Gauss–Legendre algorithm: Difference between revisions

Revision as of 07:17, 8 April 2013

Revision as of 20:58, 18 April 2013

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The method is based on the individual work of [[Carl Friedrich Gauss]] (1777–1855) and [[Adrien-Marie Legendre]] (1752–1833) combined with modern algorithms for multiplication and [[square root]]s. It repeatedly replaces two numbers by their [[arithmetic mean|arithmetic]] and [[geometric mean]], in order to approximate their [[arithmetic-geometric mean]].

The version presented below is also known as the '''Gauss-Euler, Brent–Salamin (or Salamin–Brent) algorithm''';<ref>[[Richard Brent (scientist)|Brent, Richard]] ''Old and New Agorithms for pi'', Letters to the Editor, Notices of the AMS 60(1), p. 7</ref> it was independently discovered in 1975 by [[Richard Brent (scientist)|Richard Brent]] and [[Eugene Salamin (mathematician)|Eugene Salamin]]. It was used to compute the first 206,158,430,000 decimal digits of π on September 18 to 20, 1999, and the results were checked with [[Borwein's algorithm]].

== Algorithm ==

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| accessdate=8 September 2007

}}</ref>

<ref name="salamin1">[[Eugene Salamin (mathematician)|Salamin, Eugene]]. ''Computation of pi'', Charles Stark Draper Laboratory ISS memo 74–19, 30 January, 1974, Cambridge, Massachusetts</ref>

<ref name="salamin2">{{Citation

| last=Salamin

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| author-link=Eugene Salamin (mathematician)

| publication-date=

| date=1976

| year=1976

| title=Computation of pi Using Arithmetic-Geometric Mean

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{{reflist}}

{{DEFAULTSORT:Gauss-Legendre algorithm}}

[[pt:Algoritmo_de_Gauss-Legendre]]

[[Category:Pi algorithms]]

[[pt:Algoritmo_de_GaussAlgoritmo de Gauss-Legendre]]