| 构建复杂Dixon矩阵递归算法的改进 |
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| 引用本文： | 王颖,刘忠.构建复杂Dixon矩阵递归算法的改进[J].华中科技大学学报(自然科学版),2011(8):96-99. |
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| 作者姓名： | 王颖 刘忠 |
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| 作者单位： | 中国科学院成都计算机应用研究所;四川建筑职业技术学院计算机工程系; |
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| 基金项目： | 国家自然科学基金资助项目(10771205); 国家科技重大专项资助项目(2009ZX09313-024); 四川省学术和技术带头人培养资金资助项目; 四川建筑职业技术学院科研项目 |
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| 摘 要： | 针对多于5个变元的复杂多项式系统的Dixon矩阵的构建问题,基于递归算法提出了一种改进算法.采用动态规划的思想,自下而上地构建Dixon矩阵,避免了Dixon多项式的重复计算,并给出了使用该算法计算Dixon矩阵的具体实例.该算法与递归算法一样,可以在同样的计算平台上处理其他方法所不能解决的一些复杂多项式系统求解问题,但与递归算法相比,减少了须要计算的Dixon多项式的数量,提高了计算效率.
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| 关 键 词： | 结式理论 Dixon多项式 Dixon矩阵 消元法 形式幂级数 |
Improving the recursive algorithm to construct complicated Dixon matrices |
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| Wang Ying Liu Zhong.Improving the recursive algorithm to construct complicated Dixon matrices[J].JOURNAL OF HUAZHONG UNIVERSITY OF SCIENCE AND TECHNOLOGY.NATURE SCIENCE,2011(8):96-99. |
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| Authors: | Wang Ying Liu Zhong |
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| Institution: | Wang Ying1 Liu Zhong2(1 Chengdu Institute of Computer Applications,Chinese Academy of Sciences,Chengdu 610041,China,2 Computer Engineering Department,Sichuan College of Architectural Technology,Deyang 618000,Sichuan China) |
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| Abstract: | Based on existing recursive algorithm,an improved algorithm was proposed to construct the Dixon matrices.The improved algorithm used the dynamic programming ideas.The Dixon matrices were built by the algorithm from the bottom up.It avoided computing the Dixon polynomials repeatedly,and the sample that a Dixon matrix was calculated using the improved algorithm was given.The improved algorithm can solve some problems that cannot be tackled by other methods on the same computer platform for some complicated po... |
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| Keywords: | resultant theory Dixon polynomial Dixon matrix quantifier elimination formal power series |
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