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Using Quadruple Precision Arithmetic to Accelerate Krylov Subspace Methods on GPUs

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Parallel Processing and Applied Mathematics (PPAM 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8384))

Abstract

The convergence of the Krylov subspace methods is affected by round-off errors. The number of iterations until convergence may be decreased by reducing round-off errors through the use of quadruple precision arithmetic instead of double precision. We implemented the CG and BiCGStab methods using quadruple precision arithmetic and compared the performance with the standard double precision implementations on an NVIDIA Tesla K20X GPU. Our results show that in some cases our implementations using quadruple precision arithmetic outperform the double precision versions. We will show that quadruple precision arithmetic is not costly for the CG and BiCGStab methods on GPUs and the use of quadruple precision arithmetic may be a more effective alternative to the use of preconditioning.

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Acknowledgment

This research was supported by JST, CREST.

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Authors and Affiliations

  1. Graduate School of Systems and Information Engineering, University of Tsukuba, Tsukuba, Japan

    Daichi Mukunoki

  2. Faculty of Engineering, Information and Systems, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki, 305–8573, Japan

    Daisuke Takahashi

  3. Japan Society for the Promotion of Science, 5-3-1 Kojimachi, Chiyoda-ku, Tokyo, 102-0083, Japan

    Daichi Mukunoki

Authors
  1. Daichi Mukunoki
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  2. Daisuke Takahashi
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Corresponding author

Correspondence to Daichi Mukunoki .

Editor information

Editors and Affiliations

  1. Institute of Computer and Information Science, Czestochowa University of Technology, Czestochowa, Poland

    Roman Wyrzykowski

  2. University of Tennessee, Department of Computer Science, Knoxville, Tennessee, USA

    Jack Dongarra

  3. Institute of Computer and Information Science, Czestochowa University of Technology, Czestochowa, Poland

    Konrad Karczewski

  4. Technical University of Denmark Informatics and Mathematical Modelling, Kongens Lyngby, Denmark

    Jerzy Waśniewski

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Mukunoki, D., Takahashi, D. (2014). Using Quadruple Precision Arithmetic to Accelerate Krylov Subspace Methods on GPUs. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Waśniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2013. Lecture Notes in Computer Science(), vol 8384. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55224-3_59

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  • DOI: https://doi.org/10.1007/978-3-642-55224-3_59

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-55223-6

  • Online ISBN: 978-3-642-55224-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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