# Determining the early exercise curve of an American option

When I have found the price of an American option using, say, a finite difference scheme - how do I find the early exercise curve from this solution?

Here is my idea: What I have is the price of the option on a $$(t_i, s_j)$$-grid. Denote this solution $$p_{ij}$$. What I can do is for each $$i$$ to compare the solution to the theoretical payoff $$g(s)$$. The point where the difference $$|g(s_j)- p_{ij}|$$ is less than some threshold will trace out the curve.

I guess this will work, but not sure how thorough it is. Are there better methods?