On the Study of Highly Reliable Symbolic-Numeric Computation for Algebraic Problems with Empirical Data
Project/Area Number |
21500026
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Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Single-year Grants |
Section | 一般 |
Research Field |
Fundamental theory of informatics
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Research Institution | Tokai University (2010-2011) NTT Communication Science Laboratories (2009) |
Principal Investigator |
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Co-Investigator(Kenkyū-buntansha) |
SHIRAYANAGI Kioshi 東邦大学, 理学部, 教授 (80396176)
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Project Period (FY) |
2009 – 2011
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Project Status |
Completed (Fiscal Year 2011)
|
Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2009: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
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Keywords | 多項式 / 代数方程式 / 誤差 / 数値数式融合計算 / 安定化理論 / 連立代数方程式 / 近似 / 零点 / 根 / 凸包構成 / 整除性 / グレブナ基底 |
Research Abstract |
We proposed highly reliable symbolic-numeric computation methods for algebraic problems with empirical data. Some main results are as follows.(1) An algorithm to determine divisibility of polynomials.(2) A new application of stabilization techniques.(3) An algorithm to compute the maximal perturbations for preserving properties of solutions of a polynomial system. Furthermore, we analyzed computing time to find a real univariate polynomial that has a zero in a given complex domain and is nearest to a given real univariate polynomial.
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Report
(4 results)
Research Products
(34 results)