Interpolation

In the mathematical field of numerical analysis, interpolation is a method of constructing new data points within the range of a discrete set of known data points.

In engineering and science, one often has a number of data points, obtained by sampling or experimentation, which represent the values of a function for a limited number of values of the independent variable. It is often required to interpolate (i.e. estimate) the value of that function for an intermediate value of the independent variable. This may be achieved by curve fitting or regression analysis.

A different problem which is closely related to interpolation is the approximation of a complicated function by a simple function. Suppose the formula for some given function is known, but too complex to evaluate efficiently. A few known data points from the original function can be used to create an interpolation based on a simpler function. Of course, when a simple function is used to estimate data points from the original, interpolation errors are usually present; however, depending on the problem domain and the interpolation method used, the gain in simplicity may be of greater value than the resultant loss in accuracy.

There is also another very different kind of interpolation in mathematics, namely the "interpolation of operators". The classical results about interpolation of operators are the Riesz–Thorin theorem and the Marcinkiewicz theorem. There are also many other subsequent results.

Read more about InterpolationExample, Interpolation Via Gaussian Processes, Other Forms of Interpolation, Interpolation in Digital Signal Processing, Related Concepts

Other articles related to "interpolation":

Interpolation - Related Concepts
... In curve fitting problems, the constraint that the interpolant has to go exactly through the data points is relaxed ... It is only required to approach the data points as closely as possible (within some other constraints) ...
Stairstep Interpolation
... In image processing, stairstep interpolation is a general method for interpolating the pixels after enlarging an image ... multiple times in small increments using any interpolation algorithm that is better than nearest-neighbor interpolation, such as bilinear interpolation ... is to interpolate an image by using a bicubic interpolation which increases the image size by no more than 10% (110% of the original size) at a time until the desired size is ...
Television Standards Conversion - Standards Conversion Methods in Common Use - Interfield Interpolation
... Interfield Interpolation is a technique in which new frames are created by blending adjacent frames, rather than repeating a single frame ... is more complex and computationally expensive than linear interpolation, because it requires the interpolator to have knowledge of the preceding and the following frames to produce an intermediate blended frame ... Interpolation can also be used to reduce the number of scanlines in the image by averaging the colour and intensity of pixels on neighbouring lines, a technique ...
Tricubic Interpolation - See Also
... Cubic interpolation Bicubic interpolation Trilinear interpolation. ...
Motion Interpolation - Applications - PC Video Players
... Many video players for computers, include motion interpolation ... WinDVD uses Philips' TrimensionDNM for frame interpolation ... CrystalPlayer uses Motion Morphing MultiSampling for frame interpolation ...