There are several formal kinds of interpolation, including linear interpolation, polynomial interpolation, and piecewise constant interpolation.

Best Linear Unbiased Interpolation, Distribution, and Extrapolation of Time Series by Related Series Gregory C. Chow and An-loh Lin The Review of Economics and Statistics , pp. 372-375 (4 pages) ...

Polynomial interpolation to analytic functions can be very accurate, depending on the distribution of the interpolation nodes. However, in equispaced nodes and the like, besides being badly ...