17387

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

Wajih Halim Boukaram, George Turkiyyah, Hatem Ltaief, David E. Keyes
Extreme Computing Research Center (ECRC), King Abdullah University of Science and Technology (KAUST), Thuwal 23955, Saudi Arabia
arXiv:1707.05141 [cs.MS], (13 Jul 2017)

@article{boukaram2017batched,

   title={Batched QR and SVD Algorithms on GPUs with Applications in Hierarchical Matrix Compression},

   author={Boukaram, Wajih Halim and Turkiyyah, George and Ltaief, Hatem and Keyes, David E.},

   year={2017},

   month={jul},

   archivePrefix={"arXiv"},

   primaryClass={cs.MS}

}

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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.
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