An Efficient Distributed Randomized Algorithm for Solving Large Dense Symmetric Indefinite Linear Systems

TitleAn Efficient Distributed Randomized Algorithm for Solving Large Dense Symmetric Indefinite Linear Systems
Publication TypeJournal Article
Year of Publication2014
AuthorsBaboulin, M., D. Becker, G. Bosilca, A. Danalis, and J. Dongarra
JournalParallel Computing
Volume40
Issue7
Pagination213-223
Date Published07-2014
KeywordsDistributed linear algebra solvers, LDLT factorization, PaRSEC runtime, Randomized algorithms, Symmetric indefinite systems
AbstractRandomized algorithms are gaining ground in high-performance computing applications as they have the potential to outperform deterministic methods, while still providing accurate results. We propose a randomized solver 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. The contribution of this paper is to propose efficient kernels for applying random butterfly transformations and a new distributed implementation combined with a runtime (PaRSEC) that automatically adjusts data structures, data mappings, and the scheduling as systems scale up. Both the parallel distributed solver and the supporting runtime environment are innovative. To our knowledge, the randomization approach associated with this solver has never been used in public domain software for symmetric indefinite 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.
DOI10.1016/j.parco.2013.12.003
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