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Talk:Arithmetic-geometric mean: Difference between revisions
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→On Using The Arithmetric Geometric Mean to Calculate Pi: format tweak
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I have included examples of using the agm to calculate Pi:
: http://rosettacode.org/wiki/Pi#C.2B.2B
: http://rosettacode.org/wiki/Pi#using_agm▼
▲http://rosettacode.org/wiki/Pi#using_agm
Proof and details of the algorithm used are described:
: http://mathdl.maa.org/images/upload_library/22/Ford/Almkvist-Berndt585-608.pdf
The paper begins with an investigation of why the agm is such an efficient algorithm, and proves that it converges quadratically. From this section one should remeber equation (1) which defines c. Read through to Theorem 5 (derived from Theorems 3&4). If you have remembered the definition of c this should remind you of the above implementations.
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