Mathematical Reliability of Parallel Computations with Indefinite-order Operations
| Project/Area Number |
18K18719
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| Research Category |
Grant-in-Aid for Challenging Research (Exploratory)
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| Allocation Type | Multi-year Fund |
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| Review Section |
Medium-sized Section 12:Analysis, applied mathematics, and related fields
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| Research Institution | Kyoto University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
吉川 仁 京都大学, 情報学研究科, 准教授 (90359836)
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| Project Period (FY) |
2018-06-29 – 2020-03-31
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| Project Status |
Completed (Fiscal Year 2019)
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| Budget Amount *help |
¥6,110,000 (Direct Cost: ¥4,700,000、Indirect Cost: ¥1,410,000)
Fiscal Year 2019: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2018: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
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| Keywords | 数値解析学 / 並列計算 / 信頼性 / 科学・技術数値計算 / 数値解析 / ハイパフォーマンスコンピューティング |
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| Outline of Final Research Achievements |
We discussed the reliability of parallel execution of numerical schemes. The main target in numerical computations is solving systems of linear equations, and we treated the Gauss-Seidel iteration in the current research. The results are (1) construction of a mathematical model of parallel execution status, (2) proving a sufficient condition for convergence, and (3) constructing a counter example where
the serial computation converges and the parallel execution diverges. Practicality of the proposed criteria is also shown by applying it to computation appeared in science and technology.
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| Academic Significance and Societal Importance of the Research Achievements |
数値計算は，現代社会を支える基盤技術であり，その理論的な信頼性の担保は必須である．従来，このような分野は理論数値解析学で扱われてきたが，昨今の急速な計算機ハードウエアの高性能化，特に並列計算環境の進歩との乖離も否めない．特に処理速度のみに着目して無秩序な並列化がおこなわれると，従来理論・手法では信頼性があったものが正しく動かず，数値計算が支える生活や技術開発の停滞が危惧される．この点に対し，本研究では数値計算の「正しさ」の枠組みを再考するとともに，大学学部教育での問題意識の提示，実用性，昨今のデータ科学における「再現性」との共通点など，多様な話題を包含する研究テーマである．
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Report
(3 results)
Research Products
(22 results)
