A fast algorithm that approximates a low rank LU decomposition is presented. In order to achieve a low complexity, the algorithm uses sparse random projections combined with FFT-based random projections. The asymptotic approximation error of the algorithm is analyzed and a theoretical error bound is presented. Finally, numerical examples illustrate that for a similar approximation error, the sparse LU algorithm is faster than recent state-of-the-art methods. The algorithm is completely parallelizable and can fully run on a GPU. The performance is tested on a GPU card showing a significant speed-up improvement in the running time in comparison to a sequential execution.
- LU decomposition
- Random matrices
- Sparse Johnson–Lindenstrauss transform
- Sparse matrices