Interpolation

:This article is about interpolation in mathematics. See also interpolation (music) and interpolation (manuscripts).

Related Topics:
Interpolation (music) - Interpolation (manuscripts)

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In the mathematical subfield of numerical analysis, interpolation is a method of constructing new data points from a discrete set of known data points.

Related Topics:
Mathematical - Numerical analysis - Discrete - Set

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In engineering and science one often has a number of data points, as obtained by sampling or some experiment, and tries to construct a function which closely fits those data points. This is called curve fitting. Interpolation is a specific case of curve fitting, in which the function must go exactly through the data points.

Related Topics:
Engineering - Science - Sampling - Experiment - Curve fitting

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A different problem which is closely related to interpolation is the approximation of a complicated function by a simple function. Suppose we know the function but it is too complex to evaluate efficiently. Then we could pick a few known data points from the complicated function and try to interpolate those data points to construct a simpler function. Of course when using the simple function to calculate new data points we usually do not receive the same result as when using the original function, but depending on the problem domain and the interpolation method used the gain in simplicity might offset the error.

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It should be mentioned that there is also another very different kind of interpolation in mathematics, namely the ``interpolation of operators". The classical results about

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interpolation of operators are the Riesz-Thorin theorem

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and the Marcinkiewicz theorem and there are many other subsequent

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results.

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