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High-Performance SVD Partial Spectrum Computation

DescriptionWe introduce a new singular value decomposition (SVD) solver based on the QR-based Dynamically Weighted Halley (QDWH) algorithm for computing the partial spectrum SVD (QDWHpartial-SVD) problems. By optimizing the rational function underlying the algorithms only in the desired part of the spectrum, QDWHpartial-SVD algorithm efficiently computes a fraction (say 1-20%) of the most significant singular values/vectors. We develop a high-performance implementation of QDWHpartial-SVD on distributed-memory manycore systems and demonstrate their numerical robustness. We perform a benchmarking campaign against their counterparts from the state-of-the-art numerical libraries across various matrix sizes using up to 36K MPI processes. Experimental results show performance speedups for QDWHpartial-SVD up to 6X and 2X against PDGESVD from ScaLAPACK and KSVD, respectively. We also report energy consumption for these algorithms and demonstrate how QDWHpartial-SVD can further outperform PDGESVD in that regard by performing fewer memory-bound operations.

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