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Complex Computations, Arithmetic-Geometric Mean

Arithmetic-Geometric Mean or Common Mean: AGM(x, y) = MeanC(x, y)
is defined by an algorithm. Let a_0 = x and g_0 = y, then iterating
a_n+1 = (a_n + g_n)/2
g_n+1 = +/−sqrt(a_n*g_n)
until a_n = g_n.
Each time g_n+1 = +/−sqrt(a_n*g_n) is computed, pick the + or − to
minimize |a_n+1 − g_n+1|.
if ever a_n+1 = g_n+1 or g_n+1 = 0, the answer is g_n+1.
Also, AGM(x, 0) = AGM(0, y) = 0.

See: Arithmetic-Geometric Mean -- From MathWorld
And: Wolfram Function Evaluation -- ArithmeticGeometricMean
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Changes last made on Wednesday, 15-Feb-06 20:51:55 PST