Randomized LU decomposition

Randomized algorithms play a central role in low rank approximations of large matrices. In this paper, the scheme of the randomized SVD is extended to a randomized LU algorithm. Several error bounds are introduced, that are based on recent results from random matrix theory related to subgaussian matrices. The bounds also improve the existing bounds of already known randomized SVD algorithm. The algorithm is fully parallelized and thus can utilize efficiently GPUs without any CPU-GPU data transfer. Numerical examples, which illustrate the performance of the algorithm and compare it to other decomposition methods, are presented.