{{Short description|Approximating an arbitrary function with a well-behaved one}} {{distinguish|Curve fitting}} [[File:Step function approximation.png|alt=Several approximations of a step function|thumb|Several progressively more accurate approximations of the step function]] [[File:Regression pic gaussien dissymetrique bruite.svg|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.<ref>{{Cite book|last1=Lakemeyer|first1=Gerhard|url=https://books.google.com/books?id=PW1qCQAAQBAJ&dq=%22function+approximation+is%22&pg=PA49|title=RoboCup 2006: Robot Soccer World Cup X|last2=Sklar|first2=Elizabeth|last3=Sorrenti|first3=Domenico G.|last4=Takahashi|first4=Tomoichi|date=2007-09-04|publisher=Springer|isbn=978-3-540-74024-7|language=en}}</ref>{{Better source needed|reason=Find a source that actually explicitly makes this kind of definition; this one doesn't quite do so|date=January 2022}} The need for function approximations arises, for example, predicting the growth of microbes in microbiology.<ref name=":0">{{Cite journal|last1=Basheer|first1=I.A.|last2=Hajmeer|first2=M.|date=2000|title=Artificial neural networks: fundamentals, computing, design, and application|url=https://web.archive.org/web/20230627001502/ethologie.unige.ch/etho5.10/pdf/basheer.hajmeer.2000.fundamentals.design.and.application.of.neural.networks.review.pdf|journal=Journal of Microbiological Methods|volume=43|issue=1|pages=3–31|doi=10.1016/S0167-7012(00)00201-3|pmid=11084225|s2cid=18267806 }}</ref> Function approximations are used where theoretical models are unavailable or hard to compute.<ref name=":0"/>
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>{{Cite book|last1=Mhaskar|first1=Hrushikesh Narhar|url=https://books.google.com/books?id=643OA9qwXLgC&dq=%22approximation+theory%22&pg=PA1|title=Fundamentals of Approximation Theory|last2=Pai|first2=Devidas V.|date=2000|publisher=CRC Press|isbn=978-0-8493-0939-7|language=en}}</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>{{Cite journal|last1=Charte|first1=David|last2=Charte|first2=Francisco|last3=García|first3=Salvador|last4=Herrera|first4=Francisco|date=2019-04-01|title=A snapshot on nonstandard supervised learning problems: taxonomy, relationships, problem transformations and algorithm adaptations|url=https://doi.org/10.1007/s13748-018-00167-7|journal=Progress in Artificial Intelligence|language=en|volume=8|issue=1|pages=1–14|doi=10.1007/s13748-018-00167-7|arxiv=1811.12044|s2cid=53715158|issn=2192-6360}}</ref>
==See also== *Approximation theory *Fitness approximation *Kriging *Least squares (function approximation) *Radial basis function network
{{DEFAULTSORT:Function Approximation}} Category:Regression analysis Category:Statistical approximations == References == {{Reflist}}
{{DEFAULTSORT:Function Approximation}} Category:Regression analysis Category:Statistical approximations
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