Steffensen's Method is a type of meta - iterative method leveraging [[Aitken's Delta Squared]] to 'boost' a [[Linear Convergence|linearly convergent]] method (ex. [[Fixed Point Method]]) .
With our method $M$, iterate $3$ times. Use these three values with [[Aitken's Delta Squared]] to get the next iteration. Iterate $M$ two more times, and then use the past three with [[Aitken's Delta Squared]] and so on.
$ \begin{align}
M(x_{n}) &\to M(x_{n+1}) \\
&\to M(x_{n+2}) \\
&\to A_{\Delta^{2}}\pa{
M(x_{n}) \to M(x_{n+1}) \to M(x_{n+2})
}\\
&\to M(\cdots) \\
&\to \cdots
\end{align}
$
The [[Numerical Analysis Error Bounds|Error Bound]] / [[Order of Convergence]] of this method is dependent on the specific method.
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