You can turn any problem involving the [[Roots]] of a [[Function]] into a [[Fixed Point|fixed point problem by:]] $\huge \begin{align} \exists p : f(p)=0 \end{align} $ $\huge g(x) = f(x) +x $ $g(x)$ will now have a [[Fixed Point]] at $g(p)$. $\huge g(p) = f(p) + p = p\\ $ Note that for this to world, $g'(p) \in (-1,1)$, or $f'(p)\in (-2,0)$. If our function does not satisfy our bounds, we could use a scaled version of $f$ to force it to have less of a chance of derivative not in the bounds. $\huge g(x) = \gamma f(x)+x $ If $\gamma$ is too high, then this method won't convergence - but if $\gamma$ is too low then this will take more iterations.