Is a higher [[Order of Convergence]] better?
Let say we have two methods:
Method 1 $\alpha = 2$
Method 2 $\alpha = 3$
Method 2 might not neccasarily be 'better', it could be doing *more work per iteration*.
In the case where method 2 is [[Linear Convergence]]:
$\huge \begin{align}
M_{1} : \alpha = 2, x_{n+1} = x_n^{2}
\end{align}$
$\huge \begin{align}
M_{2} : \alpha = 1, x_{n+1} = \frac{1}{100} x_n
\end{align}$