| Project/Area Number |
19700004
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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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 |
TERUI Akira University of Tsukuba, 大学院・数理物質科学研究科, 助教 (80323260)
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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 |
¥3,380,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥480,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2007: ¥1,300,000 (Direct Cost: ¥1,300,000)
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| Keywords | 計算代数 / 数式処理 / 数式・数値融合計算 / 記号的Newton法 / 近似GCD / 数値最適化 / 勾配射影法 / 代数方程式 / べき級数根 / 非線形最適化 / 同時反復公式 / Pade近似 |
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| Research Abstract |
This research has been focused on so-called symbolic Newton method for calculating power-series roots, with respect to a pre-defined main variable, of multivariate polynomials. First, we have developed iteration formulae for calculating all the power-series roots simultaneously. Then, we have investigated for methods for eliminating multiple or closed factors which may appear in the initial factors of the symbolic Newton method. We have developed an iterative method for calculating an approximate greatest common divisor (GCD) of univariate polynomials based on the gradient projection method, with much stability and efficiency.
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