Given a set of distinct points (sometimes referred to as nodal points or nodes) and arbitrary associated function values , the interpolation problem amounts to finding (in this case) a polynomial of degree less than or equal to such that for .
It can be shown that there is one and only one such polynomial. Existence can be shown by explicit construction: suppose one had
Defining the interpolation error byand . In other words, if we assume the ordering , then can actually be outside . For example, if , then . Sometimes, approximating by when is called extrapolation, and interpolation only if , even though an interpolating polynomial is used as approximation.
Living Rev. Relativity 15, (2012), 9
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