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.)

for unknown target function 𝑔(𝑥); only a set of points of the form (𝑥, 𝑔(𝑥)) is provided. Depending on the structure of the domain and codomain of 𝑔, several techniques for approximating g may be applicable. For example:

• if the codomain of 𝑔 is the set of real numbers, one is dealing with interpolation, extrapolation, regression analysis, and curve fitting
• if the codomain of 𝑔 is a finite set, one is dealing with classification