Function approximation should not be confused with Curve fitting.
In general, a function approximation problem asks us to select a function that closely matches ("approximates") a function in a task-specific way.[1] The need for function approximations arises, for example, predicting the growth of microbes in microbiology.[2] Function approximations are used where theoretical models are unavailable or hard to compute.[2]
First, for known target functions approximation theory is the branch of numerical analysis that investigates how certain known functions (for example, special functions) can be approximated by a specific class of functions (for example, polynomials or rational functions) that often have desirable properties (inexpensive computation, continuity, integral and limit values, etc.).[3]
Secondly, 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 (range or target set) of g is a finite set, one is dealing with a classification problem instead.[4]
