Far-Field Compression for Fast Kernel Summation Methods in High Dimensions.

We consider fast kernel summations in high dimensions: given a large set of points in d dimensions (with d≫3) and a pair-potential function (the kernel function), we compute a weighted sum of all pairwise kernel interactions for each point in the set. Direct summation is equivalent to a (dense) matrix–vector multiplication and scales quadratically with the number of points. Fast kernel summation algorithms reduce this cost to log-linear or linear complexity.