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Improvement of Convergence and Performance for the Krylov Subspace Methods using High-Precision Arithmetic

Research Project

Project/Area Number 25330141
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field High performance computing
Research InstitutionUniversity of Tsukuba

Principal Investigator

HASEGAWA Hidehiko  筑波大学, 図書館情報メディア系, 教授 (20164824)

Co-Investigator(Kenkyū-buntansha) 石渡 恵美子  東京理科大学, 理学部第一部応用数学科, 教授 (30287958)
Project Period (FY) 2013-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords高精度演算 / 混合精度演算 / Double-double演算 / Quad-double演算 / 反復法 / リスタート / 疎行列 / 連立一次方程式 / ベクトル化 / ハイパフォーマンス・コンピューティング / 多倍長計算 / 数値解析 / 倍々精度演算 / クリロフ部分空間法 / 3重対角化 / MATLAB / 混合精度 / オブジェクト指向 / 混合制度演算 / 反復解法
Outline of Final Research Achievements

The Krylov Subspace Methods have some problems such as slow convergence rate or divergence, difficulty of parallelization of preconditioners, and rounding errors. The use of High-Precision arithmetic has a possibility to eliminate these problems, however it's costly.

We choose Double-double and Quad-double arithmetics as High-Precision arithmetic. The use of High-Precision arithmetic improved iterative process in Krylov Subspace methods, but did not improve a tridiagonalization process in Lanczos tridiagonalization method. From these results, the use of High-Precision arithmetic is effective for many algorithms, but not for all. To reduce computation cost, we combined three different arithmetic precisions such as double, Double-double, and Quad-double. There are many kind of combinations, and some of them were practically effective, but there was no method to fit for all test problems. As a software library we should resolve a problem how to relate combination methods and test problems.

Report

(6 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Research-status Report
  • 2015 Research-status Report
  • 2014 Research-status Report
  • 2013 Research-status Report
  • Research Products

    (9 results)

All 2017 2015 2014 2013 Other

All Journal Article (4 results) (of which Peer Reviewed: 4 results,  Acknowledgement Compliant: 1 results) Presentation (5 results) (of which Int'l Joint Research: 2 results,  Invited: 1 results)

  • [Journal Article] Comparison of Tridiagonalization Methods Using High-Precision Arithmetic with MuPAT2017

    • Author(s)
      Ino Ryoya、Asami Kohei、Ishiwata Emiko、Hasegawa Hidehiko
    • Journal Title

      Lecture Notes in Computational Science and Engineering 117

      Volume: - Pages: 125-141

    • DOI

      10.1007/978-3-319-62426-6_9

    • ISBN
      9783319624242, 9783319624266
    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Comparison of Tridiagonalization Methods using High Precision Arithmetic with MuPAT on Scilab2017

    • Author(s)
      K. Asami, R. Ino, E. Ishiwata, and H. Hasegawa
    • Journal Title

      Proceedings on International Workshop on Eigenvalue Problems: Algorithms; Software and Applications, in Petascale Computing

      Volume: 印刷中

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Effectiveness of sparse data structure for double-double and quad-double arithmetics2014

    • Author(s)
      T. Saito, S. Kikkawa, E. Ishiwata, and H. Hasegawa
    • Journal Title

      Lecture Notes in Computer Science 8384

      Volume: 8384 Pages: 643-651

    • DOI

      10.1007/978-3-642-55224-3_60

    • ISBN
      9783642552236, 9783642552243
    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Scilabにおける高精度演算環境 MuPAT の実装2013

    • Author(s)
      吉川 慧子,斉藤 翼, 石渡 恵美子, 長谷川 秀彦
    • Journal Title

      図書館情報メディア研究

      Volume: Vol. 11, No. 1 Pages: 23-46

    • NAID

      120005348371

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Presentation] Robust and Fast BiCG Method using SIMD-Accelerated DD Arithmetic2017

    • Author(s)
      H. Hasegawa and T. Hishinuma
    • Organizer
      The International Conference on Preconditioning Techniques for Scientific and Industrial Applications (Preconditioning 2017), Poster Presentation
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] MATLAB上での高精度演算の実装について2017

    • Author(s)
      長谷川 秀彦, 椎葉 健, 石渡 恵美子
    • Organizer
      第16回情報科学技術フォーラム
    • Related Report
      2017 Annual Research Report
  • [Presentation] Eigenvalue computation using High Precision Arithmetic Toolbox MuPAT on Scilab2015

    • Author(s)
      Kohei Asami, Ryoya Ino, Emiko Ishiwata, and Hidehiko Hasegawa
    • Organizer
      Poster presentation at International Workshop on Eigenvalue Problems: Algorithms; Software and Applications, in Petascale Computing
    • Place of Presentation
      EPOCHAL TSUKUBA, Tsukuba, Japan
    • Year and Date
      2015-09-14
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] Effectiveness of sparse data structure for double-double and quad-double arithmetics2013

    • Author(s)
      T. Saito, S. Kikkawa, E. Ishiwata, and H. Hasegawa
    • Organizer
      the Tenth International Conference on Parallel Processing and Applied Mathematics (PPAM 2013)
    • Place of Presentation
      Polish-Japanese Institute of Information Technology, Warsaw, Poland
    • Related Report
      2013 Research-status Report
  • [Presentation] 高精度演算を用いた混合精度反復法

    • Author(s)
      長谷川 秀彦
    • Organizer
      日本応用数理学会 三部会連携「応用数理セミナー」
    • Place of Presentation
      東京大学本郷キャンパス,東京都文京区
    • Related Report
      2013 Research-status Report
    • Invited

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Published: 2014-07-25   Modified: 2019-07-29  

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