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Performance Analysis of the Householder-Type Parallel Tall-Skinny QR Factorizations Toward Automatic Algorithm Selection

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High Performance Computing for Computational Science -- VECPAR 2014 (VECPAR 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8969))

Abstract

We consider computing tall-skinny QR factorizations on a large-scale parallel machine. We present a realistic performance model and analyze the difference of the parallel execution time between Householder QR and TSQR. Our analysis indicates the possibility that TSQR becomes slower than Householder QR as the number of columns of the target matrix increases. We aim for estimating the difference and selecting the faster algorithm by using models, which falls into auto-tuning. Numerical experiments on the K computer support our analysis and show our success in determining the faster algorithm.

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Notes

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    Operated at the RIKEN Advanced Institute for Computational Science.

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Acknowledgments

The authors would like to thank the anonymous referees for their valuable comments. The first author appreciates the fruitful discussion with Dr. Mark Hoemmen at iWAPT2014. This research was supported by JST, CREST and used computational resources of the K computer provided by the RIKEN AICS through the HPCI System Research project (Project ID:hp120170).

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Authors and Affiliations

  1. RIKEN Advanced Institute for Computational Science, Kobe, Japan

    Takeshi Fukaya & Toshiyuki Imamura

  2. The University of Electro-Communications, Tokyo, Japan

    Yusaku Yamamoto

  3. JST CREST, Tokyo, Japan

    Takeshi Fukaya, Toshiyuki Imamura & Yusaku Yamamoto

Authors
  1. Takeshi Fukaya
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  2. Toshiyuki Imamura
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  3. Yusaku Yamamoto
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Corresponding author

Correspondence to Takeshi Fukaya .

Editor information

Editors and Affiliations

  1. IRIT, ENSEEIHT, Toulouse Cedex, France

    Michel Daydé

  2. Lawrence Berkeley National Laboratory, Berkeley, California, USA

    Osni Marques

  3. Information Technology Center, The University of Tokyo, Tokyo, Japan

    Kengo Nakajima

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© 2015 Springer International Publishing Switzerland

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Fukaya, T., Imamura, T., Yamamoto, Y. (2015). Performance Analysis of the Householder-Type Parallel Tall-Skinny QR Factorizations Toward Automatic Algorithm Selection. In: Daydé, M., Marques, O., Nakajima, K. (eds) High Performance Computing for Computational Science -- VECPAR 2014. VECPAR 2014. Lecture Notes in Computer Science(), vol 8969. Springer, Cham. https://doi.org/10.1007/978-3-319-17353-5_23

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  • DOI: https://doi.org/10.1007/978-3-319-17353-5_23

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-17352-8

  • Online ISBN: 978-3-319-17353-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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