https://wiki.sarg.dev/index.php?action=history&feed=atom&title=Function_approximationFunction approximation - Revision history2026-04-14T01:31:16ZRevision history for this page on the wikiMediaWiki 1.44.2https://wiki.sarg.dev/index.php?title=Function_approximation&diff=215317&oldid=prev93.99.190.128 at 12:49, 30 October 20252025-10-30T12:49:11Z<p></p>
<p><b>New page</b></p><div>{{Short description|Approximating an arbitrary function with a well-behaved one}}<br />
{{distinguish|Curve fitting}}<br />
[[File:Step function approximation.png|alt=Several approximations of a step function|thumb|Several progressively more accurate approximations of the [[step function]]]]<br />
[[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]]<br />
In general, a '''function approximation''' problem asks us to select a [[function (mathematics)|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">{{Cite journal|last1=Basheer|first1=I.A.|last2=Hajmeer|first2=M.|date=2000|title=Artificial neural networks: fundamentals, computing, design, and application|url=http://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><br />
<br />
First, for known target functions [[approximation theory]] is the branch of [[numerical analysis]] that investigates how certain known functions (for example, [[special function]]s) can be approximated by a specific class of functions (for example, [[polynomial]]s or [[rational function]]s) 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><br />
<br />
Secondly, for example, if ''g'' is an operation on the [[real number]]s, 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 [[statistical classification|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><br />
<br />
== References ==<br />
{{Reflist}}<br />
<br />
==See also==<br />
*[[Approximation theory]]<br />
*[[Fitness approximation]]<br />
*[[Kriging]]<br />
*[[Least squares (function approximation)]]<br />
*[[Radial basis function network]]<br />
<br />
{{DEFAULTSORT:Function Approximation}}<br />
[[Category:Regression analysis]]<br />
[[Category:Statistical approximations]]<br />
<br />
<br />
{{mathanalysis-stub}}<br />
{{statistics-stub}}</div>93.99.190.128