PBBFMM3D: a parallel black-box algorithm for kernel matrix-vector multiplication
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We introduce PBBFMM3D, a parallel black-box method for computing kernel matrix-vector multiplication, where the underlying kernel is a non-oscillatory function in three dimensions. While a naive method requires Ø(N^2) computation, PBBFMM3D reduces the cost to Ø(N) work. In particular, our algorithm requires only the ability to evaluate the kernel function, and is thus a black-box method. To further accelerate the computation on shared-memory machines, a parallel algorithm is presented and implemented using , which achieved at most 19× speedup on 32 cores in our numerical experiments. A real-world application in geostatistics is also presented, where PBBFMM3D is used in computing the truncated eigen-decomposition (a.k.a., principle component analysis) of a covariance matrix (a.k.a., graph Laplacian).
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