  The pivoted QLP decomposition is computed through two consecutive pivoted QR
decompositions, and provides an approximation to the singular value
decomposition. This work is concerned with a partial QLP decomposition of
low-rank matrices computed through randomization, termed Randomized Unpivoted
QLP (RU-QLP). Like pivoted QLP, RU-QLP is rank-revealing and yet it utilizes
random column sampling and the unpivoted QR decomposition. The latter
modifications allow RU-QLP to be highly parallelizable on modern computational
platforms. We provide an analysis for RU-QLP, deriving bounds in spectral and
Frobenius norms on: i) the rank-revealing property; ii) principal angles
between approximate subspaces and exact singular subspaces and vectors; and
iii) low-rank approximation errors. Effectiveness of the bounds is illustrated
through numerical tests. We further use a modern, multicore machine equipped
with a GPU to demonstrate the efficiency of RU-QLP. Our results show that
compared to the randomized SVD, RU-QLP achieves a speedup of up to 7.1 times on
the CPU and up to 2.3 times with the GPU.
