alt=Several approximations of a step function|thumb|Several progressively more accurate approximations of the [[step function]]
alt=An asymmetrical Gaussian function fit to a noisy curve using regression.|thumb|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. The need for function approximations arises, for example, predicting the growth of microbes in microbiology. Function approximations are used where theoretical models are unavailable or hard to compute.
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.
See also
- Approximation theory
- Fitness approximation
- Kriging
- Least squares (function approximation)
- Radial basis function network