2009 Fiscal Year Final Research Report
Study on Calculating Power-series Roots of Multivariate Algebraic Equations
| 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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| 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 |
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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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