Function approximation
Approximating an arbitrary function with a well-behaved one
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.
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.).
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.
Sources and credits
This article is adapted from the Wikipedia article “Function approximation”, written by its contributors and licensed under CC BY-SA 4.0. Fathomly has changed the layout, removed citation markers, navigation and maintenance notices, and adjusted punctuation. This adapted version is shared under the same license. For references, see the original article.
Images, from Wikimedia Commons:
- Step function approximation.png by Hersle, CC BY-SA 4.0
- Regression pic gaussien dissymetrique bruite.svg by Cdang, CC BY-SA 3.0
Fathomly is not affiliated with or endorsed by the Wikimedia Foundation. Spotted a problem? Tell us.
