I appologize in advance if this question is silly. I need to compute the root of
\begin{equation} u -f(u) =0 \end{equation}
Where $u$ is a real vector and $f(u)$ is a real-vector valued function. I started with Newton's method (which worked), but then realized a much simpler method would be an iterative solution
\begin{equation} u_{i+1} = f(u_{i}) \end{equation}
This is much quicker and apparently as accurate/stable as Newton's method.
Now the questions:
- Is this the correct approach or should I use a different method?
- Is there anything that can be said about it's convergence rate, stability, acc, etc?
- Is it globally convergent?
Thank you all in advance for the attention.