[cscheid]

It's not cutting off. It's replacing many long-range effects with a single one weighted more (and done it carefully so that the floating-point error is literally smaller than you could tell).

There's even better methods that take O(n) time, like the fast multipole expansion ones.

[darkmighty]

Btw this goes into numerical analysis, and O(-) is important but so is error convergence. I imagine these big-O figures are for a constant error, but I figure the asymptotic may change behavior as the other parameter changes.