Category of elements - Revision history

en>Yobot: WP:CHECKWIKI error fixes using AWB (10093)

2014-05-05T12:05:16Z

WP:CHECKWIKI error fixes using AWB (10093)

← Older revision		Revision as of 14:05, 5 May 2014
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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 which aims to find an approximation such that the maximum error is minimized. Suppose we seek to approximate the function f(~~'~~'x'') by~~ a ~~function p(''x'') on the interval [''a'',''b'']~~. Then a minimax approximation algorithm will aim to find a function p(''x'') 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>~~		Marvella is what you can call her but it's not the most female name out there. What I adore performing is taking part in baseball but I haven't made a dime with it. South Dakota is exactly where me and my husband reside and my family loves it. For many years I've been working as a payroll clerk.<br><br>Also visit my web blog - [http://www.videoworld.com/blog/211112 at home std testing]
	~~::<math>\max_{a \leq x \leq b}\|f(x)-p(x)\|~~.~~</math>~~

	~~==Polynomial approximations==~~

	~~The [[Weierstrass approximation theorem]] states that every continuous function defined on a closed interval [a,b] can be uniformly approximated~~ as ~~closely as desired by~~ a ~~polynomial function~~.<~~ref name="phillips" /~~>

	Polynomial expansions such as the [[Taylor series]] expansion are often convenient for theoretical work but less useful for practical applications. For practical work it is often desirable to minimize the maximum absolute or relative error of a polynomial fit for any given number of terms in an effort to reduce computational expense of repeated evaluation.

	~~One popular minimax approximation algorithm is the [[Remez algorithm]]. [[Chebyshev polynomials of the first kind]] closely approximate the minimax polynomial.~~<~~ref~~>~~{{cite~~ web ~~\| url = http://mathworld.wolfram.com/MinimaxPolynomial.html \| title = Minimax Polynomial \| publisher = Wolfram MathWorld \| accessdate= 2012~~-~~09-03}}</ref>~~

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

	~~==References==~~

	~~{{Reflist}}~~

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


	~~{{algorithm-stub}}~~

en>Mark viking: Added wl

2014-01-12T00:38:09Z

Added wl

← Older revision		Revision as of 02:38, 12 January 2014
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	~~I am Oscar and I totally dig~~ that ~~name~~. ~~Since she was 18 she~~'~~s been working as~~ a ~~meter reader but she~~'~~s usually needed her personal company~~. ~~South Dakota is her beginning place but she needs~~ to ~~transfer because~~ of ~~her family members~~. The ~~preferred hobby~~ for ~~my children and me~~ is to ~~perform baseball and I'm trying~~ to ~~make it a profession~~.<~~br><br~~>~~Also visit my~~ web ~~site :: [~~http://~~immbooks~~.com/~~blogs~~/~~post~~/~~44599 immbooks~~.com]		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 which aims to find an approximation such that the maximum error is minimized. Suppose we seek to approximate the function f(''x'') by a function p(''x'') on the interval [''a'',''b'']. Then a minimax approximation algorithm will aim to find a function p(''x'') 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>
			::<math>\max_{a \leq x \leq b}\|f(x)-p(x)\|.</math>

			==Polynomial approximations==

			The [[Weierstrass approximation theorem]] states that every continuous function defined on a closed interval [a,b] can be uniformly approximated as closely as desired by a polynomial function.<ref name="phillips" />

			Polynomial expansions such as the [[Taylor series]] expansion are often convenient for theoretical work but less useful for practical applications. For practical work it is often desirable to minimize the maximum absolute or relative error of a polynomial fit for any given number of terms in an effort to reduce computational expense of repeated evaluation.

			One popular minimax approximation algorithm is the [[Remez algorithm]]. [[Chebyshev polynomials of the first kind]] closely approximate the minimax polynomial.<ref>{{cite web \| url = http://mathworld.wolfram.com/MinimaxPolynomial.html \| title = Minimax Polynomial \| publisher = Wolfram MathWorld \| accessdate= 2012-09-03}}</ref>

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

			==References==

			{{Reflist}}

			[[Category:Numerical analysis]]


			{{algorithm-stub}}

en>Cesme'es at 18:53, 26 January 2011

2011-01-26T18:53:01Z

New page

I am Oscar and I totally dig that name. Since she was 18 she's been working as a meter reader but she's usually needed her personal company. South Dakota is her beginning place but she needs to transfer because of her family members. The preferred hobby for my children and me is to perform baseball and I'm trying to make it a profession.<br><br>Also visit my web site :: [http://immbooks.com/blogs/post/44599 immbooks.com]