Study of the Influence of Perturbations on Algebraic Problems
| Project/Area Number |
15K00025
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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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| Research Field |
Theory of informatics
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| Research Institution | Tokyo University of Science |
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Principal Investigator |
Sekigawa Hiroshi 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) |
2015-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | 摂動 / 誤差 / 安定性 / 多項式 / 代数方程式 / 数値数式融合計算 / 安定化理論 / 近似 / 行列 / 最短ベクトル / グレブナ基底 / 有理標準形 / 一般逆行列 |
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| Outline of Final Research Achievements |
Sometimes algebraic problems become meaningless due to errors in the coefficients of polynomials and equations in the problems. In such cases, we investigate the influence of perturbations of coefficients and pose meaningful related problems using the concept of "nearest problems." We construct algorithms that efficiently solve the posed problems, especially problems of algebraic equations. Furthermore, we study utilization methods of stabilizing techniques that make the constructed algorithms more efficient. Some main results are as follows: (1) Algorithms to construct the polynomial that is nearest to a given polynomial among the polynomials with given zeros. (2) Algorithms for interpolation of polynomials whose values contain errors. (3) Confirmation of effectiveness of stabilization techniques and new applications of stabilization techniques.
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Report
(4 results)
Research Products
(32 results)
