High Performance Polar Decomposition on Distributed Memory Systems
KAUST DepartmentApplied Mathematics and Computational Science Program
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Extreme Computing Research Center
Online Publication Date2016-08-09
Print Publication Date2016
Permanent link to this recordhttp://hdl.handle.net/10754/622144
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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