It is obvious that for any given $f(x)$ there exists $g(x)$ such that $f(x)=0 \Leftrightarrow g(x)=x$. We could use this fact to solve any root finding problem using fixed point iteration method, only if $g(x)$ promises convergence of the fixed point iteration method.
So I was wondering if there exists an algorithm that takes $f(x)$ and returns appropriate $g(x)$ and $x_0$ such that $x_{i+1}=g(x_i)$ converges to a root of $f(x)$.