Gauss–Legendre algorithm: Difference between revisions

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The '''Gauss–Legendre algorithm''' is an [[algorithm]] to compute the digits of [[Pi|{{pi}}]]. It is notable for being rapidly convergent, with only 25 iterations producing 45 million correct digits of {{pi}}. However, it has some drawbacks (for example, it is [[Random-access_memory|computer memory]]-intensive) and therefore all record-breaking calculations sincefor 2009many years have used other methods, almost always the [[Chudnovsky algorithm]]. insteadFor details, see [[chronology of computation of π|Chronology of computation of {{pi}}]].

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]].