Interpolant

In univariate interpolation, an interpolant is a function  which agrees with a particular function  at a set of known points  and which is used to compute values for  at points , .

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.

REFERENCES:

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