Aitken's method

Concept

$$y_{k+2}=x_{k+2}-\frac{{\Delta }_2^2}{{\Delta }_2-{\Delta }_1}$$

where

$${\Delta }_1=x_{k+1}-x_k$$ $${\Delta }_2=x_{k+2}-x_{k+1}$$

this method is used to accelerating linearly converge

for k = 0, 2, 4, ...
	x_{k + 1} = g(x_k)
	x_{k + 2} = g(x_{k + 1})
	calc deltas
	x_{k + 2} = x_{k + 2} - Delta_2^2 / (Detla_2 - Delta_1)