Accurate and High Performance Computational Methods for Numerical Linear Algebra

• Project/Area Number: 25730076
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: High performance computing
• Research Institution: Shibaura Institute of Technology
• Principal Investigator: Ozaki Katsuhisa 芝浦工業大学, システム理工学部, 准教授 (90434282)
• Project Period (FY): 2013-04-01 – 2017-03-31
• Project Status: Completed (Fiscal Year 2016)
• Budget Amount: ¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000); Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
• Keywords: 誤差解析 / ハイパフォーマンスコンピューティング / 数値解析 / 丸め誤差解析 / 高性能計算 / 精度保証付き数値計算 / 浮動小数点演算 / 線形計算 / 事前誤差解析

Outline of Final Research Achievements

Floating-point arithmetic is widely used for scientific computing. Because information of binary floating-point numbers is finite, rounding error may occur. If rounding errors accumulate, then an inaccurate result may be obtained. If a problem is large scale, then the problem of rounding errors will be more serious. We proposed accurate and high performance computational methods for numerical linear algebra, especially, matrix multiplication, LU decomposition, and Cholesky decomposition.

Research Products

• [Presentation] ブロックコレスキー分解を用いた連立一次方程式の数値解の精度保証法 (2017)
  • Author(s): 寺尾 剛史，尾崎 克久
  • Organizer: 日本応用数理学会研究部会連合発表会
  • Place of Presentation: 電気通信大学
  • Year and Date: 2017-03-06
• [Presentation] Improvement of error bound for dot product with unit in the first place (2016)
  • Author(s): Katsuhisa Ozaki
  • Organizer: The 2nd International Conference and Summer School Numerical Computations: Theory and Algorithms (NUMTA2016)
  • Place of Presentation: Pizzo, Italy
  • Year and Date: 2016-06-19
  • Int'l Joint Research
• [Presentation] Block Computations for Interval Arithmetic and Verified Numerical Computations for Linear Systems (2016)
  • Author(s): Katsuhisa Ozaki
  • Organizer: 5th European Seminar on Computing (ESCO2016)
  • Place of Presentation: Pilsen, Czech Republic
  • Year and Date: 2016-06-05
  • Int'l Joint Research
• [Presentation] 浮動小数点演算による内積の誤差解析について (2016)
  • Author(s): 樋口 裕幸，尾崎 克久
  • Organizer: 日本応用数理学会研究部会連合発表会
  • Place of Presentation: 神戸学院大学
  • Year and Date: 2016-03-05
• [Presentation] ブロックコレスキー分解を用いた行列に対する正定値性の保証とその応用 (2016)
  • Author(s): 寺尾 剛史，尾崎 克久
  • Organizer: 日本応用数理学会研究部会連合発表会
  • Place of Presentation: 神戸学院大学
  • Year and Date: 2016-03-05
• [Presentation] Block Computations and Verified Numerical Computations for Linear Systems (2014)
  • Author(s): K. Ozaki, T. Ogita, S. Oishi
  • Organizer: The 33rd JSST Annual Conference
  • Place of Presentation: 北九州国際会議場
  • Year and Date: 2014-09-29 – 2014-09-30
• [Presentation] 連立一次方程式に対する自動精度保証法の改善 (2014)
  • Author(s): 尾崎克久, 荻田武史, 大石進一
  • Organizer: 平成26年日本応用数理学会年会
  • Place of Presentation: 政策研究大学院大学
  • Year and Date: 2014-09-03 – 2014-09-05
• [Presentation] Residual Bounds for Triangular Systems by Grouped Block Implementation (2014)
  • Author(s): K. Ozaki, T. Ogita, S. Oishi
  • Organizer: The 10th East Asia SIAM Conference
  • Place of Presentation: Ambassador City Jomtien
  • Year and Date: 2014-06-23 – 2014-06-25
• [Presentation] Inverse Matrix of Triangular Matrices for Verified Numerical Computations (2014)
  • Author(s): 尾崎克久, 荻田武史, 大石進一
  • Organizer: 日本応用数理学会研究部会連合発表会
  • Place of Presentation: 京都大学