Function approximation
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In general, a function approximation problem asks us to select a function among a Template:Citation needed spanScript error: No such module "Unsubst". that closely matches ("approximates") a Template:Citation needed span in a task-specific way.[1]Template:Better source needed The need for function approximations arises in many branches of applied mathematics, and computer science in particular Template:Why,Script error: No such module "Unsubst". such as predicting the growth of microbes in microbiology.[2] Function approximations are used where theoretical models are unavailable or hard to compute.[2]
One can distinguishScript error: No such module "Unsubst". 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 (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]
Second, the target function, call it g, may be unknown; instead of an explicit formula, only a set of points of the form (x, g(x)) is provided.Script error: No such module "Unsubst". 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 (range or target set) of g is a finite set, one is dealing with a classification problem instead.[4]
To some extent, the different problems (regression, classification, fitness approximation) have received a unified treatment in statistical learning theory, where they are viewed as supervised learning problems.Script error: No such module "Unsubst".
References
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