Category:Aitken's Method

This category contains results about Aitken's Method.
Definitions specific to this category can be found in Definitions/Aitken's Method.

Aitken's method is a technique to make an iterated mapping converge more quickly.

Let $f$ be the iterated mapping in question:

$x_{r + 1} = \map f {x_r}$

Starting with the values $x_0$, $x_1$ and $x_2$, Aitken's method recalculates $x_{r + 1}$ as:

$x_{r + 1} = x_r - \dfrac {\paren {\Delta x_{r - 1} }^2} {\Delta^2 x_{r - 2} }$

where $\Delta$ denotes the forward difference operator.

This is then used as the starting point for the next iteration.