Function approximation

A function approximation problem asks us to select a function among a well-defined class that closely matches (approximates) a target function.

There are two major classes of function approximation problems. For known target functions approximation theory investigates how certain known functions can be approximated by a specific class of functions (for example, polynomials or rational functions).

In the second class of problems, the target function (say f) may be unknown. Instead of an explicit formula, only a set of points of the form (x, g(x)) is provided.