On the Study of Highly Reliable Symbolic-Numeric Computation for Algebraic Problems with Empirical Data

经验数据代数问题高可靠符号数值计算的研究

• 批准号: 21500026
• 负责人: SEKIGAWA Hiroshi
• 金额: $ 2.83万
• 依托单位: Tokai University (2010-2011)NTT Communication Science Laboratories (2009)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2011
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21500026/
• 关键词: 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

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.

我们针对经验数据的代数问题提出了高度可靠的符号数值计算方法。主要结果如下：(1)确定多项式整除性的算法。(2)稳定技术的新应用。(3)计算最大扰动以保持多项式系统解的性质的算法。此外，我们分析了计算时间，以找到在给定复域中具有零并且最接近给定实单变量多项式的实单变量多项式。

项目成果

Solvability of Bivariate Polynomial Systems under Perturbation

摄动下双变量多项式系统的可解性

• 发表时间: 2010
• 作者: Takako Nakatani;Narihito Kondo;Junko Shirogane;Haruhiko Kaiya;Shozo Hori;and Keiichi Katamine;H. Sekigawa and K. Shirayanagi
• 通讯作者: H. Sekigawa and K. Shirayanagi

連立代数方程式の解の個数を保つ摂動限界

保留联立代数方程解数的扰动极限

• 发表时间: 2012
• 作者: 関川浩;白柳潔
• 通讯作者: 白柳潔

Isolated real zero of a real polynomial system under perturbation

• DOI: 10.1145/2016567.2016591
• 发表时间: 2011-07
• 期刊: ACM Commun. Comput. Algebra
• 作者: Hiroshi Sekigawa;Kiyoshi Shirayanagi

Deciding Divisibility between Polynomials with Inexact Coefficients

确定具有不精确系数的多项式之间的整除性

• 发表时间: 2009
• 期刊: ACM Communications in Computer Algebra
• 影响因子: 0.1
• 作者: 高嶋隆太;鳥海重喜;H. Nakayama and H. Sekigawa
• 通讯作者: H. Nakayama and H. Sekigawa

Computing the nearest polynomial with a zero in a given domain by using piecewise rational functions

• DOI: 10.1016/j.jsc.2011.08.012
• 发表时间: 2011-12
• 期刊: J. Symb. Comput.
• 作者: Hiroshi Sekigawa