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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.
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. [1][2] In engineering and science, one often has a number of data points, obtained by sampling or experimentation, which represent ...
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] Given a set of n + 1 data points , with no two the same, a polynomial function is said to interpolate the data if for each .
In mathematics, bilinear interpolation is a method for interpolating functions of two variables (e.g., x and y) using repeated linear interpolation. It is usually applied to functions sampled on a 2D rectilinear grid, though it can be generalized to functions defined on the vertices of (a mesh of) arbitrary convex quadrilaterals.
Nearest neighbor interpolation on a uniform 2D grid (black points). Each coloured cell indicates the area in which all the points have the black point in the cell as their nearest black point. Nearest-neighbor interpolation (also known as proximal interpolation or, in some contexts, point sampling) is a simple method of multivariate ...
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 polynomials of high degree over a set of equispaced interpolation points. It was discovered by Carl David Tolmé Runge (1901 ...
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 polynomial of degree less than n that takes the same value at n given points as a given function.
Multivariate interpolation. In numerical analysis, multivariate interpolation is interpolation on functions of more than one variable (multivariate functions); when the variates are spatial coordinates, it is also known as spatial interpolation. The function to be interpolated is known at given points and the interpolation problem consists of ...