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What is an interpolation?

What is an interpolation? Here are some definitions.

Noun
  1. (music) An abrupt change in elements, with continuation of the first idea.
  2. (mathematics) The process of estimating the value of a function at a point from its values at nearby points.
  3. (computing) The process of including and processing externally-fetched data in a document or program; see interpolate.
  4. That which is introduced or inserted, especially something foreign or spurious.
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Examples
The result keeps the sharpness of bicubic interpolation while smoothing the isophotes to reduce jagged pixelization artifacts.
This can then be developed through fragmentation of the integral component parts and the interpolation of rogue or stray texts.
The interpolation adds nothing to the dramatic situation, which has been swamped by then anyway.
This book is a treatise on infinite series, summation, interpolation and quadrature.
The interpolation of guitars into the duo's sonic soup has been discussed extensively.
All interpolators have a stop method which is called when the interpolation is finished.

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