Bounded-error compression of particle data from hierarchical approximate methods
SC '99 Proceedings of the 1999 ACM/IEEE conference on Supercomputing
Bounded-error compression of particle data from hierarchical approximate methods
SC '99 Proceedings of the 1999 ACM/IEEE conference on Supercomputing
Compression of particle data from hierarchical approximate methods
ACM Transactions on Mathematical Software (TOMS)
A Cost Optimal Parallel Algorithm for Computing Force Field in N-Body Simulations
COCOON '98 Proceedings of the 4th Annual International Conference on Computing and Combinatorics
Dynamic Compressed Hypertoctrees with Application to the N-Body Problem
Proceedings of the 19th Conference on Foundations of Software Technology and Theoretical Computer Science
On well-separated sets and fast multipole methods
Applied Numerical Mathematics
Adaptive fast multipole methods on the GPU
The Journal of Supercomputing
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Greengard's $N$-body algorithm claims to compute the pairwise interactions in a system of $N$ particles in $O(N)$ time for a fixed precision. In this paper, we show that the choice of precision is not independent of $N$ and has a lower bound of $\log N$. We use this result to show that Greengard's algorithm is not $O(N)$.