Function approximation

Several progressively more accurate approximations of the step function

An asymmetrical Gaussian function fit to a noisy curve using regression

In general, a function approximation problem asks us to select a function that closely matches ("approximates") a function in a task-specific way.<ref>Template:Cite book</ref>Template:Better source needed The need for function approximations arises, for example, predicting the growth of microbes in microbiology.<ref name=":0">Template:Cite journal</ref> Function approximations are used where theoretical models are unavailable or hard to compute.<ref name=":0">Template:Cite journal</ref>

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.).<ref>Template:Cite book</ref>

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.<ref>Template:Cite journal</ref>

See also

• Approximation theory
• Fitness approximation
• Kriging
• Least squares (function approximation)
• Radial basis function network

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