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For a given set of points in space, a Voronoi diagram is a decomposition of space into cells, one for each given point, so that anywhere in space, the closest given point is inside the cell. This is equivalent to nearest neighbor interpolation, by assigning the function value at the given point to all the points inside the cell. [ 3 ]
A sound choice of which extrapolation method to apply relies on a priori knowledge of the process that created the existing data points. Some experts have proposed the use of causal forces in the evaluation of extrapolation methods. [2] Crucial questions are, for example, if the data can be assumed to be continuous, smooth, possibly periodic, etc.
The purple-shaded region is the new Voronoi cell, after inserting the point to be interpolated (black dot). The weights represent the intersection areas of the purple-cell with each of the seven surrounding cells. Natural-neighbor interpolation or Sibson interpolation is a method of spatial interpolation, developed by Robin Sibson. [1]
Spigot algorithm — algorithms that can compute individual digits of a real number; Approximations of π: Liu Hui's π algorithm — first algorithm that can compute π to arbitrary precision; Leibniz formula for π — alternating series with very slow convergence; Wallis product — infinite product converging slowly to π/2
An example of Richardson extrapolation method in two dimensions. In numerical analysis , Richardson extrapolation is a sequence acceleration method used to improve the rate of convergence of a sequence of estimates of some value A ∗ = lim h → 0 A ( h ) {\displaystyle A^{\ast }=\lim _{h\to 0}A(h)} .
Furthermore, you only need to do O(n) extra work if an extra point is added to the data set, while for the other methods, you have to redo the whole computation. Another method is preferred when the aim is not to compute the coefficients of p ( x ), but only a single value p ( a ) at a point x = a not in the original data set.
In 1971, Rolland Hardy developed a method of interpolating scattered data using interpolants of the form () = = ‖ ‖ +. This is interpolation using a basis of shifted multiquadric functions, now more commonly written as φ ( r ) = 1 + ( ε r ) 2 {\displaystyle \varphi (r)={\sqrt {1+(\varepsilon r)^{2}}}} , and is the first instance of radial ...
Schemes defined for scattered data on an irregular grid are more general. They should all work on a regular grid, typically reducing to another known method. Nearest-neighbor interpolation; Triangulated irregular network-based natural neighbor