 # Interpolation

In numerical mathematics, the term interpolation (Latin: inter = between and polire = to smooth, grind) describes a class of problems and procedures. For given data (e.g. measured values), a continuous function is to be found which maps these data; the so-called interpolant or interpolating. One says then, the function interpolates the data. Simply explained, sometimes only single points of a function are known, but not the analytical description, by which the function could be evaluated at arbitrary points. The goal of the interpolation is therefore to connect the points by a curve, so that the unknown function can be estimated at the intervening points. Also, an interpolation function can be used to approximate a particularly complicated function by a simpler one. There are several solutions for the problem of the interpolation, it must be found thus at the beginning a suitable approach functions. Depending on the starting functions, a different interpolant results. Also the approximation quality depends on the approach of the interpolation. The extrapolation, which is related to the interpolation, deals with the approximation to values which exceed a definition range of given measurement data.