Gauss–Legendre algorithm: Difference between revisions

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Line 26: :<math>3.1415926535897932382\dots</math> :<math>3.14159265358979323846264338327950288419711\dots</math> :<math>3.141592653589793238462643383279502884197169399375105820974944592307816406286208998625\dots</math> ~~:<math>3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986256\dots</math>~~ The algorithm has [[quadratic convergence]], which essentially means that the number of correct digits doubles with each [[iteration]] of the algorithm. Line 112: === 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 ==