Gauss–Legendre algorithm: Difference between revisions

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The algorithm has [[quadratic convergence]], which essentially means that the number of correct digits doubles with each [[iteration]] of the algorithm.

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=== Elementary proof with integral calculus ===

The Gauss-Legendre algorithm can be proven to give results converging to π<math>\pi</math> using only integral calculus. This is done here<ref>{{citation|title=Recent Calculations of π: The Gauss-Salamin Algorithm|last1=Lord|first1=Nick|doi=10.2307/3619132|year=1992|journal=The Mathematical Gazette|volume=76|issue=476|pages=231–242|jstor=3619132|s2cid=125865215 }}</ref> and here.<ref>{{citation|title=Easy Proof of Three Recursive π-Algorithms|last1=Milla|first1=Lorenz|arxiv=1907.04110|year=2019}}</ref>

== See also ==