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Software Automatic Tuning pp 87–101Cite as

Automatic Tuning of the Division Number in the Multiple Division Divide-and-Conquer for Real Symmetric Eigenproblem

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Abstract

In this study, we propose a novel algorithm which estimates the optimal division number in the multiple division divide-and-conquer (DCk) for real symmetric tridiagonal eigenproblem. Using the proposed algorithm, we establish an automatically tuned DCk algorithm (ATDCk), in which the quasi-optimal division number used in DCk is automatically determined by a simple but efficient pre-test to the input matrix, prior to the main computation of the eigenvalues and eigenvectors. The efficiency of the ATDCk is confirmed by numerical experiment covering a wide range of test matrices including the physical and statistical models as well as the matrix market. The comparison with the LAPACK routine DSTEVD based on the usual divide-and-conquer with the division number 2 (DC2) is also made.

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Acknowledgements

This work was partially supported by Grant-in-Aid for Scientific Research (C) No.19560058.

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Authors and Affiliations

  1. Graduate School of Science and Engineering, Saitama University, Saitama, Japan

    Takaomi Shigehara

Authors
  1. Yusuke Ishikawa
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  2. Junichi Tamura
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  3. Yutaka Kuwajima
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  4. Takaomi Shigehara
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Corresponding author

Correspondence to Takaomi Shigehara .

Editor information

Editors and Affiliations

  1. Central Research Laboratory, Hitachi Ltd., Higashi-Koigakubo 1-280, Kokubunji-shi, Tokyo, 185-8601, Japan

    Ken Naono

  2. Cray, Inc., Jackson St. 380, St Paul, 55101, Minnesota, USA

    Keita Teranishi

  3. Dept. Computer & Information Sciences, University of Delaware, Smith Hall 101, Newark, 19716, Delaware, USA

    John Cavazos

  4. Dept. Computer Science, University of Tokyo, Hongo 7-3-1, Tokyo, 113-0033, Japan

    Reiji Suda

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© 2011 Springer New York

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Ishikawa, Y., Tamura, J., Kuwajima, Y., Shigehara, T. (2011). Automatic Tuning of the Division Number in the Multiple Division Divide-and-Conquer for Real Symmetric Eigenproblem. In: Naono, K., Teranishi, K., Cavazos, J., Suda, R. (eds) Software Automatic Tuning. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-6935-4_6

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  • DOI: https://doi.org/10.1007/978-1-4419-6935-4_6

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4419-6934-7

  • Online ISBN: 978-1-4419-6935-4

  • eBook Packages: EngineeringEngineering (R0)

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