Skip to main content
SpringerLink
Log in

A Massively Parallel Dense Symmetric Eigensolver with Communication Splitting Multicasting Algorithm

  • Conference paper
High Performance Computing for Computational Science – VECPAR 2010 (VECPAR 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6449))

Abstract

In this paper, we propose a process grid free algorithm for a massively parallel dense symmetric eigensolver with a communication splitting multicasting algorithm. In this algorithm, a tradeoff exists between speed and memory space to keep the Householder vectors. As a result of a performance evaluation with the T2K Open Supercomputer (U. Tokyo) and the RX200S5, we obtain the performance with 0.86x and 0.95x speed-downs and 1/2 memory space compared to the conventional algorithm for a square process grid. We also show a new algorithm for small-sized matrices in massively parallel processing that takes an appropriately small value of p of the process grid p x q. In this case, the execution time of inverse transformation is negligible.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Inaba, T., Tsunekawa, N., Hirano, T., Yoshihiro, T., Kashiwagi, H., Sato, F.: Density Functional Calculation of the Electronic Structure on Insulin Hexamer. Chemical Physics Letters 434(4-6), 331–335 (2007)

    Article  Google Scholar 

  2. Dongarra, J.J., Hammarling, S.J., Sorensen, D.C.: Block Reduction of Matrices to Condensed Forms for Eigenvalue Computations. Journal of Computational and Applied Mathematics 27, 215–227 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bischof, C.H., Marques, M., Sun, X.: Parallel Bandreduction and Tridiagonalization. In: Proceedings of Sixth SIAM Conference on Parallel Processing for Scientific Computing, pp. 22–24 (1993)

    Google Scholar 

  4. Katagiri, T., Kanada, Y.: An Efficient Implementation of Parallel Eigenvalue Computation for Massively Parallel Processing. Parallel Computing 27(14), 1831–1845 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  5. Katagiri, T., Kise, K., Honda, H., Yuba, T.: ABCLib_DRSSED: A Parallel Eigensolver with an Auto-tuning Facility. Parallel Computing 32(3), 231–250 (2006)

    Article  Google Scholar 

  6. ABCLib_DRSSED home page, http://www.abc-lib.org/main1.html

  7. Imamura, T.: How To Develop The Eigenvalue Solver Which Organizes Beyond Hundred Thousand Cores. IPSJ SIG Notes  2009-HPC-121(19) (2009) (in Japanese)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Information Technology Center, The University of Tokyo, 2-11-16 Yayoi, Bunkyo-ku, Tokyo, 113-8658, Japan

    Takahiro Katagiri

  2. Advanced Center for Computing and Communication, RIKEN, 2-1 Hirosawa, Wako-shi, Saitama, 351-0198, Japan

    Shoji Itoh

Authors
  1. Takahiro Katagiri
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shoji Itoh
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Faculdade de Engenharia da, Universidade do Porto, Rua Dr. Roberto Frias s/n, 4200-465, Porto, Portugal

    José M. Laginha M. Palma

  2. INP (ENSEEIHT) IRIT, University of Toulouse, rue Charles-Camichel, CEDEX 7, 31071, Toulouse, France

    Michel Daydé

  3. Lawrence Berkeley National Laboratory, Berkeley, USA

    Osni Marques

  4. Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, s/n, 4200-465, Porto, Portugal

    João Correia Lopes

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Katagiri, T., Itoh, S. (2011). A Massively Parallel Dense Symmetric Eigensolver with Communication Splitting Multicasting Algorithm. In: Palma, J.M.L.M., Daydé, M., Marques, O., Lopes, J.C. (eds) High Performance Computing for Computational Science – VECPAR 2010. VECPAR 2010. Lecture Notes in Computer Science, vol 6449. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19328-6_15

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-19328-6_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-19327-9

  • Online ISBN: 978-3-642-19328-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation