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2013-01-09T01:20:06Z

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← Older revision		Revision as of 03:20, 9 January 2013
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	~~I am 24 years old~~ and ~~my name~~ is ~~Emely Brazil~~. ~~I life in Kobenhavn V~~ (~~Denmark~~).<br><br>~~Stop~~ by ~~my blog~~ ... ~~[http:~~//~~hipsterpunk~~.~~com~~/u/~~raubx/ Here is your mountain bike sizing.~~]		In [[mathematics]], the '''Fekete problem''' is, given a natural number ''N'' and a real ''s'' ≥ 0, to find the points ''x''<sub>1</sub>,...,''x''<sub>''N''</sub> on the [[2-sphere]] for which the ''s''-energy, defined by

			:<math> \sum_{1 \leq i < j \leq N} \\|x_i - x_j \\|^{-s} </math>

			for ''s'' > 0 and by

			:<math> \sum_{1 \leq i < j \leq N} \log \\|x_i - x_j \\|^{-1} </math>

			for ''s'' = 0, is minimal. For ''s'' > 0, such points are called ''s''-''Fekete points'', and for ''s'' = 0, ''logarithmic Fekete points'' (see {{harvtxt\|Saff\|Kuijlaars\|1997}}).
			More generally, one can consider the same problem on the ''d''-dimensional sphere, or on a [[Riemannian manifold]] (in which case \|\|''x''<sub>''i''</sub> −''x''<sub>''j''</sub>\|\| is replaced with the Riemannian distance between ''x''<sub>''i''</sub> and ''x''<sub>''j''</sub>).

			The problem originated in the paper by {{harvs\|txt\|first=Michael\|last=Fekete\|\|authorlink=Michael Fekete\|year=1923}} who considered the one-dimensional, ''s'' = 0 case, answering a question of [[Issai Schur]].

			An algorithmic version of the Fekete problem is number 7 on the list of problems discussed by {{harvtxt\|Smale\|1998}}.

			==References==
			*{{Citation \| last1=Bendito \| first1=E. \| last2=Carmona \| first2=A. \| last3=Encinas \| first3=A. M. \| last4=Gesto \| first4=J. M. \| last5=Gómez \| first5=A. \| last6=Mouriño \| first6=C. \| last7=Sánchez \| first7=M. T. \| title=Computational cost of the Fekete problem. I. The forces method on the 2-sphere \| doi=10.1016/j.jcp.2009.01.021 \| mr=2513833 \| year=2009 \| journal=Journal of Computational Physics \| issn=0021-9991 \| volume=228 \| issue=9 \| pages=3288–3306}}
			*{{Citation \| last1=Fekete \| first1=M. \| author-link=Michael Fekete\|title=Über die Verteilung der Wurzeln bei gewissen algebraischen Gleichungen mit ganzzahligen Koeffizienten \| doi=10.1007/BF01504345 \| mr=1544613 \| year=1923 \| journal=[[Mathematische Zeitschrift]] \| issn=0025-5874 \| volume=17 \| issue=1 \| pages=228–249}}
			*{{cite journal\|ref=harv\|mr=1439152\|last1=Saff\|first1=E. B.\|last2=Kuijlaars\|first2=A. B. J.\|title=Distributing many points on a sphere\|journal=Math. Intelligencer\|volume=19\|year=1997\|issue=1\|pages=5–11\|doi=10.1007/BF03024331}}
			*{{Citation \| last1=Smale \| first1=Stephen \| authorlink = Stephen Smale \| title=Mathematical problems for the next century \| doi=10.1007/BF03025291 \| mr=1631413 \| year=1998 \| journal=[[The Mathematical Intelligencer]] \| issn=0343-6993 \| volume=20 \| issue=2 \| pages=7–15}}

			[[Category:Mathematical analysis]]
			[[Category:Approximation theory]]

132.199.101.221: /* Definition */

2012-06-11T13:33:51Z

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I am 24 years old and my name is Emely Brazil. I life in Kobenhavn V (Denmark).<br><br>Stop by my blog ... [http://hipsterpunk.com/u/raubx/ Here is your mountain bike sizing.]

Banach bundle (non-commutative geometry) - Revision history

en>Addbot: Bot: Removing Orphan Tag (No longer an Orphan) (Report Errors)

132.199.101.221: /* Definition */