Minimax approximation algorithm - Revision history

Artoria2e5 at 13:10, 27 September 2021

2021-09-27T13:10:00Z

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	One popular minimax approximation algorithm is the [[Remez algorithm]].		One popular minimax approximation algorithm is the [[Remez algorithm]].

		⚫	==References==
		⚫	{{Reflist}}

	==External links==		==External links==
	*[http://mathworld.wolfram.com/MinimaxApproximation.html Minimax approximation algorithm at MathWorld]		*[http://mathworld.wolfram.com/MinimaxApproximation.html Minimax approximation algorithm at MathWorld]

⚫	==References==

⚫	{{Reflist}}

	[[Category:Numerical analysis]]		[[Category:Numerical analysis]]

David Eppstein: Nathalie Revol

2021-07-14T23:03:19Z

Nathalie Revol

← Previous revision		Revision as of 23:03, 14 July 2021
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	A '''minimax approximation algorithm''' (or '''L<sup>∞</sup> approximation''' or '''uniform approximation''') is a method to find an approximation of a [[mathematical function]] that minimizes maximum error.<ref name="Muller_2010">{{cite book \|author-last1=Muller \|author-first1=Jean-Michel \|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 \|author-last8=Stehlé \|author-first8=Damien \|author-last9=Torres \|author-first9=Serge \|title=Handbook of Floating-Point 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><ref name="phillips">{{Cite book \| doi = 10.1007/0-387-21682-0_2 \| first = George M. \| last = Phillips\| chapter = Best Approximation \| title = Interpolation and Approximation by Polynomials \| url = https://archive.org/details/interpolationapp00phil_282 \| url-access = limited \| series = CMS Books in Mathematics \| pages = [https://archive.org/details/interpolationapp00phil_282/page/n63 49]–11 \| year = 2003 \| publisher = Springer \| isbn = 0-387-00215-4 }}</ref>		A '''minimax approximation algorithm''' (or '''L<sup>∞</sup> approximation''' or '''uniform approximation''') is a method to find an approximation of a [[mathematical function]] that minimizes maximum error.<ref name="Muller_2010">{{cite book \|author-last1=Muller \|author-first1=Jean-Michel \|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 of Floating-Point 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><ref name="phillips">{{Cite book \| doi = 10.1007/0-387-21682-0_2 \| first = George M. \| last = Phillips\| chapter = Best Approximation \| title = Interpolation and Approximation by Polynomials \| url = https://archive.org/details/interpolationapp00phil_282 \| url-access = limited \| series = CMS Books in Mathematics \| pages = [https://archive.org/details/interpolationapp00phil_282/page/n63 49]–11 \| year = 2003 \| publisher = Springer \| isbn = 0-387-00215-4 }}</ref>

	For example, given a function <math>f</math> defined on the interval <math>[a,b]</math> and a degree bound <math>n</math>, a minimax polynomial approximation algorithm will find a polynomial <math>p</math> of degree at most <math>n</math> to minimize		For example, given a function <math>f</math> defined on the interval <math>[a,b]</math> and a degree bound <math>n</math>, a minimax polynomial approximation algorithm will find a polynomial <math>p</math> of degree at most <math>n</math> to minimize

Monkbot: Task 18 (cosmetic): eval 3 templates: del empty params (2×); hyphenate params (1×);

2020-12-30T08:28:06Z

Task 18 (cosmetic): eval 3 templates: del empty params (2×); hyphenate params (1×);

← Previous revision		Revision as of 08:28, 30 December 2020
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	A '''minimax approximation algorithm''' (or '''L<sup>∞</sup> approximation''' or '''uniform approximation''') is a method to find an approximation of a [[mathematical function]] that minimizes maximum error.<ref name="Muller_2010">{{cite book \|author-last1=Muller \|author-first1=Jean-Michel \|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 \|author-last8=Stehlé \|author-first8=Damien \|author-last9=Torres \|author-first9=Serge \|title=Handbook of Floating-Point 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><ref name="phillips">{{Cite book \| doi = 10.1007/0-387-21682-0_2 \| first = George M. \| last = Phillips\| chapter = Best Approximation \| title = Interpolation and Approximation by Polynomials \| url = https://archive.org/details/interpolationapp00phil_282 \| url-access = limited \| series = CMS Books in Mathematics \| pages = [https://archive.org/details/interpolationapp00phil_282/page/n63 49]–11 \| year = 2003 \| publisher = Springer \| isbn = 0-387-00215-4 ~~\| pmid = \| pmc =~~ }}</ref>		A '''minimax approximation algorithm''' (or '''L<sup>∞</sup> approximation''' or '''uniform approximation''') is a method to find an approximation of a [[mathematical function]] that minimizes maximum error.<ref name="Muller_2010">{{cite book \|author-last1=Muller \|author-first1=Jean-Michel \|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 \|author-last8=Stehlé \|author-first8=Damien \|author-last9=Torres \|author-first9=Serge \|title=Handbook of Floating-Point 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><ref name="phillips">{{Cite book \| doi = 10.1007/0-387-21682-0_2 \| first = George M. \| last = Phillips\| chapter = Best Approximation \| title = Interpolation and Approximation by Polynomials \| url = https://archive.org/details/interpolationapp00phil_282 \| url-access = limited \| series = CMS Books in Mathematics \| pages = [https://archive.org/details/interpolationapp00phil_282/page/n63 49]–11 \| year = 2003 \| publisher = Springer \| isbn = 0-387-00215-4 }}</ref>

	For example, given a function <math>f</math> defined on the interval <math>[a,b]</math> and a degree bound <math>n</math>, a minimax polynomial approximation algorithm will find a polynomial <math>p</math> of degree at most <math>n</math> to minimize		For example, given a function <math>f</math> defined on the interval <math>[a,b]</math> and a degree bound <math>n</math>, a minimax polynomial approximation algorithm will find a polynomial <math>p</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 \| ~~authorlink~~=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><ref name="powell">{{cite book \| chapter = 7: The theory of minimax approximation \| first = M. J. D. \| last= Powell \| author-link=Michael J. D. Powell \| year = 1981 \| publisher= Cambridge University Press \| title = Approximation Theory and Methods \| isbn = 0521295149}}</ref>

	==Polynomial approximations==		==Polynomial approximations==

InternetArchiveBot: Bluelink 2 books for verifiability (prndis)) #IABot (v2.0) (GreenC bot

2020-05-26T08:40:55Z

Bluelink 2 books for verifiability (prndis)) #IABot (v2.0) (GreenC bot

← Previous revision		Revision as of 08:40, 26 May 2020
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	A '''minimax approximation algorithm''' (or '''L<sup>∞</sup> approximation''' or '''uniform approximation''') is a method to find an approximation of a [[mathematical function]] that minimizes maximum error.<ref name="Muller_2010">{{cite book \|author-last1=Muller \|author-first1=Jean-Michel \|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 \|author-last8=Stehlé \|author-first8=Damien \|author-last9=Torres \|author-first9=Serge \|title=Handbook of Floating-Point Arithmetic \|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=376}}</ref><ref name="phillips">{{Cite book \| doi = 10.1007/0-387-21682-0_2 \| first = George M. \| last = Phillips\| chapter = Best Approximation \| title = Interpolation and Approximation by Polynomials \| series = CMS Books in Mathematics \| pages = ~~49–11~~ \| year = 2003 \| publisher = Springer \| isbn = 0-387-00215-4 \| pmid = \| pmc = }}</ref>		A '''minimax approximation algorithm''' (or '''L<sup>∞</sup> approximation''' or '''uniform approximation''') is a method to find an approximation of a [[mathematical function]] that minimizes maximum error.<ref name="Muller_2010">{{cite book \|author-last1=Muller \|author-first1=Jean-Michel \|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 \|author-last8=Stehlé \|author-first8=Damien \|author-last9=Torres \|author-first9=Serge \|title=Handbook of Floating-Point 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><ref name="phillips">{{Cite book \| doi = 10.1007/0-387-21682-0_2 \| first = George M. \| last = Phillips\| chapter = Best Approximation \| title = Interpolation and Approximation by Polynomials \| url = https://archive.org/details/interpolationapp00phil_282 \| url-access = limited \| series = CMS Books in Mathematics \| pages = [https://archive.org/details/interpolationapp00phil_282/page/n63 49]–11 \| year = 2003 \| publisher = Springer \| isbn = 0-387-00215-4 \| pmid = \| pmc = }}</ref>

	For example, given a function <math>f</math> defined on the interval <math>[a,b]</math> and a degree bound <math>n</math>, a minimax polynomial approximation algorithm will find a polynomial <math>p</math> of degree at most <math>n</math> to minimize		For example, given a function <math>f</math> defined on the interval <math>[a,b]</math> and a degree bound <math>n</math>, a minimax polynomial approximation algorithm will find a polynomial <math>p</math> of degree at most <math>n</math> to minimize

Filipović Zoran at 12:20, 8 May 2019

2019-05-08T12:20:12Z

← Previous revision		Revision as of 12:20, 8 May 2019
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	A '''minimax approximation algorithm''' (or '''L<sup>∞</sup> approximation''' or '''uniform approximation''') is a method to find an approximation of a [[mathematical function]] that minimizes maximum error.<ref name="Muller_2010">{{cite book \|author-last1=Muller \|author-first1=Jean-Michel \|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 \|author-last8=Stehlé \|author-first8=Damien \|author-last9=Torres \|author-first9=Serge \|title=Handbook of Floating-Point Arithmetic \|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=376}}</ref><ref name="phillips">{{Cite book \| doi = 10.1007/0-387-21682-0_2 \| first = George M. \| last = Phillips\| chapter = Best Approximation \| title = Interpolation and Approximation by Polynomials \| series = CMS Books in Mathematics \| pages = 49–11 \| year = 2003 \| publisher = Springer \| isbn = 0-387-00215-4 \| pmid = \| pmc = }}</ref>		A '''minimax approximation algorithm''' (or '''L<sup>∞</sup> approximation''' or '''uniform approximation''') is a method to find an approximation of a [[mathematical function]] that minimizes maximum error.<ref name="Muller_2010">{{cite book \|author-last1=Muller \|author-first1=Jean-Michel \|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 \|author-last8=Stehlé \|author-first8=Damien \|author-last9=Torres \|author-first9=Serge \|title=Handbook of Floating-Point Arithmetic \|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=376}}</ref><ref name="phillips">{{Cite book \| doi = 10.1007/0-387-21682-0_2 \| first = George M. \| last = Phillips\| chapter = Best Approximation \| title = Interpolation and Approximation by Polynomials \| series = CMS Books in Mathematics \| pages = 49–11 \| year = 2003 \| publisher = Springer \| isbn = 0-387-00215-4 \| pmid = \| pmc = }}</ref>

	For example, given a function <math>f</math> defined on the interval <math>[a,b]</math> and a degree bound <math>n</math>, a minimax polynomial approximation algorithm will find a polynomial <math>p</math> of degree at most <math>n</math> to minimize<ref name="powell">{{cite book \| chapter = 7: The theory of minimax approximation \| first = M. J. D. \| last= Powell \| authorlink=Michael J. D. Powell \| year = 1981 \| publisher= Cambridge University Press \| title = Approximation Theory and Methods \| isbn = 0521295149}}</ref>		For example, given a function <math>f</math> defined on the interval <math>[a,b]</math> and a degree bound <math>n</math>, a minimax polynomial approximation algorithm will find a polynomial <math>p</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 \| authorlink=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==		==Polynomial approximations==

Filipović Zoran at 12:19, 8 May 2019

2019-05-08T12:19:19Z

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	A '''minimax approximation algorithm''' (or '''L<sup>∞</sup> approximation'''<ref name="Muller_2010">{{cite book \|author-last1=Muller \|author-first1=Jean-Michel \|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 \|author-last8=Stehlé \|author-first8=Damien \|author-last9=Torres \|author-first9=Serge \|title=Handbook of Floating-Point Arithmetic \|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=376}}</ref> ~~or '''uniform approximation'''~~<ref name="phillips">{{Cite book \| doi = 10.1007/0-387-21682-0_2 \| first = George M. \| last = Phillips\| chapter = Best Approximation \| title = Interpolation and Approximation by Polynomials \| series = CMS Books in Mathematics \| pages = 49–11 \| year = 2003 \| publisher = Springer \| isbn = 0-387-00215-4 \| pmid = \| pmc = }}</ref>~~) is a method to find an approximation of a [[mathematical function]] that minimizes maximum error.~~		A '''minimax approximation algorithm''' (or '''L<sup>∞</sup> approximation''' or '''uniform approximation''') is a method to find an approximation of a [[mathematical function]] that minimizes maximum error.<ref name="Muller_2010">{{cite book \|author-last1=Muller \|author-first1=Jean-Michel \|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 \|author-last8=Stehlé \|author-first8=Damien \|author-last9=Torres \|author-first9=Serge \|title=Handbook of Floating-Point Arithmetic \|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=376}}</ref><ref name="phillips">{{Cite book \| doi = 10.1007/0-387-21682-0_2 \| first = George M. \| last = Phillips\| chapter = Best Approximation \| title = Interpolation and Approximation by Polynomials \| series = CMS Books in Mathematics \| pages = 49–11 \| year = 2003 \| publisher = Springer \| isbn = 0-387-00215-4 \| pmid = \| pmc = }}</ref>

	For example, given a function <math>f</math> defined on the interval <math>[a,b]</math> and a degree bound <math>n</math>, a minimax polynomial approximation algorithm will find a polynomial <math>p</math> of degree at most <math>n</math> to minimize<ref name="powell">{{cite book \| chapter = 7: The theory of minimax approximation \| first = M. J. D. \| last= Powell \| authorlink=Michael J. D. Powell \| year = 1981 \| publisher= Cambridge University Press \| title = Approximation Theory and Methods \| isbn = 0521295149}}</ref>		For example, given a function <math>f</math> defined on the interval <math>[a,b]</math> and a degree bound <math>n</math>, a minimax polynomial approximation algorithm will find a polynomial <math>p</math> of degree at most <math>n</math> to minimize<ref name="powell">{{cite book \| chapter = 7: The theory of minimax approximation \| first = M. J. D. \| last= Powell \| authorlink=Michael J. D. Powell \| year = 1981 \| publisher= Cambridge University Press \| title = Approximation Theory and Methods \| isbn = 0521295149}}</ref>

Magioladitis: clean up using AWB

2016-12-05T23:52:29Z

clean up using AWB

← Previous revision		Revision as of 23:52, 5 December 2016
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	A '''minimax approximation algorithm''' (or '''L<sup>∞</sup> approximation'''<ref name="Muller_2010">{{cite book \|author-last1=Muller \|author-first1=Jean-Michel \|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 \|author-last8=Stehlé \|author-first8=Damien \|author-last9=Torres \|author-first9=Serge \|title=Handbook of Floating-Point Arithmetic \|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~~-10~~ 0-8176-4704-X (print) --> \|page=376}}</ref> or '''uniform approximation'''<ref name="phillips">{{Cite book \| doi = 10.1007/0-387-21682-0_2 \| first = George M. \| last = Phillips\| chapter = Best Approximation \| title = Interpolation and Approximation by Polynomials \| series = CMS Books in Mathematics \| pages = 49–11 \| year = 2003 \| publisher = Springer \| isbn = 0-387-00215-4 \| pmid = \| pmc = }}</ref>) is a method to find an approximation of a [[mathematical function]] that minimizes maximum error.		A '''minimax approximation algorithm''' (or '''L<sup>∞</sup> approximation'''<ref name="Muller_2010">{{cite book \|author-last1=Muller \|author-first1=Jean-Michel \|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 \|author-last8=Stehlé \|author-first8=Damien \|author-last9=Torres \|author-first9=Serge \|title=Handbook of Floating-Point Arithmetic \|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=376}}</ref> or '''uniform approximation'''<ref name="phillips">{{Cite book \| doi = 10.1007/0-387-21682-0_2 \| first = George M. \| last = Phillips\| chapter = Best Approximation \| title = Interpolation and Approximation by Polynomials \| series = CMS Books in Mathematics \| pages = 49–11 \| year = 2003 \| publisher = Springer \| isbn = 0-387-00215-4 \| pmid = \| pmc = }}</ref>) is a method to find an approximation of a [[mathematical function]] that minimizes maximum error.

	For example, given a function <math>f</math> defined on the interval <math>[a,b]</math> and a degree bound <math>n</math>, a minimax polynomial approximation algorithm will find a polynomial <math>p</math> of degree at most <math>n</math> to minimize<ref name="powell">{{cite book \| chapter = 7: The theory of minimax approximation \| first = M. J. D. \| last= Powell \| authorlink=Michael J. D. Powell \| year = 1981 \| publisher= Cambridge University Press \| title = Approximation Theory and Methods \| isbn = 0521295149}}</ref>		For example, given a function <math>f</math> defined on the interval <math>[a,b]</math> and a degree bound <math>n</math>, a minimax polynomial approximation algorithm will find a polynomial <math>p</math> of degree at most <math>n</math> to minimize<ref name="powell">{{cite book \| chapter = 7: The theory of minimax approximation \| first = M. J. D. \| last= Powell \| authorlink=Michael J. D. Powell \| year = 1981 \| publisher= Cambridge University Press \| title = Approximation Theory and Methods \| isbn = 0521295149}}</ref>

Tom.Reding: /* References */Rem stub tag (class = non-stub & non-list) using AWB

2016-06-29T20:33:36Z

References: Rem stub tag (class = non-stub & non-list) using AWB

← Previous revision		Revision as of 20:33, 29 June 2016
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	[[Category:Numerical analysis]]		[[Category:Numerical analysis]]


	{{algorithm-stub}}

Matthiaspaul: improved ref

2016-05-09T21:17:47Z

improved ref

← Previous revision		Revision as of 21:17, 9 May 2016
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	A '''minimax approximation algorithm''' (or '''L<sup>∞</sup> approximation'''<ref>{{cite book \| ~~title = Handbook of Floating~~-~~Point Arithmetic \| page~~ = ~~376~~ \| ~~publisher = Springer \| year = 2009 \| isbn = 081764704X \|~~ first1=Jean-Michel \| ~~last1=Muller\|~~last2=Brisebarre \| first2=Nicolas \| last3=de Dinechin \| first3=Florent \| last4=Jeannerod \| first4=Claude-Pierre \| last5=Lefèvre \| first5=Vincent \| last6=Melquiond \| first6=Guillaume \| last7=Revol \| first7=Nathalie \| last8=Stehlé \| first8=Damien \| last9=Torres \| first9=Serge \| ~~display~~-~~authors~~=1 }}</ref> or '''uniform approximation'''<ref name="phillips">{{Cite book \| doi = 10.1007/0-387-21682-0_2 \| first = George M. \| last = Phillips\| chapter = Best Approximation \| title = Interpolation and Approximation by Polynomials \| series = CMS Books in Mathematics \| pages = 49–11 \| year = 2003 \| publisher = Springer \| isbn = 0-387-00215-4 \| pmid = \| pmc = }}</ref>) is a method to find an approximation of a [[mathematical function]] that minimizes maximum error.		A '''minimax approximation algorithm''' (or '''L<sup>∞</sup> approximation'''<ref name="Muller_2010">{{cite book \|author-last1=Muller \|author-first1=Jean-Michel \|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 \|author-last8=Stehlé \|author-first8=Damien \|author-last9=Torres \|author-first9=Serge \|title=Handbook of Floating-Point Arithmetic \|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-10 0-8176-4704-X (print) --> \|page=376}}</ref> or '''uniform approximation'''<ref name="phillips">{{Cite book \| doi = 10.1007/0-387-21682-0_2 \| first = George M. \| last = Phillips\| chapter = Best Approximation \| title = Interpolation and Approximation by Polynomials \| series = CMS Books in Mathematics \| pages = 49–11 \| year = 2003 \| publisher = Springer \| isbn = 0-387-00215-4 \| pmid = \| pmc = }}</ref>) is a method to find an approximation of a [[mathematical function]] that minimizes maximum error.

	For example, given a function <math>f</math> defined on the interval <math>[a,b]</math> and a degree bound <math>n</math>, a minimax polynomial approximation algorithm will find a polynomial <math>p</math> of degree at most <math>n</math> to minimize<ref name="powell">{{cite book \| chapter = 7: The theory of minimax approximation \| first = M. J. D. \| last= Powell \| authorlink=Michael J. D. Powell \| year = 1981 \| publisher= Cambridge University Press \| title = Approximation Theory and Methods \| isbn = 0521295149}}</ref>		For example, given a function <math>f</math> defined on the interval <math>[a,b]</math> and a degree bound <math>n</math>, a minimax polynomial approximation algorithm will find a polynomial <math>p</math> of degree at most <math>n</math> to minimize<ref name="powell">{{cite book \| chapter = 7: The theory of minimax approximation \| first = M. J. D. \| last= Powell \| authorlink=Michael J. D. Powell \| year = 1981 \| publisher= Cambridge University Press \| title = Approximation Theory and Methods \| isbn = 0521295149}}</ref>

Dexbot: Bot: Deprecating Template:Cite doi and some minor fixes

2015-09-02T11:11:08Z

Bot: Deprecating Template:Cite doi and some minor fixes

← Previous revision		Revision as of 11:11, 2 September 2015
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	A '''minimax approximation algorithm''' (or '''L<sup>∞</sup> approximation'''<ref>{{cite book \| title = Handbook of Floating-Point Arithmetic \| page = 376 \| publisher = Springer \| year = 2009 \| isbn = 081764704X \| first1=Jean-Michel \| last1=Muller\|last2=Brisebarre \| first2=Nicolas \| last3=de Dinechin \| first3=Florent \| last4=Jeannerod \| first4=Claude-Pierre \| last5=Lefèvre \| first5=Vincent \| last6=Melquiond \| first6=Guillaume \| last7=Revol \| first7=Nathalie \| last8=Stehlé \| first8=Damien \| last9=Torres \| first9=Serge \| display-authors=1 }}</ref> or '''uniform approximation'''<ref name="phillips">{{~~cite~~ ~~doi~~ \| 10.1007/0-387-21682-0_2}}</ref>) is a method to find an approximation of a [[mathematical function]] that minimizes maximum error.		A '''minimax approximation algorithm''' (or '''L<sup>∞</sup> approximation'''<ref>{{cite book \| title = Handbook of Floating-Point Arithmetic \| page = 376 \| publisher = Springer \| year = 2009 \| isbn = 081764704X \| first1=Jean-Michel \| last1=Muller\|last2=Brisebarre \| first2=Nicolas \| last3=de Dinechin \| first3=Florent \| last4=Jeannerod \| first4=Claude-Pierre \| last5=Lefèvre \| first5=Vincent \| last6=Melquiond \| first6=Guillaume \| last7=Revol \| first7=Nathalie \| last8=Stehlé \| first8=Damien \| last9=Torres \| first9=Serge \| display-authors=1 }}</ref> or '''uniform approximation'''<ref name="phillips">{{Cite book \| doi = 10.1007/0-387-21682-0_2 \| first = George M. \| last = Phillips\| chapter = Best Approximation \| title = Interpolation and Approximation by Polynomials \| series = CMS Books in Mathematics \| pages = 49–11 \| year = 2003 \| publisher = Springer \| isbn = 0-387-00215-4 \| pmid = \| pmc = }}</ref>) is a method to find an approximation of a [[mathematical function]] that minimizes maximum error.

	For example, given a function <math>f</math> defined on the interval <math>[a,b]</math> and a degree bound <math>n</math>, a minimax polynomial approximation algorithm will find a polynomial <math>p</math> of degree at most <math>n</math> to minimize<ref name="powell">{{cite book \| chapter = 7: The theory of minimax approximation \| first = M. J. D. \| last= Powell \| authorlink=Michael J. D. Powell \| year = 1981 \| publisher= Cambridge University Press \| title = Approximation Theory and Methods \| isbn = 0521295149}}</ref>		For example, given a function <math>f</math> defined on the interval <math>[a,b]</math> and a degree bound <math>n</math>, a minimax polynomial approximation algorithm will find a polynomial <math>p</math> of degree at most <math>n</math> to minimize<ref name="powell">{{cite book \| chapter = 7: The theory of minimax approximation \| first = M. J. D. \| last= Powell \| authorlink=Michael J. D. Powell \| year = 1981 \| publisher= Cambridge University Press \| title = Approximation Theory and Methods \| isbn = 0521295149}}</ref>