| Project/Area Number |
19300001
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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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 |
SASAKI Tateaki University of Tsukuba, 名誉教授 (80087436)
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| Co-Investigator(Kenkyū-buntansha) |
SAKURAI Tetsuya 筑波大学, 大学院・システム情報工学研究科, 教授 (60187086)
TERUI Akira 筑波大学, 大学院・数理物質科学研究科, 助教 (80323260)
KAI Hiroshi 愛媛大学, 大学院・理工学研究科, 准教授 (10274341)
KAKO Fujio 奈良女子大学, 理学部, 教授 (90152610)
FUKUI Tetsuo 武庫川女子大学, 生活環境学部, 教授 (70218890)
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| Project Period (FY) |
2007 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥13,260,000 (Direct Cost: ¥10,200,000、Indirect Cost: ¥3,060,000)
Fiscal Year 2009: ¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2008: ¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2007: ¥5,720,000 (Direct Cost: ¥4,400,000、Indirect Cost: ¥1,320,000)
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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 / 数値解析 / 浮動小数グレブナー基底 / 近似グレブナー基底 / 大規模固有地問題 / 多変数代数方程式の解法 / 数式文章編集システム / 多変数代数関数の特異点での展開 / 近似代数 / 近似代数計算システム / 数値数式融合計算 / 連立代数方程式とDixon終結式 / 多変数代数関数の級数展開 / 特異点とHensel級数 / 製係数多項式の近似因数分解 / 近似代数システム / 拡張ヘンゼル級数 / 大規模一般化固有地問題 |
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| Research Abstract |
For computing Groebner bases with inaccurate input coefficients, we clarified origins of instability and proposed a stable method "high-precision method with effective floating-point numbers". As for series expansion of multivariate algebraic function at singular point, we devised a method which gives the series in a compact form, derived a simple expansion formula, and clarified many properties of convergence and many-valuedness. We devised a method which computes only eigenvalues located in a specified domain, and applied the method to large-scale chemical computations successfully. We made Japanese algebra system GAL run on C.
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