Randomized Rank-Revealing QLP for Low-Rank Matrix Decomposition

The pivoted QLP decomposition is computed through two consecutive QR decompositions. It an approximation to the computationally prohibitive singular value (SVD). This work concerned with a partial of matrices exploitation random sampling. method presented tailored for low-rank and called Randomized Unpivoted (RU-QLP). Like QLP, RU-QLP rank-revealing yet it utilizes randomized column sampling unpivoted decomposition. latter modifications allow be highly scalable parallelizable on advanced computational platforms. We provide analysis RU-QLP, thereby bringing insights into its characteristics performance behavior. In particular, we derive bounds in terms both spectral Frobenius norms on: i) property; ii) principal angles between approximate subspaces exact vectors; iii) errors approximations. Effectiveness illustrated numerical tests. further use modern, multicore machine equipped GPU demonstrate efficiency RU-QLP. Our results show that compared SVD, achieves speedup up 7.1 8.5 times using CPU 2.3 5.8 dense sparse matrices, respectively.