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vigdorchik/secant

Created June 6, 2014 07:59
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secant
Prelude> let eps = 0.00000001
Prelude> let fix f x_1 x_2 = let f_x = x_1 - (f x_1)*(x_1 - x_2)/((f x_1) - (f x_2)) in if abs (f_x - x_1) < eps then f_x else fix f f_x x_1
Prelude> let root a = fix ((flip (-)) a . flip (^) 3) (a-1) (a+1)
Prelude> root 27
3.0
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Prelude> let eps = 0.00000001
Prelude> let n = 10000
Prelude> let fix f x y m = let z = x - (f x)*(x-y)/((f x) - (f y)) in if abs (z - x) < eps || m>n then z else fix f z x (m+1)
Prelude> let root a = fix ((flip (-)) a . flip (^) 3) (a-1) (a+1) 0
Prelude> root 27
3.0
Prelude> root 6000000000000000000000000
NaN

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