Error Estimates for the Fast Multipole Method. II. The Three-Dimensional Case

The fast multipole method is a new and interesting method for computing long range interactions in particle systems. Although the method already has been implemented and compared to traditional and other methods with respect to accuracy and speed, no accurate error estimates of the fast multipole method have been given. In this paper we develop an explicit though complicated form for the error in the three dimensional case, and derive an estimate for it. The estimate has a simple analytic form which will allow its use in tuning the method for best efficiency and for comparison of the method with other methods at the same accuracy.