Definition:Aitken's Method

Definition

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.

Also see

• Results about Aitken's method can be found here.

Source of Name

This entry was named for Alexander Craig Aitken.

Sources

• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Aitken's method (in numerical methods)
• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): Aitken's method (in numerical analysis)