In univariate interpolation, an interpolant is a function L=L(x) which agrees with a particular function f at a set of known points x_0,x_1,x_2,...,x_n and which is used to compute values for f(x) at points x!=x_i, i=0,1,2,...,n.

Modulo a change of notation, the above definition translates verbatim to multivariate interpolation models as well.

Generally speaking, the properties required of the interpolant are the most fundamental designations between various interpolation models. For example, the main difference between the linear and spline interpolation models is that the interpolant of the prior is required merely to be piecewise linear whereas spline interpolants are assumed to be piecewise polynomial and globally smooth.

See also


This entry contributed by Christopher Stover

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Itô, K. (Ed.). "Interpolation." Section 223 (XV.2) in Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, pp. 843-847, 1980.

Cite this as:

Stover, Christopher. "Interpolant." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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