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Update 2_Algorithms.md
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s-baumann committed Jan 17, 2019
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Expand Up @@ -9,7 +9,7 @@ $x_{i+1} = x_i - \frac{g(x_i)}{g^\prime(x_i)}$

**FixedPointAcceleration.jl** approximates the derivative $g^\prime(x_i)$ so that we use an estimated fixed point of:

$x_{i+1} = x_i - \frac{g(x_i)}{ \frac{ g(x_i) - g(x_{i-1})}{x_i-x_{i-1}} }$
$\text{Next Guess} = x_i - \frac{g(x_i)}{ \frac{ g(x_i) - g(x_{i-1})}{x_i-x_{i-1}} }$

The implementation of the Newton method in this package uses this formula to predict the fixed point given two previous iterates.[^1] This method is designed for use with scalar functions.

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