Progressive Optimization of Batched LU Factorization on GPUs

This paper presents a progressive approach for optimizing the batched LU factorization on graphics processing units (GPUs). The paper shows that the reliance on level-3 BLAS routines for performance does not really pay off, and that it is indeed important to pay attention to the memory-bound part of the algorithm, especially when the problem size is very small. In this context, we develop a size-aware multi-level blocking technique that utilizes different granularities for kernel fusion according to the problem size. Our experiments, which are conducted on a Tesla V100 GPU, show that the multi-level blocking technique achieves speedups for single/double precisions that are up to 3.28×/2.69× against the generic LAPACK-style implementation. It is also up to 8.72×/7.2× faster than the cuBLAS library for single and double precisions, respectively. The developed solution is integrated into the open-source MAGMA library.