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Excerpt from Parallelizing the Adaptive Fast Multipole Method on a Shared Memory MIMD Machine
Hence the multipole method can be viewed as a fast algorithm for applying a Hilbert matrix to an arbitrary vector. In this form, the problem has been studied by several others but the multipole algorithm appears to be the most practical computational approach. The multipole algorithm makes use of a multipole expansion to compute forces between groups of particles that are well-separated in the plane. It is based on the following theorem, a proof of which can be found in [7. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
