ERROR-ESTIMATES FOR THE FAST MULTIPOLE METHOD .1. THE 2-DIMENSIONAL CASE

The Greengard-Rokhlin algorithm is a new and interesting method for co mputing long-range interactions in particle systems. Although the meth od already has been implemented and claimed to be superior to traditio nal and other methods, no reliable estimates of the size of the error of the method have been given. We illustrate what the error actually i s for the two-dimensional case, and derive an estimate for it. The est imate has a simple analytic form which will allow its use in tuning th e algorithm for best efficiency.