| Project/Area Number |
18K11172
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 60010:Theory of informatics-related
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| Research Institution | Tokyo University of Science |
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Principal Investigator |
Sekigawa Hirosi 東京理科大学, 理学部第一部応用数学科, 教授 (00396178)
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| Co-Investigator(Kenkyū-buntansha) |
白柳 潔 東邦大学, 理学部, 教授 (80396176)
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| Project Period (FY) |
2018-04-01 – 2021-03-31
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| Project Status |
Completed (Fiscal Year 2020)
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| Budget Amount *help |
¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2020: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 摂動 / 誤差 / 安定性 / 代数方程式 / 多項式 / 数値数式融合計算 / 安定化理論 |
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| Outline of Final Research Achievements |
Some algebraic problems can be unstable if they contain errors, for example, in the coefficients of polynomials. In such cases, we carried out research on the influence of perturbations of coefficients, methods for posing stable related problems, and algorithms that efficiently solve the posed problems. Furthermore, we studied the application of the stabilization techniques that make the constructed algorithms more efficient. Our main results are as follows: (1) The continuity of the roots of simultaneous algebraic equations satisfying some conditions with respect to the coefficients. (2) Algorithms for interpolation of black-box polynomials whose values contain errors. (3) Confirmation of the effectiveness of the stabilization techniques and a log method based on the techniques.
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| Academic Significance and Societal Importance of the Research Achievements |
計算機により数学的な計算を行う方法には数値計算と数式処理の二つがある。数値計算は計算が高速かつ、入力データに誤差があっても計算可能だが、結果の保証が必要である。数式処理は結果は信頼できるが、計算が低速であり、誤差のある入力は受け付けない。
本研究の成果は、信頼性の高い数式処理を基礎に、数値計算、数式処理双方の長所を合わせ持つ計算方法を確立する一歩となるものである。こういった計算方法は様々な分野における数学的な計算に利用できる可能性を秘めている。
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