19 lines
821 B
Text
19 lines
821 B
Text
{{wikipedia|Arithmetic-geometric mean}}
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;task:
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Write a function to compute the [[wp:Arithmetic-geometric mean|arithmetic-geometric mean]] of two numbers.
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[http://mathworld.wolfram.com/Arithmetic-GeometricMean.html]
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The arithmetic-geometric mean of two numbers can be (usefully) denoted as <math>\mathrm{agm}(a,g)</math>, and is equal to the limit of the sequence:
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: <math>a_0 = a; \qquad g_0 = g</math>
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: <math>a_{n+1} = \tfrac{1}{2}(a_n + g_n); \quad g_{n+1} = \sqrt{a_n g_n}.</math>
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Since the limit of <math>a_n-g_n</math> tends (rapidly) to zero with iterations, this is an efficient method.
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Demonstrate the function by calculating:
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:<math>\mathrm{agm}(1,1/\sqrt{2})</math>
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;Also see:
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* [http://mathworld.wolfram.com/Arithmetic-GeometricMean.html mathworld.wolfram.com/Arithmetic-Geometric Mean]
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<br><br>
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