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

• Project/Area Number: 15K15939
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Theory of informatics
• Research Institution: Waseda 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: ¥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.

Research Products

• [Int'l Joint Research] ハンブルグ工科大学(ドイツ)
• [Journal Article] Interval arithmetic with fixed rounding mode (2016)
  • Author(s): S. M. Rump, T. Ogita, Y. Morikura, S. Oishi
  • Journal Title: NOLTA Volume: 7 Issue: 3 Pages: 362-373
  • DOI: 10.1587/nolta.7.362
  • NAID: 130005161827
  • ISSN: 2185-4106
  • 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
  • Invited
• [Presentation] Fast enclosure for matrix multiplication on a GPU (2016)
  • 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
  • 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
• [Presentation] Performance Evaluation of Verified Computation for Linear Systems on Parallel Computers (2016)
  • 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
  • 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
• [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
  • Invited
• [Presentation] Verification method for large-scale linear systems without directed rounding (2015)
  • Author(s): Yusuke Morikura, Ozaki Katsuhisa and Shin’ichi Oishi
  • Organizer: Crest Workshop
  • Place of Presentation: 伊東
  • Year and Date: 2015-10-24
  • Int'l Joint Research
• [Presentation] Verification method for large-scale linear systems (2015)
  • 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
• [Presentation] Verification method for large-scale linear systems (2015)
  • 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
  • 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
• [Presentation] GPU computation in verified computation (2015)
  • Author(s): Yusuke Morikura
  • Organizer: Joint Seminar on Numerical Analysis at Niigata University
  • Place of Presentation: Niigata University
  • Year and Date: 2015-09-03
  • Int'l Joint Research
• [Book] 計算科学のためのHPC技術１ (2017)
  • 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