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An Error Resilience Strategy of a Complex Moment-Based Eigensolver

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Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing (EPASA 2015)

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 117))

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Abstract

Recently, complex moment-based eigensolvers have been actively developed in highly parallel environments to solve large and sparse eigenvalue problems. In this paper, we provide an error resilience strategy of a Rayleigh–Ritz type complex moment-based parallel eigensolver for solving generalized eigenvalue problems. Our strategy is based on an error bound of the eigensolver in the case that soft-errors like bit-flip occur. Using the error bound, we achieve an inherent error resilience of the eigensolver that does not require standard checkpointing and replication techniques in the most time-consuming part.

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References

  1. Asakura, J., Sakurai, T., Tadano, H., Ikegami, T., Kimura, K.: A numerical method for nonlinear eigenvalue problems using contour integrals. JSIAM Lett. 1, 52–55(2009)

    Article  MathSciNet  MATH  Google Scholar 

  2. Asakura, J., Sakurai, T., Tadano, H., Ikegami, T., Kimura, K.: A numerical method for polynomial eigenvalue problems using contour integral. Jpn. J. Ind. Appl. Math. 27, 73–90 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  3. Beyn, W.-J.: An integral method for solving nonlinear eigenvalue problems. Lin. Algor. Appl. 436, 3839–3863 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  4. ELSES matrix library, http://www.elses.jp/matrix/

  5. Ikegami, T., Sakurai, T.: Contour integral eigensolver for non-Hermitian systems: a Rayleigh-Ritz-type approach. Taiwan. J. Math. 14, 825–837 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  6. Ikegami, T., Sakurai, T., Nagashima, U.: A filter diagonalization for generalized eigenvalue problems based on the Sakurai-Sugiura projection method. J. Comput. Appl. Math. 233, 1927–1936 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  7. Imakura, A., Sakurai, T.: Block Krylov-type complex moment-based eigensolvers for solving generalized eigenvalue problems. Numer. Algor. 75, 413–433 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  8. Imakura, A., Du, L., Sakurai, T.: A block Arnoldi-type contour integral spectral projection method for solving generalized eigenvalue problems. Appl. Math. Lett. 32, 22–27 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  9. Imakura, A., Du, L., Sakurai, T.: Error bounds of Rayleigh–Ritz type contour integral-based eigensolver for solving generalized eigenvalue problems. Numer. Algor. 71, 103–120 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  10. Imakura, A., Du, L., Sakurai, T.: Relationships among contour integral-based methods for solving generalized eigenvalue problems. Jpn. J. Ind. Appl. Math. 33, 721–750 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  11. Kravanja, P., Sakurai, T., van Barel, M.: On locating clusters of zeros of analytic functions. BIT 39, 646–682 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  12. Polizzi, E.: A density matrix-based algorithm for solving eigenvalue problems. Phys. Rev. B 79, 115112 (2009)

    Article  Google Scholar 

  13. Sakurai, T., Sugiura, H.: A projection method for generalized eigenvalue problems using numerical integration. J. Comput. Appl. Math. 159, 119–128 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  14. Sakurai, T. Tadano, H.: CIRR: a Rayleigh-Ritz type method with counter integral for generalized eigenvalue problems. Hokkaido Math. J. 36, 745–757 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  15. Sakurai, T., Futamura, Y., Tadano, H.: Efficient parameter estimation and implementation of a contour integral-based eigensolver. J. Algor. Comput. Technol. 7, 249–269 (2014)

    Article  MathSciNet  Google Scholar 

  16. Schofield, G., Chelikowsky, J.R., Saad, Y.: A spectrum slicing method for the Kohn-Sham problem. Comput. Phys. Commun. 183, 497–505 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  17. Tang, P.T.P., Polizzi, E.: FEAST as a subspace iteration eigensolver accelerated by approximate spectral projection. SIAM J. Matrix Anal. Appl. 35, 354–390 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  18. Yokota, S., Sakurai, T.: A projection method for nonlinear eigenvalue problems using contour integrals. JSIAM Lett. 5, 41–44 (2013)

    Article  MathSciNet  Google Scholar 

  19. z-Pares, http://zpares.cs.tsukuba.ac.jp/

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Acknowledgements

The authors would like to thank the anonymous referees for their useful comments. This research was supported partly by University of Tsukuba Basic Research Support Program Type A, JST/CREST, JST/ACT-I (Grant No. JPMJPR16U6) and KAKENHI (Grant Nos. 25286097, 25870099, 17K12690). This research in part used computational resources of COMA provided by Interdisciplinary Computational Science Program in Center for Computational Sciences, University of Tsukuba.

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Authors and Affiliations

  1. University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki, 305-8573, Japan

    Akira Imakura, Yasunori Futamura & Tetsuya Sakurai

Authors
  1. Akira Imakura
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  2. Yasunori Futamura
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  3. Tetsuya Sakurai
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Corresponding author

Correspondence to Akira Imakura .

Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Tsukuba, Tsukuba, Ibaraki, Japan

    Tetsuya Sakurai

  2. Department of Electrical Engineering and Computer Science, Nagoya University, Nagoya, Aichi, Japan

    Shao-Liang Zhang

  3. RIKEN Advanced Institute for Computational Science, Kobe, Hyogo, Japan

    Toshiyuki Imamura

  4. Department of Communication Engineering and Informatics, University of Electro-Communications, Graduate School of Informatics and Engineering, Tokyo, Japan

    Yusaku Yamamoto

  5. Department of Particle Physics, University of Tsukuba, Tsukuba, Ibaraki, Japan

    Yoshinobu Kuramashi

  6. Department of Applied Mathematics and Physics, Tottori University, Tottori, Japan

    Takeo Hoshi

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Imakura, A., Futamura, Y., Sakurai, T. (2017). An Error Resilience Strategy of a Complex Moment-Based Eigensolver. In: Sakurai, T., Zhang, SL., Imamura, T., Yamamoto, Y., Kuramashi, Y., Hoshi, T. (eds) Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing. EPASA 2015. Lecture Notes in Computational Science and Engineering, vol 117. Springer, Cham. https://doi.org/10.1007/978-3-319-62426-6_1

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