Search results
Results from the WOW.Com Content Network
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 .
Linear interpolation on a set of data points (x0, y0), (x1, y1), ..., (xn, yn) is defined as piecewise linear, resulting from the concatenation of linear segment interpolants between each pair of data points. This results in a continuous curve, with a discontinuous derivative (in general), thus of differentiability class .
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.
A simple example of an interpolation inequality — one in which all the u k are the same u, but the norms ‖·‖ k are different — is Ladyzhenskaya's inequality for functions :, which states that whenever u is a compactly supported function such that both u and its gradient ∇u are square integrable, it follows that the fourth power of u is integrable and [2]
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 ...
The projected points, in red, are the Chebyshev nodes. In numerical analysis, Chebyshev nodes are a set of specific real algebraic numbers, used as nodes for polynomial interpolation. They are the projection of equispaced points on the unit circle onto the real interval the diameter of the circle. The Chebyshev nodes of the first kind, also ...