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On the Design, Development, and Analysis of Optimized Matrix-Vector Multiplication Routines for Coprocessors

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High Performance Computing (ISC High Performance 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9137))

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Abstract

The manycore paradigm shift, and the resulting change in modern computer architectures, has made the development of optimal numerical routines extremely challenging. In this work, we target the development of numerical algorithms and implementations for Xeon Phi coprocessor architecture designs. In particular, we examine and optimize the general and symmetric matrix-vector multiplication routines (gemv/symv), which are some of the most heavily used linear algebra kernels in many important engineering and physics applications. We describe a successful approach on how to address the challenges for this problem, starting with our algorithm design, performance analysis and programing model and moving to kernel optimization. Our goal, by targeting low-level and easy to understand fundamental kernels, is to develop new optimization strategies that can be effective elsewhere for use on manycore coprocessors, and to show significant performance improvements compared to existing state-of-the-art implementations. Therefore, in addition to the new optimization strategies, analysis, and optimal performance results, we finally present the significance of using these routines/strategies to accelerate higher-level numerical algorithms for the eigenvalue problem (EVP) and the singular value decomposition (SVD) that by themselves are foundational for many important applications.

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Acknowledgments

This material is based upon work supported by the National Science Foundation under Grant No. ACI-1339822, the Department of Energy, and Intel. The results were obtained in part with the financial support of the Russian Scientific Fund, Agreement N14-11-00190.

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Authors and Affiliations

  1. University of Tennessee Knoxville, Knoxville, USA

    Khairul Kabir, Azzam Haidar, Stanimire Tomov & Jack Dongarra

  2. Oak Ridge National Laboratory, Oak Ridge, USA

    Jack Dongarra

  3. University of Manchester, Manchester, UK

    Jack Dongarra

Authors
  1. Khairul Kabir
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  2. Azzam Haidar
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  3. Stanimire Tomov
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  4. Jack Dongarra
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Corresponding author

Correspondence to Azzam Haidar .

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Editors and Affiliations

  1. Deutsches Klimarechenzentrum (DKRZ), Hamburg, Germany

    Julian M. Kunkel

  2. Deutsches Klimarechenzentrum (DKRZ), Hamburg, Germany

    Thomas Ludwig

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Kabir, K., Haidar, A., Tomov, S., Dongarra, J. (2015). On the Design, Development, and Analysis of Optimized Matrix-Vector Multiplication Routines for Coprocessors. In: Kunkel, J., Ludwig, T. (eds) High Performance Computing. ISC High Performance 2015. Lecture Notes in Computer Science(), vol 9137. Springer, Cham. https://doi.org/10.1007/978-3-319-20119-1_5

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  • DOI: https://doi.org/10.1007/978-3-319-20119-1_5

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