In general, afunction approximation problem asks us to select afunction that closely matches ("approximates") a function in a task-specific way.[1][better source needed] The need for function approximations arises, for example, predicting the growth of microbes inmicrobiology.[2] Function approximations are used where theoretical models are unavailable or hard to compute.[2]
First, for known target functionsapproximation theory is the branch ofnumerical analysis that investigates how certain known functions (for example,special functions) can be approximated by a specific class of functions (for example,polynomials orrational functions) that often have desirable properties (inexpensive computation, continuity, integral and limit values, etc.).[3]
Secondly, for example, ifg is an operation on thereal numbers, techniques ofinterpolation,extrapolation,regression analysis, andcurve fitting can be used. If thecodomain (range or target set) ofg is a finite set, one is dealing with aclassification problem instead.[4]
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