# Category: Interpolation

Hermite interpolation
In numerical analysis, Hermite interpolation, named after Charles Hermite, is a method of polynomial interpolation, which generalizes Lagrange interpolation. Lagrange interpolation allows computing a
Runge's phenomenon
In the mathematical field of numerical analysis, Runge's phenomenon (German: [ˈʁʊŋə]) is a problem of oscillation at the edges of an interval that occurs when using polynomial interpolation with polyn
Hermite spline
In the mathematical subfield of numerical analysis, a Hermite spline is a spline curve where each polynomial of the spline is in Hermite form.
Motion interpolation
Motion interpolation or motion-compensated frame interpolation (MCFI) is a form of video processing in which intermediate animation frames are generated between existing ones by means of interpolation
Brahmagupta's interpolation formula
Brahmagupta's interpolation formula is a second-order polynomial interpolation formula developed by the Indian mathematician and astronomer Brahmagupta (598–668 CE) in the early 7th century CE. The Sa
Unisolvent functions
In mathematics, a set of n functions f1, f2, ..., fn is unisolvent (meaning "uniquely solvable") on a domain Ω if the vectors are linearly independent for any choice of n distinct points x1, x2 ... xn
Bézier curve
A Bézier curve (/ˈbɛz.i.eɪ/ BEH-zee-ay) is a parametric curve used in computer graphics and related fields. A set of discrete "control points" defines a smooth, continuous curve by means of a formula.
De Boor's algorithm
In the mathematical subfield of numerical analysis de Boor's algorithm is a polynomial-time and numerically stable algorithm for evaluating spline curves in B-spline form. It is a generalization of de
Kochanek–Bartels spline
In mathematics, a Kochanek–Bartels spline or Kochanek–Bartels curve is a cubic Hermite spline with tension, bias, and continuity parameters defined to change the behavior of the tangents. Given n + 1
Nearest-neighbor interpolation
Nearest-neighbor interpolation (also known as proximal interpolation or, in some contexts, point sampling) is a simple method of multivariate interpolation in one or more dimensions. Interpolation is
Simple rational approximation
Simple rational approximation (SRA) is a subset of interpolating methods using rational functions. Especially, SRA interpolates a given function with a specific rational function whose poles and zeros
Hierarchical RBF
In computer graphics, a hierarchical RBF is an interpolation method based on Radial basis functions (RBF). Hierarchical RBF interpolation has applications in the construction of shape models in 3D com
Transfinite 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 on the boundary. This method is applied in geomet
Barnes interpolation
Barnes interpolation, named after Stanley L. Barnes, is the interpolation of unevenly spread data points from a set of measurements of an unknown function in two dimensions into an analytic function o
Interpolation
In the mathematical field of numerical analysis, interpolation is a type of estimation, a method of constructing (finding) new data points based on the range of a discrete set of known data points. In
Polynomial interpolation
In numerical analysis, polynomial interpolation is the interpolation of a given data set by the polynomial of lowest possible degree that passes through the points of the dataset. Given a set of n + 1
Regression-kriging
In applied statistics and geostatistics, regression-kriging (RK) is a spatial prediction technique that combines a regression of the dependent variable on auxiliary variables (such as parameters deriv
Multivariate interpolation
In numerical analysis, multivariate interpolation is interpolation on functions of more than one variable; when the variates are spatial coordinates, it is also known as spatial interpolation. The fun
Variation diminishing property
In mathematics, the variation diminishing property of certain mathematical objects involves diminishing the number of changes in sign (positive to negative or vice versa).
A radial basis function (RBF) is a real-valued function whose value depends only on the distance between the input and some fixed point, either the origin, so that , or some other fixed point , called
Curve-fitting compaction
Curve-fitting compaction is data compaction accomplished by replacing data to be stored or transmitted with an analytical expression. Examples of curve-fitting compaction consisting of discretization
Mimetic interpolation
In mathematics, mimetic interpolation is a method for interpolating differential forms. In contrast to other interpolation methods, which estimate a field at a location given its values on neighboring
Newton polynomial
In the mathematical field of numerical analysis, a Newton polynomial, named after its inventor Isaac Newton, is an interpolation polynomial for a given set of data points. The Newton polynomial is som
Regionalized variable theory
Regionalized variable theory (RVT) is a geostatistical method used for interpolation in space. The concept of the theory is that interpolation from points in space should not be based on a smooth cont
Non-uniform rational B-spline
Non-uniform rational basis spline (NURBS) is a mathematical model using basis splines (B-splines) that is commonly used in computer graphics for representing curves and surfaces. It offers great flexi
Cubic Hermite spline
In numerical analysis, a cubic Hermite spline or cubic Hermite interpolator is a spline where each piece is a third-degree polynomial specified in Hermite form, that is, by its values and first deriva
Thiele's interpolation formula
In mathematics, Thiele's interpolation formula is a formula that defines a rational function from a finite set of inputs and their function values . The problem of generating a function whose graph pa
In polynomial interpolation of two variables, the Padua points are the first known example (and up to now the only one) of a unisolvent point set (that is, the interpolating polynomial is unique) with
Polyharmonic spline
In applied mathematics, polyharmonic splines are used for function approximation and data interpolation. They are very useful for interpolating and fitting scattered data in many dimensions. Special c
Sarason interpolation theorem
In mathematics complex analysis, the Sarason interpolation theorem, introduced by Sarason, is a generalization of the and Nevanlinna–Pick interpolation.
Motion interpolation (computer graphics)
Motion interpolation is a programming technique in data-driven character animation that creates transitions between example motions and extrapolates new motions. Example motions are often created thro
Identifiability analysis
Identifiability analysis is a group of methods found in mathematical statistics that are used to determine how well the parameters of a model are estimated by the quantity and quality of experimental
Spline interpolation
In the mathematical field of numerical analysis, spline interpolation is a form of interpolation where the interpolant is a special type of piecewise polynomial called a spline. That is, instead of fi
Trigonometric interpolation
In mathematics, trigonometric interpolation is interpolation with trigonometric polynomials. Interpolation is the process of finding a function which goes through some given data points. For trigonome
Radial basis function interpolation
Radial basis function (RBF) interpolation is an advanced method in approximation theory for constructing high-order accurate interpolants of unstructured data, possibly in high-dimensional spaces. The
Neville's algorithm
In mathematics, Neville's algorithm is an algorithm used for polynomial interpolation that was derived by the mathematician Eric Harold Neville in 1934. Given n + 1 points, there is a unique polynomia
Abel–Goncharov interpolation
In mathematics, Abel–Goncharov interpolation determines a polynomial such that various higher derivatives are the same as those of a given function at given points. It was introduced by Whittaker and
Birkhoff interpolation
In mathematics, Birkhoff interpolation is an extension of polynomial interpolation. It refers to the problem of finding a polynomial p of degree d such that certain derivatives have specified values a
Polynomial and rational function modeling
In statistical modeling (especially process modeling), polynomial functions and rational functions are sometimes used as an empirical technique for curve fitting.
Aitken interpolation
Aitken interpolation is an algorithm used for polynomial interpolation that was derived by the mathematician Alexander Aitken. It is similar to Neville's algorithm. See also Aitken's delta-squared pro
Slerp
In computer graphics, Slerp is shorthand for spherical linear interpolation, introduced by Ken Shoemake in the context of quaternion interpolation for the purpose of animating 3D rotation. It refers t
Nevanlinna–Pick interpolation
In complex analysis, given initial data consisting of points in the complex unit disc and target data consisting of points in , the Nevanlinna–Pick interpolation problem is to find a holomorphic funct
Linear interpolation
In mathematics, linear interpolation is a method of curve fitting using linear polynomials to construct new data points within the range of a discrete set of known data points.
Kriging
In statistics, originally in geostatistics, kriging or Kriging, also known as Gaussian process regression, is a method of interpolation based on Gaussian process governed by prior covariances. Under s
Monotone cubic interpolation
In the mathematical field of numerical analysis, monotone cubic interpolation is a variant of cubic interpolation that preserves monotonicity of the data set being interpolated. Monotonicity is preser
Numerical smoothing and differentiation
No description available.
Extrapolation
In mathematics, extrapolation is a type of estimation, beyond the original observation range, of the value of a variable on the basis of its relationship with another variable. It is similar to interp
B-spline
In the mathematical subfield of numerical analysis, a B-spline or basis spline is a spline function that has minimal support with respect to a given degree, smoothness, and domain partition. Any splin
Markov chain geostatistics
Markov chain geostatistics uses Markov chain spatial models, simulation algorithms and associated spatial correlation measures (e.g., transiogram) based on the Markov chain random field theory, which
Perfect spline
In the mathematical subfields function theory and numerical analysis, a univariate polynomial spline of order is called a perfect spline if its -th derivative is equal to or between knots and changes
Spline (mathematics)
In mathematics, a spline is a special function defined piecewise by polynomials.In interpolating problems, spline interpolation is often preferred to polynomial interpolation because it yields similar
Gal's accurate tables
Gal's accurate tables is a method devised by Shmuel Gal to provide accurate values of special functions using a lookup table and interpolation. It is a fast and efficient method for generating values
Interpolation (computer graphics)
In the context of live-action and computer animation, interpolation is inbetweening, or filling in frames between the key frames. It typically calculates the in-between frames through use of (usually)
Discrete spline interpolation
In the mathematical field of numerical analysis, discrete spline interpolation is a form of interpolation where the interpolant is a special type of piecewise polynomial called a discrete spline. A di
Curve fitting
Curve fitting is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, possibly subject to constraints. Curve fitting can involve either inte
Lagrange polynomial
In numerical analysis, the Lagrange interpolating polynomial is the unique polynomial of lowest degree that interpolates a given set of data. Given a data set of coordinate pairs with the are called n
Lebesgue constant
In mathematics, the Lebesgue constants (depending on a set of nodes and of its size) give an idea of how good the interpolant of a function (at the given nodes) is in comparison with the best polynomi
Linear predictive analysis
Linear predictive analysis is a simple form of first-order extrapolation: if it has been changing at this rate then it will probably continue to change at approximately the same rate, at least in the