| 求对称多项式方程组所有解的同伦算法 |
| |
| 引用本文： | 储钟武,王秋群. 求对称多项式方程组所有解的同伦算法[J]. 宁波工程学院学报, 1994, 0(1) |
| |
| 作者姓名： | 储钟武 王秋群 |
| |
| 作者单位： | 哈尔滨工业大学数学系(储钟武)，郑州中国银行(王秋群) |
| |
| 摘 要： | 本文对初等对称多项式组P（Z）构造了同伦H（t，a，Z），证明了几乎对所有aU＝｛（Z1，…，Zn）C~n|Zi≠Zj,i一动，i≠j｝，0为它的正则值，而Hn(-1)（0）由n！条光滑曲线组成，且每条曲线关于t为严格单调的。在此基础上导出了一种关于求对称多项式方程组F（Z）＝0所有解的同伦算法，它比用一般同伦去解这类问题可节省大量机时。
|
| 关 键 词： | 对称多项式 同伦算法 同伦曲线 正则值 |
A Homotopy Method for Computing All Solutions to Systems of Symmetric Polynomial Equations |
| |
| Chu Zhongwu. A Homotopy Method for Computing All Solutions to Systems of Symmetric Polynomial Equations[J]. Journal of Ningbo University of Technology, 1994, 0(1) |
| |
| Authors: | Chu Zhongwu |
| |
| Affiliation: | Chu Zhongwu(Harbin Institute of Technology)Wang Qiuqun(Zheng Zhou Bank of China) |
| |
| Abstract: | In this paper for the set of elemntary symmetric polynomials P(z) we construct a homotopy H(t,a,z) .and have proved for almost allis the regular value of H,Ha(-1) (O) consists of n! smooth curves,and each curve is strictly monotonic for Basedt on these theorems we have derived a homotopy algorithm for computing all solutions to systems of symmmetric polynomial equations, by comparing thismethod with general homotopy method to solve such class of problems can be saved muchcomputer time. |
| |
| Keywords: | Symmetric polynomial Homotopy method Homotopy curve Regular value |
| 本文献已被 CNKI 等数据库收录！ |
