Publisher's Synopsis
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.
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