# 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.

### Other articles related to "interpolation":

Interpolation - Related Concepts
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Stairstep Interpolation
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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 ...