Comment by whinvik

The problem with Newton's method is that it is provably convergent but only if you are sufficiently close to the solution. That basically means that the initial condition that you chose for solving the problem is very important. What this paper seems to suggest is that their method is globally convergent and they produce the algortithm to do it, although there is some tuning that needs to be done. So in theory, with their method we will always get to a solution, no matter the initial condition we chose.