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An efficient distributed randomized solver with application to large dense linear systems

Randomized algorithms are gaining ground in high-performance computing applications as they have the potential to outperform deterministic methods, while still providing accurate results. In this paper, we propose a randomized algorithm for distributed multicore architectures to efficiently solve large dense symmetric indefinite linear systems that are encountered, for instance, in parameter estimation problems or electromagnetism simulations. This solver combines an efficient implementation of a multiplicative preconditioning based on recursive random matrices, with a runtime (DAGuE) that automatically adjusts data structures, data mappings, and the scheduling as systems scale up. Both the solver and the supporting runtime environment are innovative. To our knowledge, this is the first parallel distributed solver for large dense symmetric indefinite systems, and the randomization approach associated with this solver has never been used in public domain software for such systems. The underlying runtime framework allows seamless data mapping and task scheduling, mapping its capabilities to the underlying hardware features of heterogeneous distributed architectures. The performance of our software is similar to that obtained for symmetric positive definite systems, but requires only half the execution time and half the amount of data storage of a general dense solver.