High Performance Polar Decomposition on Distributed Memory Systems
KAUST DepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Extreme Computing Research Center
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AbstractThe polar decomposition of a dense matrix is an important operation in linear algebra. It can be directly calculated through the singular value decomposition (SVD) or iteratively using the QR dynamically-weighted Halley algorithm (QDWH). The former is difficult to parallelize due to the preponderant number of memory-bound operations during the bidiagonal reduction. We investigate the latter scenario, which performs more floating-point operations but exposes at the same time more parallelism, and therefore, runs closer to the theoretical peak performance of the system, thanks to more compute-bound matrix operations. Profiling results show the performance scalability of QDWH for calculating the polar decomposition using around 9200 MPI processes on well and ill-conditioned matrices of 100K×100K problem size. We study then the performance impact of the QDWH-based polar decomposition as a pre-processing step toward calculating the SVD itself. The new distributed-memory implementation of the QDWH-SVD solver achieves up to five-fold speedup against current state-of-the-art vendor SVD implementations. © Springer International Publishing Switzerland 2016.
CitationSukkari D, Ltaief H, Keyes D (2016) High Performance Polar Decomposition on Distributed Memory Systems. Lecture Notes in Computer Science: 605–616. Available: http://dx.doi.org/10.1007/978-3-319-43659-3_44.
SponsorsFor computer time, this research used the resources from the Swiss National Supercomputing Centre (CSCS) in Lugano, Switzerland.
Conference/Event name22nd International Conference on Parallel and Distributed Computing, Euro-Par 2016