Error Convergence Process of the Multipole Expansion

We focus on the truncation error of the multipole expansion for the multilevel fast multipole algorithm and investigate the condition to minimize it. When the buffer size is small compared to the machine precision, the conventional selection rules do not hold, and the new approach which we have recently proposed is needed. However, this method is still not sufficient to minimize the error for small buffer cases. We will show that the information about the placement of true worst-case interaction is needed.link_to_subscribed_fulltex