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In numerical analysis, polynomial interpolation is the interpolation of a given bivariate data set by the polynomial of lowest possible degree that passes through the points of the dataset. [ 1 ]
A solver based on polynomial interpolation that relies on PEP solvers. A solver based on rational interpolation (NLEIGS). MFN can be used to compute the action of a matrix function on a vector. A restarted Krylov solver.
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 polynomial of degree ≤ n which goes through the given points. Neville's algorithm evaluates this polynomial.
Barnes interpolation; Bilinear interpolation; Bicubic interpolation; Bézier surface; Lanczos resampling; Delaunay triangulation; Bitmap resampling is the application of 2D multivariate interpolation in image processing. Three of the methods applied on the same dataset, from 25 values located at the black dots. The colours represent the ...
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 process or Aitken extrapolation .
Thin plate splines (TPS) are a spline-based technique for data interpolation and smoothing. "A spline is a function defined by polynomials in a piecewise manner." [1] [2] They were introduced to geometric design by Duchon. [3] They are an important special case of a polyharmonic spline. Robust Point Matching (RPM) is a common extension and ...
The simplest interpolation method is to locate the nearest data value, and assign the same value. In simple problems, this method is unlikely to be used, as linear interpolation (see below) is almost as easy, but in higher-dimensional multivariate interpolation, this could be a favourable choice for its speed and simplicity.
For triharmonic , () (where and are the weights and centers of ) is always a sum of total degree 5 polynomials in ,, and divided by the square root of a total degree 8 polynomial. Consider the behavior of these terms on the line x = a + t b {\displaystyle \mathbf {x} =\mathbf {a} +t\mathbf {b} } as t {\displaystyle t} approaches infinity.