2011 Fiscal Year Final Research Report
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 |
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| Section | 一般 |
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| Research Field |
Fundamental theory of informatics
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| Research Institution | Tokai University (2010-2011)
NTT Communication Science Laboratories (2009) |
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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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| Keywords | 多項式 / 代数方程式 / 誤差 / 数値数式融合計算 / 安定化理論 |
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| 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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