Scalable Hybrid Loop- And Task-Parallel Matrix Inversion For Multicore Processors

We propose a hybrid parallelization scheme for matrix inversion on multicore processors that combines a look-ahead technique to extract task-parallelism, at a high level, with loop-level parallelism to ensure an efficient utilization of the processor memory subsystem. As a result, our scheme outperforms the conventional approach for dense linear algebra operations, which simply extracts parallelism from a multi-threaded instance of the BLAS (Basic Linear Algebra Subprograms), but also the alternative based on OpenMP task-parallelism only, which is supposed to offer higher scalability. We provide an extensive collection of experiments supporting our remarks on two recent Intel- and ARM-based architectures, with a very large count of cores.