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We call matrix algorithms superfast if they use much fewer flops and memorycells than the input matrix has entries. Using such algorithms is indispensablefor Big Data Mining and Analysis, where the input matrices are so immense thatone can only access a small fraction of all their entries. A natural remedy isLow Rank Approximation (LRA) of these matrices, which is routinely computed bymeans of Cross-Approximation iterations for more than a decade of worldwideapplication in computational practice. We point out and extensively test animportant application of superfast LRA to significant acceleration of thecelebrated Fast Multipole Method, which turns it into Superfast MultipoleMethod.

QRP Variation of Cross--Approximation Iterations for Low Rank Approximation