Concept

𝑦𝑘+2=𝑥𝑘+2Δ22Δ2Δ1

where

Δ1=𝑥𝑘+1𝑥𝑘 Δ2=𝑥𝑘+2𝑥𝑘+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)