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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.
Polynomial interpolation also forms the basis for algorithms in numerical quadrature (Simpson's rule) and numerical ordinary differential equations (multigrid methods). In computer graphics, polynomials can be used to approximate complicated plane curves given a few specified points, for example the shapes of letters in typography.
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 author.As there are often several generations of copies between an extant copy of an ancient text and the original, each handwritten by different scribes, there is a natural tendency for extraneous material to be inserted into such documents over ...
Linear interpolation on a data set (red points) consists of pieces of linear interpolants (blue lines). Linear interpolation on a set of data points (x 0, y 0), (x 1, y 1), ..., (x n, y n) is defined as piecewise linear, resulting from the concatenation of linear segment interpolants between each pair of data points.
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 the problem of approximating the value of a function for a non-given point in some space when given the value of that function in points around ...
Multilinear polynomials are the interpolants of multilinear or n-linear interpolation on a rectangular grid, a generalization of linear interpolation, bilinear interpolation and trilinear interpolation to an arbitrary number of variables. This is a specific form of multivariate interpolation, not to be confused with piecewise linear
Natural neighbor interpolation has also been implemented in a discrete form, which has been demonstrated to be computationally more efficient in at least some circumstances. [5] A form of discrete natural neighbor interpolation has also been developed that gives a measure of interpolation uncertainty. [4]
In digital signal processing, upsampling, expansion, and interpolation are terms associated with the process of resampling in a multi-rate digital signal processing system. Upsampling can be synonymous with expansion , or it can describe an entire process of expansion and filtering ( interpolation ).