Performance Analysis of the Chebyshev Basis Conjugate Gradient Method on the K Computer

  • Yosuke KumagaiEmail author
  • Akihiro Fujii
  • Teruo Tanaka
  • Yusuke Hirota
  • Takeshi Fukaya
  • Toshiyuki Imamura
  • Reiji Suda
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9573)


The conjugate gradient (CG) method is useful for solving large and sparse linear systems. It has been pointed out that collective communication needed for calculating inner products becomes serious performance bottleneck when executing the CG method on massively parallel systems. Recently, the Chebyshev basis CG (CBCG) method, a communication avoiding variant of the CG method, has been proposed, and theoretical studies have shown promising results, particularly for upcoming exascale supercomputers. In this paper, we evaluate the CBCG method on an actual system, namely the K computer, to examine the potential of the CBCG method. We first construct a realistic performance model that reflects the computation on the K computer, and the model indicates that the CBCG method is faster than CG method if the number of cores is sufficient large. We then measure the execution time of both methods on the K computer, and obtained results agree with our estimation.


Communication avoiding Conjugate gradient method Linear solver 



The authors would like to thank the anonymous referees for their valuable comments. This research used the results of the “RIKEN AICS HPC computational science internship program 2014”. This research also used the computational resources of the K computer provided by the RIKEN Advanced Institute for Computational Science(Project ID: ra000005). This work was partially supported by the Japan Society for the Promotion of Science KAKENHI (grant numbers 25330144, 15H02708, and 15K16000).


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Yosuke Kumagai
    • 1
    Email author
  • Akihiro Fujii
    • 1
  • Teruo Tanaka
    • 1
  • Yusuke Hirota
    • 2
    • 3
  • Takeshi Fukaya
    • 2
    • 3
    • 4
  • Toshiyuki Imamura
    • 2
    • 3
  • Reiji Suda
    • 5
  1. 1.Kogakuin UniversityTokyoJapan
  2. 2.RIKEN Advanced Institute for Computational ScienceKobeJapan
  3. 3.JST CRESTTokyoJapan
  4. 4.Hokkaido UniversityHokkaidoJapan
  5. 5.The University of TokyoTokyoJapan

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