DFT matrix - Revision history

2607:EA00:104:3C00:91F:8914:2947:A4A5: /* Definition */

2014-05-14T19:06:47Z

Definition

en>Cuzkatzimhut: /* See also */

2014-02-25T15:37:41Z

See also

← Older revision		Revision as of 17:37, 25 February 2014
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	~~In [[mathematical analysis]], '''Bernstein's inequality'''~~ is ~~named after [[Sergei Natanovich Bernstein]]~~. ~~The inequality states that on the [[complex plane]], within the disk~~ of ~~radius 1,~~ the ~~degree of a [[polynomial]] times the maximum value of a polynomial~~ is ~~an upper bound for the similar maximum of its [[derivative]]~~.		Royal Votaw is my name but I never really liked that name. To keep birds is one of the issues he enjoys most. Arizona is her birth location and she will never transfer. She functions as a financial officer and she will not alter it anytime quickly.<br><br>Review my web-site; extended car warranty ([http://Goodtogether.com/UserProfile/tabid/43/userId/63137/Default.aspx visit this hyperlink])

	~~==Theorem==~~
	~~Let ''P'' be~~ a ~~polynomial of degree <math>n</math> on complex numbers with derivative ''P′''~~. ~~Then~~

	~~:<math>\max_{\|z\| \le 1}( \|P'(z)\| ) \le n\cdot\max_{\|z\| \le 1}( \|P(z)\| )~~ <~~/math~~>

	~~The inequality finds uses in the field of [[approximation theory]].~~

	~~Using the Bernstein's inequality we have for the ''k'':th derivative,~~

	:<~~math~~>~~\max_{\|z\| \le 1}( \|P^{(k)}(z)\| ) \le \frac{n!}{(n~~-~~k)!} \cdot\max_{\|z\| \le 1}( \|P~~(~~z)\| ). </math>~~

	~~==See also==~~

	* [~~[Markov brothers' inequality]]~~
	* [[Remez inequality]]

	~~==References==~~
	* {{cite journal \| last=Frappier \| first=Clément \| title=Note on Bernstein's inequality for the third derivative of a polynomial \| journal=J. Inequal. Pure Appl. Math. \| volume=5 \| number=1 \| at=Paper No. 7 \| year=2004 \| issn=1443-5756 \| url=http://~~www~~.~~emis.de~~/~~journals~~/~~JIPAM~~/~~images~~/~~154_03_JIPAM~~/~~154_03.pdf \| zbl=1060.30003 }}~~
	* {{cite book \| last1=Rahman \| first1=Q. I. \| last2=Schmeisser \| first2=G. \| title=Analytic theory of polynomials \| series=London Mathematical Society Monographs. New Series \| volume=26 \| location=Oxford \| publisher=[[Oxford University Press]] \| year=2002 \| isbn=0-19-853493-0 \| zbl=1072.30006 }}

	~~[[Category:Inequalities]]~~
	~~[[Category:Approximation theory]]~~
	~~[[Category:Functional analysis]]~~


	~~{{mathanalysis-stub}}~~

	~~[[it:Disuguaglianza di Bernstein]~~]

en>Maschen: remove redundant link to matrix when there is Matrix multiplication

2013-12-30T23:20:51Z

remove redundant link to matrix when there is Matrix multiplication

← Older revision		Revision as of 01:20, 31 December 2013
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	~~The author~~ is ~~called Araceli Gulledge~~. ~~Alabama has always been his house. Meter reading is where my primary income comes from but soon I'll be~~ on ~~my own. One~~ of ~~his preferred hobbies~~ is ~~playing crochet but he hasn~~'~~t made~~ a ~~dime~~ with it.<br><br>~~Also visit my web-site~~ :: ~~extended auto warranty;~~ [http://www.~~floridafruitscapes~~.~~com~~/~~UserProfile~~/~~tabid~~/95/~~userId~~/~~2508/Default~~.~~aspx talking to~~],		In [[mathematical analysis]], '''Bernstein's inequality''' is named after [[Sergei Natanovich Bernstein]]. The inequality states that on the [[complex plane]], within the disk of radius 1, the degree of a [[polynomial]] times the maximum value of a polynomial is an upper bound for the similar maximum of its [[derivative]].

			==Theorem==
			Let ''P'' be a polynomial of degree <math>n</math> on complex numbers with derivative ''P′''. Then

			:<math>\max_{\|z\| \le 1}( \|P'(z)\| ) \le n\cdot\max_{\|z\| \le 1}( \|P(z)\| ) </math>

			The inequality finds uses in the field of [[approximation theory]].

			Using the Bernstein's inequality we have for the ''k'':th derivative,

			:<math>\max_{\|z\| \le 1}( \|P^{(k)}(z)\| ) \le \frac{n!}{(n-k)!} \cdot\max_{\|z\| \le 1}( \|P(z)\| ). </math>

			==See also==

			* [[Markov brothers' inequality]]
			* [[Remez inequality]]

			==References==
			* {{cite journal \| last=Frappier \| first=Clément \| title=Note on Bernstein's inequality for the third derivative of a polynomial \| journal=J. Inequal. Pure Appl. Math. \| volume=5 \| number=1 \| at=Paper No. 7 \| year=2004 \| issn=1443-5756 \| url=http://www.emis.de/journals/JIPAM/images/154_03_JIPAM/154_03.pdf \| zbl=1060.30003 }}
			* {{cite book \| last1=Rahman \| first1=Q. I. \| last2=Schmeisser \| first2=G. \| title=Analytic theory of polynomials \| series=London Mathematical Society Monographs. New Series \| volume=26 \| location=Oxford \| publisher=[[Oxford University Press]] \| year=2002 \| isbn=0-19-853493-0 \| zbl=1072.30006 }}

			[[Category:Inequalities]]
			[[Category:Approximation theory]]
			[[Category:Functional analysis]]


			{{mathanalysis-stub}}

			[[it:Disuguaglianza di Bernstein]]

114.143.175.48: /* Four-point */

2012-04-09T06:56:04Z

Four-point

New page

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