Basic Idea of Fast Multipole Algorithm
These ideas came from many people: Appel, Barnes-Hut, Greengard and Rokhlin
Salmon (Caltech) and Warren(Los Alamos) implemented very well for astrophysics with upto 108 particles
Instead of summing over the M stars in a far away cluster, “just” replace by the contribution of the centroid
Fast Multipole “just” applies this idea recursively with a sum over multipoles extending simple centroid formula.