Abstract
We present a matrix representation for the fast Gauss transform (FGT) originally proposed by Greengard and Strain. With the matrix representation we reveal the matrix structures explored and exploited in the FGT, relate the multidimensional FGT to the one-dimensional FGT via Kronecker products, and unify various FGT versions. Based on the unifying representation, we present also a framework of FGT algorithms that demonstrates an algorithmic approach to utilizing the revealed matrix factor structures and suggests computational varieties for adapting the FGT to architecture specifics as well as application specifics to achieve optimal performance.
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