Study of Algorithm and Application of Approximate Groebner Basis
| Project/Area Number |
23500003
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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 |
Fundamental theory of informatics
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| Research Institution | University of Tsukuba |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
SAKURAI Tetsuya 筑波大学, システム情報系, 教授 (60187086)
KAKO Fujio 奈良女子大学, 自然科学系, 教授 (90152610)
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| Research Collaborator |
INABA Daiju 日本数学検定協会
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| Project Period (FY) |
2011 – 2013
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2012: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2011: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
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| Keywords | アルゴリズム理論 / 数式処理 / 数値数式融合算法 / 近似グレブナー基底 / 近似特異系と特異化 / 悪条件連立代数方程式 / パラメータ係数線形方程式系 / 疎な線形方程式系 / 近似グレブナー基底の算法 / 近似特異系 / 近似特異系の特異化 / 悪条件多項式系の良条件化 / モデルに基づく開発 / 疎なパラメータ係数線形系 / 疎線形系のパラメータ解析 / 近似線形従属関係 / 多変数代数関数 / 特異点での級数展開 / 近似無平方分解 / 近似因数分解 / ヘンゼル級数 / 近似イデアル / 悪条件方程式系の良条件化 / 特異点での多変数級数展開 |
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| Research Abstract |
Based on a proposed "approximate ideal", we constructed a theory of approximate Groebner basis, clarified the instability of Buchberger's algorithm on floating point numbbers using a developed subresultnat-like theory, and proposed an algorithm of approximate Groebner basis by stabilizing Buchberger's algorithm.
We also proposed a concept of "approximate singular system" as a multivariate polynomial ideal whose dimension is decreased by a purturbation, and presented an algorithm which recovers the dimension. Applying this operation to algebraic systems of approximately singular type, we proposed a well-conditioning method for such systems. Furthermore, we proposed an error suppressing method and a characteristics extracting method for solving parametric sparse linear systems.
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Report
(4 results)
Research Products
(49 results)
