A scalable randomized least squares solver for dense overdetermined systems

Abstract

We present a fast randomized least-squares solver for distributed-memory platforms. Our solver is based on the Blendenpik algorithm, but employs a batchwise randomized unitary transformation scheme. The batchwise transformation enables our algorithm to scale the distributed memory vanilla implementation of Blendenpik by up to ×3 and provides up to ×7.5 speedup over a state-of-the-art scalable least-squares solver based on the classic QR based algorithm. Experimental evaluations on terabyte scale matrices demonstrate excellent speedups on up to 16384 cores on a Blue Gene/Q supercomputer.