A '''minimax approximation algorithm''' (or '''L<sup>∞</sup> approximation'''<ref>{{citebookor |'''uniform titleapproximation''') =is Handbooka ofmethod Floating-Pointto Arithmeticfind |an pageapproximation =of 376a |[[mathematical publisherfunction]] =that Springer|minimizes yearmaximum error.<ref name="Muller_2010">{{cite 2009book | isbn author-last1= 081764704XMuller |author-first1=Jean-Michel | last1=Muller|author-last2=Brisebarre |author-first2=Nicolas |author-last3=de Dinechin |author-first3=Florent |author-last4=Jeannerod |author-first4=Claude-Pierre |author-last5=Lefèvre |author-first5=Vincent |author-last6=Melquiond |author-first6=Guillaume |author-last7=Revol |author-first7=Nathalie|author7-link=Nathalie Revol |author-last8=Stehlé |author-first8=Damien |author-last9=Torres |author-first9=Serge |title=Handbook displayof Floating-authorsPoint Arithmetic |url=https://archive.org/details/handbookfloating00mull_867 |url-access=limited |year=2010 |publisher=[[Birkhäuser]] |edition=1 |isbn=978-0-8176-4704-9<!-- print --> |doi=10.1007/978-0-8176-4705-6 |lccn=2009939668<!-- |id=ISBN 978-0-8176-4705-6 (online), ISBN 0-8176-4704-X (print) --> |page=[https://archive.org/details/handbookfloating00mull_867/page/n388 376]}}</ref> or '''uniform approximation'''<ref name="phillips">{{citeCite doibook | doi = 10.1007/0-387-21682-0_2}}< | first = George M. | last = Phillips| chapter = Best Approximation | title = Interpolation and Approximation by Polynomials | url = https:/ref>)/archive.org/details/interpolationapp00phil_282 is| aurl-access method= tolimited find| anseries approximation= thatCMS Books minimizesin maximumMathematics error| pages = [https://archive.org/details/interpolationapp00phil_282/page/n63 49]–11 | year = 2003 | publisher = Springer | isbn = 0-387-00215-4 }}</ref>
==Example==
For example, togiven approximate thea function <math>f(''x'')</math> by a function p(''x'')defined on the interval <math>[''a'',''b'']</math> and a degree bound <math>n</math>, a minimax polynomial approximation algorithm will find a functionpolynomial <math>p(''x'')</math> of degree at most <math>n</math> to minimize ::<math>\max_{a \leq x \leq b}|f(x)-p(x)|.</math><ref name="powell">{{cite book | chapter = 7: The theory of minimax approximation | first = M. J. D. | last= Powell | authorlinkauthor-link=Michael J. D. Powell | year = 1981 | publisher= Cambridge University Press | title = Approximation Theory and Methods | isbn = 0521295149}}</ref>
::<math>\max_{a \leq x \leq b}|f(x)-p(x)|.</math>
==Polynomial approximations==
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One popular minimax approximation algorithm is the [[Remez algorithm]].
