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International Conference on Parallel Processing and Applied Mathematics

PPAM 2013: Parallel Processing and Applied Mathematics pp 643–651Cite as

Effectiveness of Sparse Data Structure for Double-Double and Quad-Double Arithmetics

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8384))

Abstract

Double-double and Quad-double arithmetics are effective tools to reduce the round-off errors in floating-point arithmetic. However, the dense data structure for high-precision numbers in MuPAT/Scilab requires large amounts of memory and a great deal of the computation time. We implemented sparse data types ddsp and qdsp for double-double and quad-double numbers. We showed that sparse data structure for high-precision arithmetic is practically useful for solving a system of ill-conditioned linear equation to improve the convergence and obtain the accurate result in smaller computation time.

Tsubasa Saito and Satoko Kikkawa were at Tokyo University of Science while conducting this research.

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References

  1. MuPAT, http://www.mi.kagu.tus.ac.jp/qupat.html

  2. Kikkawa, S., Saito, T., Ishiwata, E., Hasegawa, H.: Development and acceleration of multiple precision arithmetic toolbox MuPAT for Scilab. JSIAM Lett. 5, 9–12 (2013)

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  9. The University of Florida Sparse Matrix Collection, http://www.cise.ufl.edu/research/sparse/matrices/

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Acknowledgement

The authors would like to thank the reviewers for their helpful comments.

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Authors and Affiliations

  1. Tokyo Metropolitan Ome Sogo High School, Tokyo, Japan

    Tsubasa Saito

  2. Canon Inc., Tokyo, Japan

    Satoko Kikkawa

  3. Tokyo University of Science, Tokyo, Japan

    Emiko Ishiwata

  4. University of Tsukuba, Tsukuba, Japan

    Hidehiko Hasegawa

Authors
  1. Tsubasa Saito
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  2. Satoko Kikkawa
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  3. Emiko Ishiwata
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  4. Hidehiko Hasegawa
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Corresponding author

Correspondence to Hidehiko Hasegawa .

Editor information

Editors and Affiliations

  1. Institute of Computer and Information Science, Czestochowa University of Technology, Czestochowa, Poland

    Roman Wyrzykowski

  2. University of Tennessee, Department of Computer Science, Knoxville, Tennessee, USA

    Jack Dongarra

  3. Institute of Computer and Information Science, Czestochowa University of Technology, Czestochowa, Poland

    Konrad Karczewski

  4. Technical University of Denmark Informatics and Mathematical Modelling, Kongens Lyngby, Denmark

    Jerzy Waśniewski

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© 2014 Springer-Verlag Berlin Heidelberg

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Saito, T., Kikkawa, S., Ishiwata, E., Hasegawa, H. (2014). Effectiveness of Sparse Data Structure for Double-Double and Quad-Double Arithmetics. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Waśniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2013. Lecture Notes in Computer Science(), vol 8384. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55224-3_60

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  • DOI: https://doi.org/10.1007/978-3-642-55224-3_60

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-55223-6

  • Online ISBN: 978-3-642-55224-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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