Some of the recently developed fast summation methods that have arisen in scientific computing are described. These methods require an amount of work proportional to N or N log N to evaluate all pairwise interactions in an ensemble of N particles. Traditional methods, by contrast, require an amount of work proportional to N2. As a result, large-scale simulations can be carried out using only modest computer resources. In combination with supercomputers, it is possible to address questions that were previously out of reach. Problems from diffusion, gravitation, and wave propagation are considered.
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