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    Batched QR and SVD Algorithms on GPUs with Applications in Hierarchical Matrix Compression

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    1-s2.0-S0167819117301461-main.pdf
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    Type
    Article
    Authors
    Boukaram, Wagih Halim
    Turkiyyah, George
    Ltaief, Hatem cc
    Keyes, David E. cc
    KAUST Department
    Applied Mathematics and Computational Science Program
    Computer Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Extreme Computing Research Center
    Date
    2017-09-14
    Permanent link to this record
    http://hdl.handle.net/10754/625473
    
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    Abstract
    We present high performance implementations of the QR and the singular value decomposition of a batch of small matrices hosted on the GPU with applications in the compression of hierarchical matrices. The one-sided Jacobi algorithm is used for its simplicity and inherent parallelism as a building block for the SVD of low rank blocks using randomized methods. We implement multiple kernels based on the level of the GPU memory hierarchy in which the matrices can reside and show substantial speedups against streamed cuSOLVER SVDs. The resulting batched routine is a key component of hierarchical matrix compression, opening up opportunities to perform H-matrix arithmetic efficiently on GPUs.
    Citation
    Halim Boukaram W, Turkiyyah G, Ltaief H, Keyes DE (2017) Batched QR and SVD Algorithms on GPUs with Applications in Hierarchical Matrix Compression. Parallel Computing. Available: http://dx.doi.org/10.1016/j.parco.2017.09.001.
    Sponsors
    The work of all four authors was supported by the Extreme Computing Research Center at the King Abdullah University of Science and Technology. We thank the NVIDIA Corporation for providing access to the P100 GPU used in this work.
    Publisher
    Elsevier BV
    Journal
    Parallel Computing
    DOI
    10.1016/j.parco.2017.09.001
    arXiv
    1707.05141
    Additional Links
    http://www.sciencedirect.com/science/article/pii/S0167819117301461
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.parco.2017.09.001
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Extreme Computing Research Center; Computer Science Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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