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Development of Accurate Numerical Method of Linear Systems Based on De Facto Standard Library

Research Project

Project/Area Number 15K15939
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Theory of informatics
Research InstitutionWaseda University

Principal Investigator

MORIKUARA Yusuke  早稲田大学, 理工学術院, 助教 (10732240)

Research Collaborator OISHI Shin'ichi  
Rump Siegfried M.  
OGITA Takeshi  
OZAKI Katsuhisa  
HUKAYA Takeshi  
MUKUNOKI Daichi  
YAMANAKA Naoya  
Project Period (FY) 2015-04-01 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords精度保証 / 高精度計算 / 連立一次方程式 / ハイパフォーマンス・コンピューティング / 情報学基礎 / 数値解析 / ハイパフォーマンスコンピューティング / 精度保証付き数値計算
Outline of Final Research Achievements

In this research, we implemented and evaluated numerical verification methods for large-scale systems of linear equations using de-facto standard numerical software libraries on super computer. In addition, we concerned with numerical verification algorithms for large-scale systems of linear equations.
We clarified that accuracy can be guaranteed for large-scale problems by combining accurate computations for matrix multiplication and error-free transformation of floating-point arithmetic on K computer.
Our algorithms obtained in this research estimates rounding error using a priori error estimate of floating-point arithmetic. Implementation of our programs are done by using de-facto standard numerical software libraries. Therefore, the program can be executed by any supercomputer based on the IEEE 754 standard.

Report

(3 results)
  • 2016 Annual Research Report   Final Research Report ( PDF )
  • 2015 Research-status Report
  • Research Products

    (14 results)

All 2017 2016 2015 Other

All Int'l Joint Research (1 results) Journal Article (1 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 1 results,  Open Access: 1 results) Presentation (11 results) (of which Int'l Joint Research: 5 results,  Invited: 2 results) Book (1 results)

  • [Int'l Joint Research] ハンブルグ工科大学(ドイツ)

    • Related Report
      2016 Annual Research Report
  • [Journal Article] Interval arithmetic with fixed rounding mode2016

    • Author(s)
      S. M. Rump, T. Ogita, Y. Morikura, S. Oishi
    • Journal Title

      Nonlinear Theory and Its Applications, IEICE

      Volume: 7 Issue: 3 Pages: 362-373

    • DOI

      10.1587/nolta.7.362

    • NAID

      130005161827

    • ISSN
      2185-4106
    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Presentation] 行列の正則性の判定における単精度近似逆行列を用いた前処理の評価2017

    • Author(s)
      森倉悠介,大石進一
    • Organizer
      第5回 大規模並列数値計算技術に関する研究集会― 多倍長計算と精度保証 ―
    • Place of Presentation
      理化学研究所計算科学研究機構
    • Year and Date
      2017-03-27
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] Fast enclosure for matrix multiplication on a GPU2016

    • Author(s)
      Yusuke Morikura, Yusuke Nozawa, Kouta Sekine, Masahide Kashiwagi and Shin’ichi Oishi
    • Organizer
      The 17th International Symposium on Scientific Computing, Computer Arithmetic and Verified Numerical Computations (SCAN2016)
    • Place of Presentation
      Uppsala ,Sweden
    • Year and Date
      2016-09-26
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] CUDAの丸めモード指定演算を用いた行列積の高速な包含方法2016

    • Author(s)
      森倉 悠介, 野澤 優介, 関根 晃大, 柏木 雅英, 大石 進一
    • Organizer
      2016年度日本応用数理学会 年会
    • Place of Presentation
      福岡県北九州国際会議場
    • Year and Date
      2016-09-12
    • Related Report
      2016 Annual Research Report
  • [Presentation] Performance Evaluation of Verified Computation for Linear Systems on Parallel Computers2016

    • Author(s)
      Yusuke Morikura, Daichi Mukunoki, Takeshi Fukaya, Naoya Yamanaka and Shin’ichi Oishi
    • Organizer
      ACSI2016 (Annual Meeting on Advanced Computing System and Infrastructure 2016)
    • Place of Presentation
      Centennial Hall Kyushu University School of Medicine
    • Year and Date
      2016-01-19
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] 大規模並列計算機における連立1次方程式の精度保証付き数値計算に対する性能評価2016

    • Author(s)
      森倉 悠介, 椋木 大地, 深谷 猛, 山中 脩也, 大石 進一
    • Organizer
      第157回ハイパフォーマンスコンピューティング研究発表会
    • Place of Presentation
      沖縄県産業支援センター
    • Related Report
      2016 Annual Research Report
  • [Presentation] 事前誤差評価を用いた線形計算の精度保証 誤差解析から大規模計算まで2015

    • Author(s)
      森倉 悠介
    • 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 工学部6号館
    • Year and Date
      2015-12-24
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] Verification method for large-scale linear systems without directed rounding2015

    • Author(s)
      Yusuke Morikura, Ozaki Katsuhisa and Shin’ichi Oishi
    • Organizer
      Crest Workshop
    • Place of Presentation
      伊東
    • Year and Date
      2015-10-24
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] Verification method for large-scale linear systems2015

    • Author(s)
      森倉 悠介, 尾崎 克久, 大石 進一
    • Organizer
      JST/CREST-さきがけ数学シンポジウム 2015 22世紀社会創造のための数学 Mathematics for the 22nd Century
    • Place of Presentation
      ステーションコンファレンス東京
    • Year and Date
      2015-09-30
    • Related Report
      2015 Research-status Report
  • [Presentation] Verification method for large-scale linear systems2015

    • Author(s)
      Yusuke Morikura, Katsuhisa Ozaki and Shin’ichi Oishi
    • Organizer
      Seto-Inland-Sea-Rim Workshop on Mathematical Sciences
    • Place of Presentation
      八丈島
    • Year and Date
      2015-09-27
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] LU分解の事前誤差評価を用いた連立一次方程式の精度保証付き数値計算法におけるH行列の性質を用いた正則性の検証法と誤差評価式の提案2015

    • Author(s)
      南畑 淳史, 森倉 悠介, 荻田 武史, 大石 進一
    • Organizer
      日本応用数理学会2015年度年会
    • Place of Presentation
      金沢大学角間キャンパス
    • Year and Date
      2015-09-09
    • Related Report
      2015 Research-status Report
  • [Presentation] GPU computation in verified computation2015

    • Author(s)
      Yusuke Morikura
    • Organizer
      Joint Seminar on Numerical Analysis at Niigata University
    • Place of Presentation
      Niigata University
    • Year and Date
      2015-09-03
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Book] 計算科学のためのHPC技術12017

    • Author(s)
      下司雅章 編/片桐孝洋,中田真秀,渡辺宙志,山本有作,吉井範行,Jaewoon Jung,杉田有治,石村和也,大石進一,関根晃太,森倉悠介,黒田久泰 著
    • Total Pages
      300
    • Publisher
      大阪大学出版会
    • Related Report
      2016 Annual Research Report

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Published: 2015-04-16   Modified: 2018-03-22  

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