The article is quite readable. I'm a layperson too, but here's what I made of the methods provided: 1- The first method finds a constant that guarantees conver

The article is quite readable. I'm a layperson too, but here's what I made of the methods provided: 1- The first method finds a constant that guarantees convergence of newtons method to the solution; they then iterate it a few times and verify the result is almost stationary. 2- They use a set with parameter r that is guaranteed to contain a solution if it's contained in a ball of radius r; they then show that a given small ball around the candidate solution contains this set (they were able to do that because this set gets smaller faster than the radius).