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Method for estimating new data within known data points
In the mathematical field of numerical analysis, interpolation is a type of estimation, a method of constructing (finding) new data points based on the
Interpolation
Method of curve fitting
In mathematics, linear interpolation (sometimes lerp) is a method of curve fitting using linear polynomials to construct new data points within the range
Linear_interpolation
Extension of cubic spline interpolation
In mathematics, bicubic interpolation is an extension of cubic spline interpolation (a method of applying cubic interpolation to a data set) for interpolating
Bicubic_interpolation
Topics referred to by the same term
Look up interpolation in Wiktionary, the free dictionary. Interpolation is a method of constructing new data points within the range of a discrete set
Interpolation (disambiguation)
Interpolation_(disambiguation)
Method of interpolating functions on a 2D grid
mathematics, bilinear interpolation is a method for interpolating functions of two variables (e.g., x and y) using repeated linear interpolation. It is usually
Bilinear_interpolation
Method for interpolating the pixels after enlarging an image
using any interpolation algorithm that is better than nearest-neighbor interpolation such as; bilinear interpolation, and bicubic interpolation. A common
Stairstep_interpolation
Variant of cubic interpolation that preserves monotonicity
mathematical field of numerical analysis, monotone cubic interpolation is a variant of cubic interpolation that preserves monotonicity of the data set being
Monotone_cubic_interpolation
Method of multivariate interpolation
Nearest-neighbor interpolation (also known as proximal interpolation or, in some contexts, point sampling) is a simple method of multivariate interpolation in one
Nearest-neighbor interpolation
Nearest-neighbor_interpolation
Topics referred to by the same term
Interpolation theorem may refer to: Craig interpolation in logic Marcinkiewicz interpolation theorem about non-linear operators Riesz–Thorin interpolation
Interpolation_theorem
Mathematical method
In the mathematical field of numerical analysis, spline interpolation is a form of interpolation where the interpolant is a special type of piecewise polynomial
Spline_interpolation
Form of interpolation
In numerical analysis, polynomial interpolation is the interpolation of a given data set by the polynomial of lowest possible degree that passes through
Polynomial_interpolation
Rerecording music to use in another recording
In popular music, interpolation is the recreation of a musical element, such as a melody or lyric, in a new composition. Unlike sampling, which is the
Interpolation_(popular_music)
Form of video processing
Motion interpolation, motion-compensated frame interpolation (MCFI), or frame generation, is a form of video processing in which intermediate film, video
Motion_interpolation
Polynomials used for interpolation
Reed–Solomon error correction in coding theory. For equispaced nodes, Lagrange interpolation is susceptible to Runge's phenomenon of large oscillation. Lagrange
Lagrange_polynomial
Polynomial interpolation using derivative values
interpolation, named after Charles Hermite, is a method of polynomial interpolation, which generalizes Lagrange interpolation. Lagrange interpolation
Hermite_interpolation
Visual examples of techniques for image scaling
original image. Orchard, M.T.; Li, Xin (September 2000). New Edge Directed Interpolation (PDF). Internation Conference on Image Processing. Proceedings of 2000
Comparison gallery of image scaling algorithms
Comparison_gallery_of_image_scaling_algorithms
Replacing placeholders in a string with values
In computer programming, string interpolation (or variable interpolation, variable substitution, or variable expansion) is the process of evaluating a
String_interpolation
Addition of non authorial text
An interpolation, in relation to literature and especially ancient manuscripts, is an entry or passage in a text that was not written by the original
Interpolation_(manuscripts)
Method of solving equations
In numerical analysis, inverse quadratic interpolation is a root-finding algorithm, meaning that it is an algorithm for solving equations of the form
Inverse quadratic interpolation
Inverse_quadratic_interpolation
Signal (re-)construction algorithm
The Whittaker–Shannon interpolation formula or sinc interpolation is a method to construct a continuous-time bandlimited function from a sequence of real
Whittaker–Shannon interpolation formula
Whittaker–Shannon_interpolation_formula
Method of multivariate interpolation on a 3-dimensional regular grid
Trilinear interpolation is a method of multivariate interpolation on a 3-dimensional regular grid. It approximates the value of a function at an intermediate
Trilinear_interpolation
fundamental lemma of interpolation theory is a lemma that establishes the relationship between different methods of interpolation in Banach spaces. The
Fundamental lemma of interpolation theory
Fundamental_lemma_of_interpolation_theory
Theorem in mathematical logic
In mathematical logic, Craig's interpolation theorem is a result about the relationship between different logical theories. Roughly stated, the theorem
Craig_interpolation
In numerical analysis, transfinite interpolation is a means to construct functions over a planar domain in such a way that they match a given function
Transfinite_interpolation
Function used in computer graphics
In geometry, spherical linear interpolation, commonly abbreviated slerp, is a function which interpolates between two points on a sphere, such that spherical
Spherical linear interpolation
Spherical_linear_interpolation
Searching algorithm
Interpolation search is an algorithm for searching for a key in an array that has been ordered by numerical values assigned to the keys (key values).
Interpolation_search
Interpolation with trigonometric polynomials
In mathematics, trigonometric interpolation is interpolation with trigonometric polynomials. Interpolation is the process of finding a function which goes
Trigonometric_interpolation
Vector space in mathematics
In the field of mathematical analysis, an interpolation space is a space which lies "in between" two other Banach spaces. The main applications are in
Interpolation_space
Interpolation on functions of more than one variable
In numerical analysis, multivariate interpolation or multidimensional interpolation is interpolation on multivariate functions, having more than one variable
Multivariate_interpolation
Inequality in mathematical analysis
In the field of mathematical analysis, an interpolation inequality is an inequality of the form ‖ u 0 ‖ 0 ≤ C ‖ u 1 ‖ 1 α 1 ‖ u 2 ‖ 2 α 2 … ‖ u n ‖ n
Interpolation_inequality
Method of spatial interpolation
Natural-neighbor interpolation or Sibson interpolation is a method of spatial interpolation, developed by Robin Sibson. The method is based on Voronoi
Natural-neighbor interpolation
Natural-neighbor_interpolation
Cubic function used for interpolation
corresponding domain interval. Cubic Hermite splines are typically used for interpolation of numeric data specified at given argument values x 1 , x 2 , … , x
Cubic_Hermite_spline
Surface-approximation method
In the mathematical subfield numerical analysis, tricubic interpolation is a method for obtaining values at arbitrary points in 3D space of a function
Tricubic_interpolation
Biological theory
The Interpolation Theory, also known as the Intercalation Theory or the Antithetic Theory, is a theory that attempts to explain the origin of the alternation
Interpolation_theory
Sorting algorithm in computer science
Interpolation sort (or histogram sort) is a sorting algorithm that uses an interpolation formula to divide and conquer. It is a variant of bucket sort
Interpolation_sort
Interpolation technique for surface shading
computer graphics, Phong shading, Phong interpolation, or normal-vector interpolation shading is an interpolation technique for surface shading invented
Phong_shading
Interpolation method in computer graphics
Gouraud shading (/ɡuːˈroʊ/ goo-ROH), named after Henri Gouraud, is an interpolation method used in computer graphics to produce continuous shading of surfaces
Gouraud_shading
Color reconstruction algorithm
filter array (CFA) such as a Bayer filter. It is also known as CFA interpolation or debayering. Most modern digital cameras acquire images using a single
Demosaicing
Changing the resolution of a digital image
include New Edge-Directed Interpolation (NEDI), Edge-Guided Image Interpolation (EGGI), Iterative Curvature-Based Interpolation (ICBI), and Directional
Image_scaling
American singer-songwriter (born 2002)
Stella Lefkofsky (born August 13, 2002), better known by her stage name Stella Lefty, is an American singer-songwriter. Her 2026 country-pop single "Boston"
Stella_Lefty
Failure of convergence in interpolation
that occurs when using polynomial interpolation with polynomials of high degree over a set of equispaced interpolation points. It was discovered by Carl
Runge's_phenomenon
In the context of live-action and computer animation, interpolation is inbetweening, or filling in frames between the key frames. It typically calculates
Interpolation (computer graphics)
Interpolation_(computer_graphics)
Sufficiency theorem for reconstructing signals from samples
an interpolation formula and its proof was unclear and contained errors. The theorem may also be referred to as the cardinal theorem of interpolation. Sampling
Nyquist–Shannon sampling theorem
Nyquist–Shannon_sampling_theorem
Algorithm used for polynomial interpolation
Aitken interpolation is an algorithm used for polynomial interpolation that was derived by the mathematician Alexander Aitken. It is similar to Neville's
Aitken_interpolation
Second-order polynomial interpolation formula
Brahmagupta's interpolation formula is a second-order polynomial interpolation formula developed by the Indian mathematician and astronomer Brahmagupta
Brahmagupta's interpolation formula
Brahmagupta's_interpolation_formula
Family of interpolation and clamping functions
Smoothstep is a family of sigmoid-like interpolation and clamping functions commonly used in computer graphics, video game engines, and machine learning
Smoothstep
Method of estimating the median of a population
Pareto interpolation is a method of estimating the median and other properties of a population that follows a Pareto distribution. It is used in economics
Pareto_interpolation
Unrelated material inserted between two logically succeeding functions
For music of the Classical period, "interpolation" is defined in the context of a musical sentence or period as "unrelated material inserted between two
Interpolation (classical music)
Interpolation_(classical_music)
Method in approximation theory
Radial basis function (RBF) interpolation is an advanced method in approximation theory for constructing high-order accurate interpolants of unstructured
Radial basis function interpolation
Radial_basis_function_interpolation
In mathematics, mimetic interpolation is a method for interpolating differential forms. In contrast to other interpolation methods, which estimate a field
Mimetic_interpolation
Mathematical theory by discovered by Józef Marcinkiewicz
mathematics, particularly in functional analysis, the Marcinkiewicz interpolation theorem, discovered by Józef Marcinkiewicz (1939), is a result bounding
Marcinkiewicz interpolation theorem
Marcinkiewicz_interpolation_theorem
Directional cubic convolution interpolation (DCCI) is an edge-directed image scaling algorithm created by Dengwen Zhou and Xiaoliu Shen. By taking into
Directional cubic convolution interpolation
Directional_cubic_convolution_interpolation
Concept in machine learning
in classical machine learning. The increase usually occurs near the interpolation threshold, where the number of parameters is the same as the number
Double_descent
Mathematical framework
functional connections (TFC) is a mathematical framework for functional interpolation. It provides a method for deriving a functional—a function that operates
Theory of functional connections
Theory_of_functional_connections
Root-finding algorithm
combining the bisection method, the secant method and inverse quadratic interpolation. It has the reliability of bisection but it can be as quick as some
Brent's_method
Discrete analog of a derivative
equation, named after Isaac Newton; in essence, it is the Gregory–Newton interpolation formula (named after Isaac Newton and James Gregory), first published
Finite_difference
Type of image blur produced by a Gaussian function
In image processing, a Gaussian blur (also known as Gaussian smoothing) is the result of blurring an image by a Gaussian function (named after mathematician
Gaussian_blur
Animation technique that creates transitions between motions
Motion interpolation is a programming technique in data-driven character animation that creates transitions between example motions and interpolates new
Motion interpolation (computer graphics)
Motion_interpolation_(computer_graphics)
Color filter array
image edges. Pattern recognition interpolation, adaptive color plane interpolation, and directionally weighted interpolation all attempt to prevent zippering
Bayer_filter
Term in Biblical studies
Western non-interpolations is a term coined by F. J. A. Hort for certain phrases that are absent in the Western text-type of New Testament manuscripts
Western_non-interpolations
Technique in signal processing
fraction of the sampling interval. It is often used also for multivariate interpolation, for example to resize or rotate a digital image. It has been considered
Lanczos_resampling
Mathematical expression
an interpolation polynomial for a given set of data points. The Newton polynomial is sometimes called Newton's divided differences interpolation polynomial
Newton_polynomial
Data processing technique
Barnes interpolation, named after Stanley L. Barnes, is the interpolation of unevenly spread data points from a set of measurements of an unknown function
Barnes_interpolation
Theorem in mathematical analysis
and in particular in mathematical analysis, the Gagliardo–Nirenberg interpolation inequality is a result in the theory of Sobolev spaces that relates
Gagliardo–Nirenberg interpolation inequality
Gagliardo–Nirenberg_interpolation_inequality
South African-Ethiopian-Norwegian hip hop duo
have released eight albums as of 2018, and became known for their 2007 interpolation of the 1967 song "Beggin'" by The Four Seasons. They took their name
Madcon
Successive parabolic interpolation is a technique for finding the extremum (minimum or maximum) of a continuous unimodal function by successively fitting
Successive parabolic interpolation
Successive_parabolic_interpolation
Character in the Hindu epic Ramayana
Jabali (Sanskrit: जाबालि, romanized: Jābāli) is a character in the ancient Indian epic Ramayana. A learned Brahmin priest and an advisor of King Dasharatha
Jabali
American singer and songwriter (born 1981)
extensively made use of four-on-the-floor beats and pulsating synths, with interpolations of queer and Black dance music pioneers. Cowboy Carter was conceived
Beyoncé
Statistical method of dividing data into equal-sized intervals for analysis
linear interpolation between data points, and differ only in how the index h used to choose the point along the piecewise linear interpolation curve,
Quantile
Methods for numerical approximations
biology. Before modern computers, numerical methods often relied on hand interpolation formulas, using data from large printed tables. Since the mid-20th century
Numerical_analysis
Array that replaces runtime computation with a simpler array indexing operation
precision, lowering that precision may shrink the universe enough, and then interpolation can be used to correct for the error due to precision loss. For a trivial
Lookup_table
2026 studio album by Madonna
structured like a continuous DJ mix and includes several samples and interpolations. Its main themes are freedom, escapism, self-realization, grief, and
Confessions_II
2026 studio album by Tinashe
a little hint of country." "Nobody Wanna Dance Anymore" contains an interpolation of "Chillin" (2009), written by Olubowale Akintimehin, Gary De Carlo
Popstar_(Tinashe_album)
Problem in complex analysis
\ldots ,z_{n}} in D {\displaystyle \mathbb {D} } , the Nevanlinna–Pick interpolation problem is to find a holomorphic function φ {\displaystyle \varphi }
Nevanlinna–Pick_interpolation
Type of cryptanalytic attack
In cryptography, an interpolation attack is a type of cryptanalytic attack against block ciphers. After the two attacks, differential cryptanalysis and
Interpolation_attack
Formula in matrix theory
matrix theorem (named after J. J. Sylvester) or Lagrange−Sylvester interpolation expresses an analytic function f (A) of a matrix A as a polynomial in
Sylvester's_formula
Polynomial sequence
In mathematics, the Hermite polynomials are a classical orthogonal polynomial sequence. The polynomials arise in: signal processing as Hermitian wavelets
Hermite_polynomials
Upscaling filters for pixel art graphics
uses either bicubic or bilinear interpolation as the fallback interpolation method. Another edge-directed interpolation filter. Works by minimizing a cost
Pixel-art_scaling_algorithms
2026 studio album by Isaiah Rashad
It's Been Awful (stylized in all caps) is the third studio album by American rapper Isaiah Rashad. It was released through Top Dawg Entertainment (TDE)
It's_Been_Awful
Type of deterministic method for multivariate interpolation
weighting (IDW) is a type of deterministic method for multivariate interpolation with a known homogeneously scattered set of points. The assigned values
Inverse_distance_weighting
2026 studio album by JPEGMafia
Experimental Rap (stylized in all caps) is the sixth studio album by American rapper and record producer JPEGMafia. It was released through AWAL on May
Experimental_Rap_(album)
Texts regarded as part of the Bible
tradition. Two manuscripts exist—a longer Greek manuscript with Christian interpolations and a shorter Slavonic version. There is some uncertainty about which
Biblical_canon
Representation or imitation of a person or thing
Chopped and screwed Contrafact list Contrafactum Cover version DJ mix Interpolation Medley Music mashup Music plagiarism Musical quotation Nightcore Parody
Simulacrum
Algorithms for zeros of functions
in the neighborhood of the root. Many root-finding processes work by interpolation. This consists in using the last computed approximate values of the
Root-finding_algorithm
Open source game engine
for 2D and 3D video games made with Godot 3. Features include physics interpolation in 3D, asynchronous shader compilation, and more. Godot 3.x was placed
Godot_(game_engine)
2001 live album by Jay-Z with the Roots
an interpolation of "I Want You Back", written by Berry Gordy, Alfonso Mizell, Freddie Perren, and Deke Richards. "Takeover" contains interpolations of:
MTV_Unplugged_(Jay-Z_album)
In mathematics, Thiele's interpolation formula is a formula that defines a rational function f ( x ) {\displaystyle f(x)} from a finite set of inputs
Thiele's interpolation formula
Thiele's_interpolation_formula
English polymath (1642–1727)
regarded as "the single most significant contributor to finite difference interpolation", with many formulas created by Newton. He was the first to state Bézout's
Isaac_Newton
2025 studio album by Taylor Swift
reflects on both of their past relationships. "Father Figure" contains an interpolation of the 1987 song "Father Figure" by the singer-songwriter George Michael
The_Life_of_a_Showgirl
1966 song by Charles Aznavour
"Parce que tu crois" (French pronunciation: [paʁs kə ty kʁwa]; transl. "Because You Believe") is a song by Armenian-French singer Charles Aznavour. It
Parce_que_tu_crois
Compression method for digital images
interpolant. Fractal interpolation maintains geometric detail very well compared to traditional interpolation methods like bilinear interpolation and bicubic interpolation
Fractal_compression
Mathematical function defined piecewise by polynomials
polynomials. In interpolating problems, spline interpolation is often preferred to polynomial interpolation because it yields similar results, even when
Spline_(mathematics)
Image processing methods
multivariate interpolation: Nearest-neighbor interpolation linear interpolation bilinear interpolation cubic interpolation bicubic interpolation Bézier surface
Video_post-processing
American rapper and producer (born 1969)
hop, and for relying excessively on guest appearances, samples, and interpolations of past hits. For example, in a 1997 review of No Way Out for Billboard
Sean_Combs
Academic journal
in: computation, function theory, functional analysis, interpolation spaces and interpolation of operators, numerical analysis, space of functions, special
Constructive_Approximation
Reuse of sound recording in another recording
Instead of sampling, artists may recreate a recording, a process known as interpolation. This requires only the permission of the owners of the musical content
Sampling_(music)
Search algorithm used in sorted arrays
likely to be located near the end of the array. A common interpolation function is linear interpolation. If A {\displaystyle A} is the array, L , R {\displaystyle
Binary_search
This article lists common shading algorithms used in computer graphics. These techniques can be combined with any illumination model: Flat shading Gouraud
List of common shading algorithms
List_of_common_shading_algorithms
Theorem in mathematical analysis
interpolation theorem, introduced by Sarason (1967), is a generalization of the Caratheodory interpolation theorem and Nevanlinna–Pick interpolation.
Sarason_interpolation_theorem
Constants related to interpolation errors
, b ] {\displaystyle [a,\,b]} containing all the interpolation nodes. The process of interpolation maps the function f {\displaystyle f} to a polynomial
Lebesgue_constant
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