Definition

What is interpolation? Several answers coexist. One of them defines interpolation as an informed estimate of the unknown [1]. We prefer the following — admittedly less concise — definition: model-based recovery of continuous data from discrete data within a known range of abscissas. The reason for this preference is to allow for a clearer distinction between interpolation and extrapolation. The former postulates the existence of a known range where the model applies and asserts that the deterministically recovered continuous data is entirely described by the discrete data, whereas the latter authorizes the use of the model outside of the known range, with the implicit assumption that the model is "good" near data samples, and possibly less good

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All rights of reproduction in any form reserved elsewhere. Finally, the three most important hypotheses for interpolation are:

(1) The underlying data is continuously defined.

(2) Given data samples, it is possible to compute a data value of the underlying continuous function at any abscissa.

(3) The evaluation of the underlying continuous function at the sampling points yields the same value as the data themselves.

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