) Discrete Fourier transform (DFT) The choice
Fourier_analysis
Technique used in signal processing and data compression
A discrete cosine transform (DCT) expresses a finite sequence of data points in terms of a sum of cosine functions oscillating at different frequencies
Discrete_cosine_transform
Mythological son of Odysseus
Telemachus (/təˈlɛməkəs/ tə-LEM-ə-kəs; Ancient Greek: Τηλέμαχος, romanized: Tēlemakhos, lit. 'far-fighter') is the son of Odysseus and Penelope in Greek
Telemachus
Algorithm that estimates unknowns from a series of measurements over time
G.J. (1977). "Factorization Methods for Discrete Sequential Estimation". Factorization Methods for Discrete Sequential Estimation. Bibcode:1977fmds.book
Kalman_filter
Minimum amount of a physical entity involved in an interaction
can exist only in certain discrete values. Atoms and matter in general are stable because electrons can exist only at discrete energy levels within an atom
Quantum
Discrete-variable probability distribution
possible x {\displaystyle x} . Discretization is the process of converting a continuous random variable into a discrete one. There are three major distributions
Probability_mass_function
Industrial activity producing goods for sale using labor and machines
noted year according to World Bank: Business portal Manufacturing portal Discrete manufacturing Outline of manufacturing Process manufacturing 3D printing
Manufacturing
Equation that describes density changes of a material that is diffusing in a medium
anisotropic tensor diffusion equation, in standard discretization schemes, because direct discretization of the diffusion equation with only first order
Diffusion_equation
Integral expressing the amount of overlap of one function as it is shifted over another
similar to cross-correlation: for real-valued functions, of a continuous or discrete variable, convolution f ∗ g {\displaystyle f*g} differs from cross-correlation
Convolution
In control engineering, a discrete-event dynamic system (DEDS) is a discrete-state, event-driven system of which the state evolution depends entirely on
Discrete-event_dynamic_system
Type of topological group
discrete group is discrete. every quotient of a discrete group is discrete. the product of a finite number of discrete groups is discrete. a discrete
Discrete_group
American multinational technology company
applications. As of the first quarter of 2025, Nvidia held a 92% share of the discrete desktop and laptop GPU market. In the early-to-mid 2000s, the company invested
Nvidia
Concept in abstract algebra
In abstract algebra, a discrete valuation ring (DVR) is a principal ideal domain (PID) with exactly one non-zero maximal ideal. This means a DVR is an
Discrete_valuation_ring
analysis, discrete spline interpolation is a form of interpolation where the interpolant is a special type of piecewise polynomial called a discrete spline
Discrete_spline_interpolation
Branch of numerical analysis
methods. Mortar methods are discretization methods for partial differential equations, which use separate discretization on nonoverlapping subdomains
Numerical methods for partial differential equations
Numerical_methods_for_partial_differential_equations
Numerical method for differential equations
Exponential Euler discretization. For a time discretization ( t ) h , {\displaystyle (t)_{h},} a high-order local linear (HOLL) discretization of the ODE (4
Local_linearization_method
Point of a subset S around which there are no other points of S
up only of isolated points is called a discrete set or discrete point set (see also discrete space). Any discrete subset S of Euclidean space must be countable
Isolated_point
Mathematical term
Saddle point problems arise in the discretization of Stokes flow and in the mixed finite element discretization of Poisson's equation. For positive-definite
Ladyzhenskaya–Babuška–Brezzi condition
Ladyzhenskaya–Babuška–Brezzi_condition
Academic journal
Discrete Analysis is a mathematics journal covering the applications of analysis to discrete structures. Discrete Analysis is an arXiv overlay journal
Discrete_Analysis
Film and video terminology
A crossover is the placement of two or more otherwise discrete fictional characters, settings, or universes into the context of a single story. They can
Crossover_(fiction)
Mathematical model of the time dependence of a point in space
predict certain variables, like in the case of the discretization of Navier–Stokes equations. Discrete dynamical systems are often also called cascades
Dynamical_system
Central computer component that executes instructions
produced in large quantities. This standardization began in the era of discrete transistor mainframes and minicomputers, and has rapidly accelerated with
Central_processing_unit
Fermion discretization with four doublers
staggered fermions (also known as Kogut–Susskind fermions) are a fermion discretization that reduces the number of fermion doublers from sixteen to four. They
Staggered_fermion
Signal representation
frequency domain. A discrete frequency domain is a frequency domain that is discrete rather than continuous. For example, the discrete Fourier transform
Frequency_domain
Description of rail transport modernisation
transport began before the common era. It can be divided into several discrete periods, defined by the principal track material and power used. The Post
History_of_rail_transport
Method of encoding digital data on multiple carrier frequencies
more robust modulation or error coding to those subcarriers. The term discrete multitone modulation (DMT) denotes OFDM-based communication systems that
Orthogonal frequency-division multiplexing
Orthogonal_frequency-division_multiplexing
mortar methods are discretization methods for partial differential equations, which use separate finite element discretization on nonoverlapping subdomains
Mortar_methods
Problem of finding the best feasible solution
whether the variables are continuous or discrete: An optimization problem with discrete variables is known as a discrete optimization, in which an object such
Optimization_problem
Method for numerical differential equations
substitute these discrete elements in lieu of the continuous elements in (2). More precisely, the GDM starts by defining a Gradient Discretization (GD), which
Gradient discretisation method
Gradient_discretisation_method
Set of isolated points in the spectrum of an operator with finite-rank Riesz projectors
In mathematics, specifically in spectral theory, a discrete spectrum of a closed linear operator is defined as the set of isolated points of its spectrum
Discrete spectrum (mathematics)
Discrete_spectrum_(mathematics)
Structure that repeats in time; a novel type or phase of non-equilibrium matter
continuous translational symmetry in space is broken and replaced by the lower discrete symmetry of the periodic crystal. As the laws of physics are symmetrical
Time_crystal
Tessellation of Euclidean space
finite volume methods, finite difference methods, and in general for discretization of parameter spaces. Since the derivatives of field variables can be
Regular_grid
Scientific field of study
only in discrete steps proportional to their frequency. This, along with the photoelectric effect and a complete theory predicting discrete energy levels
Physics
Problem in discrete geometry
In discrete geometry, the Erdős distinct distances problem states that every set of points in the plane has a nearly linear number of distinct distances
Erdős distinct distances problem
Erdős_distinct_distances_problem
Topics referred to by the same term
Wiktionary, the free dictionary. Digital usually refers to something using discrete digits, often binary digits. Digital bank, a form of financial institution
Digital
Mathematical operation in signal processing
In signal processing, multidimensional discrete convolution refers to the mathematical operation between two functions f and g on an n-dimensional lattice
Multidimensional discrete convolution
Multidimensional_discrete_convolution
Solid-state electrically operated switch also used as an amplifier
Databooks Discrete Databook; 1985; Fairchild (now ON Semiconductor) Small-Signal Semiconductors Databook, 1987; Motorola (now ON semiconductor) Discrete Power
Transistor
Analog of the continuous Laplace operator
f {\displaystyle f} . In particular any discrete image, with reasonable presumptions on the discretization process, e.g. assuming band limited functions
Discrete_Laplace_operator
Dynamic discrete choice (DDC) models, also known as discrete choice models of dynamic programming, model an agent's choices over discrete options that
Dynamic_discrete_choice
Pair of positions in a sequence where two elements are out of sorted order
In computer science and discrete mathematics, an inversion in a sequence is a pair of elements that are out of their natural order. Let π {\displaystyle
Inversion (discrete mathematics)
Inversion_(discrete_mathematics)
Machine learning framework
networks is discretization invariance and discretization convergence. Unlike conventional neural networks, which are fixed on the discretization of training
Neural_operators
Partition of Earth's surface into subdivided cells
distinct identifier and represents a fixed-scale region of the space. The discretization of the Latitude/Longitude system is the most popular, and the standard
Discrete_global_grid
Hypothetical quantum of time
A chronon is a proposed quantum of time, that is, a discrete and indivisible "unit" of time as part of a hypothesis that proposes that time is not continuous
Chronon
Mathematical optimization problem restricted to integers
of Karp's 21 NP-complete problems. If some decision variables are not discrete, the problem is known as a mixed-integer programming problem. Integer linear
Integer_programming
Methods for numerical approximations
from the exact solution. Similarly, discretization induces a discretization error because the solution of the discrete problem does not coincide with the
Numerical_analysis
Roleplay involving acting as a different age
DSM-V. This research also discourages thinking of ageplay in terms of discrete pathologized identity categories, but rather as a spectrum of intersecting
Ageplay
Signal used to represent data as a sequence of discrete values
binary digit (bit). Because of this discretization, relatively small changes to the signal levels do not leave the discrete envelope, and as a result are ignored
Digital_signal
American semiconductor manufacturer
Vishay Intertechnology, Inc. is an American manufacturer of discrete semiconductors and passive electronic components founded by Polish-born businessman
Vishay_Intertechnology
In applied mathematics, a discrete Chebyshev transform (abbreviated DCT, DChT, or DTT) is an analog of the discrete Fourier transform for a function of
Discrete_Chebyshev_transform
Collection of random variables
processes are respectively referred to as discrete-time and continuous-time stochastic processes. Discrete-time stochastic processes are considered easier
Stochastic_process
transform Discrete Fourier transform, DFT Fast Fourier transform, a popular implementation of the DFT Discrete cosine transform Modified discrete cosine
List_of_transforms
cost. Accuracy depends on both discretization error and solution error. For discretization error, a given mesh is a discrete approximation of the space,
Types_of_mesh
Mathematical operation
example, in the context of the discrete-time Fourier transform (DTFT). In particular, the DTFT of the product of two discrete sequences is the periodic convolution
Circular_convolution
Branch of graph theory
T-theory is a branch of discrete mathematics dealing with analysis of trees and discrete metric spaces. T-theory originated from a question raised by Manfred
T-theory
Methods for solving differential equations
index h {\displaystyle h} should show the relation to an underlying discretization given by ( x k ) k {\displaystyle \left(x_{k}\right)_{k}} . Note here
Discontinuous_Galerkin_method
Mathematical transform on discrete signals
processing, discrete transforms (or discrete integral transform) are mathematical transforms, often linear transforms, of signals between discrete domains
Discrete_transform
Partition into two separate parts
multicategorical variables as binary variables is called dichotomization. The discretization error inherent in dichotomization is temporarily ignored for modeling
Dichotomy
Method for estimating new data within known data points
within on a triangle or tetrahedron Brahmagupta's interpolation formula Discretization Fractal interpolation Imputation (statistics) Lagrange interpolation
Interpolation
DISCRETIZATION
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Boy/Male
Tamil
Kautilya, Great scholar, Bright
Boy/Male
African, Hindu, Indian
Friends
Girl/Female
Tamil
Goddess Durga, White antelope
Boy/Male
Arabic, Muslim
Banner of Guidance
Girl/Female
Bengali, Gujarati, Hindu, Indian, Jain, Kannada, Marathi, Tamil, Telugu
Victorious
Girl/Female
German
Strong Protection
Boy/Male
Hindu, Indian
Invincible Light
Girl/Female
Sikh
Precious stone
Girl/Female
Hindu, Indian
Strong; Proud
Boy/Male
British, English
From the Estate on the Ledge
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DISCRETIZATION