Can someone please tell me the conditions under which the Newton Raphson method will not converge?
I looked around online, and couldn't find a general way to determine convergence.
For example, for the Fixed Point iteration method, there is a simple way of determining: if we have $g(x_{n})=x_{n+1}$, then $|g'(x)|<1$ implies that the series $g$ will converge to its fixed point, but in the Newton Raphson method, It seems like it is totally depends on "luck", meaning if you were lucky enough to pick a "good" initial guess or not.