| Project/Area Number |
19204008
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| Research Category |
Grant-in-Aid for Scientific Research (A)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Kobe University |
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Principal Investigator |
TAKAYAMA Nobuki Kobe University, 理学研究科, 教授 (30188099)
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| Co-Investigator(Kenkyū-buntansha) |
BRENDLE Joerg 神戸大学, システム情報学研究科, 准教授 (70301851)
FUCHINO Sakae 神戸大学, システム情報学研究科, 教授 (30292098)
FUKUYAMA Katsushi 神戸大学, 理学研究科, 教授 (60218956)
KAKIUCHI Itsuro 神戸大学, システム情報学研究科, 准教授 (90091248)
NORO Masayuki 神戸大学, 理学研究科, 教授 (50332755)
NOUMI Masatoshi 神戸大学, 自然科学系先端融合環重点研究部, 教授 (80164672)
ROSSMAN Wayne 神戸大学, 理学研究科, 教授 (50284485)
新井 敏康 神戸大学, 工学研究科, 教授 (40193049)
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| Co-Investigator(Renkei-kenkyūsha) |
ARAI Toshiyasu 千葉大学, 理学研究科, 教授 (40193049)
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| Project Period (FY) |
2007 – 2011
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| Project Status |
Completed (Fiscal Year 2010)
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| Budget Amount *help |
¥42,380,000 (Direct Cost: ¥32,600,000、Indirect Cost: ¥9,780,000)
Fiscal Year 2010: ¥11,180,000 (Direct Cost: ¥8,600,000、Indirect Cost: ¥2,580,000)
Fiscal Year 2009: ¥10,270,000 (Direct Cost: ¥7,900,000、Indirect Cost: ¥2,370,000)
Fiscal Year 2008: ¥9,880,000 (Direct Cost: ¥7,600,000、Indirect Cost: ¥2,280,000)
Fiscal Year 2007: ¥11,050,000 (Direct Cost: ¥8,500,000、Indirect Cost: ¥2,550,000)
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| Keywords | グレブナ基底 / 推定 / 数学ソフトウエア / 特殊関数 / 組み合わせ論的集合論 / 重複対数の法則 / 中心極限定理 / 極小曲面 / ホロノミック勾配降下法 / 数学ソフトエウア / Fisher-Bingham分布 / 超幾何関数 / logarithmic cohomology / Sparse SDP / 離散極小曲面 / 無矛盾性 / 特異基数 / ノンパラメトリック推測法 |
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| Research Abstract |
We hosted the 10th Asian logic conference and the third international congress on mathematical software and made broad contributions to communities to study computation and mathematical sciences. We have obtained several results. Among them, a result which could not be obtained without this project is an algorithm to find a local minimum of a given holonomic function by utilizing computer algebra algorithms and numerical algorithms for holonomic systems. We expect that this method can be applied to estimation problems in statistics, which is in progress in a new project.
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