Function approximation
In general, a function approximation problem asks us to select a function among a well-defined class that closely matches a target function in a task-specific way. The need for function approximations arises in many branches of applied mathematics, and computer science in particular.
One can distinguish two major classes of function approximation problems:
First, for known target functions approximation theory is the branch of numerical analysis that investigates how certain known functions can be approximated by a specific class of functions that often have desirable properties.
Second, the target function, call it g, may be unknown; instead of an explicit formula, only a set of points of the form is provided. Depending on the structure of the domain and codomain of g, several techniques for approximating g may be applicable. For example, if g is an operation on the real numbers, techniques of interpolation, extrapolation, regression analysis, and curve fitting can be used. If the codomain of g is a finite set, one is dealing with a classification problem instead.
To some extent, the different problems have received a unified treatment in statistical learning theory, where they are viewed as supervised learning problems.
