An Improvement of the Rational Representation for High-Dimensional Systems
文献类型：期刊论文
| 作者 | Xiao, Fanghui3,4; Lu, Dong2,5; Ma, Xiaodong1; Wang, Dingkang3,4 |
| 刊名 | JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY
 |
| 出版日期 | 2020-11-07 |
| 页码 | 18 |
| 关键词 | Comprehensive Grobner systems high-dimensional polynomial system rational representation rational univariate representation |
| ISSN号 | 1009-6124 |
| DOI | 10.1007/s11424-020-9316-4 |
| 英文摘要 | Based on the rational univariate representation of zero-dimensional polynomial systems, Tan and Zhang proposed the rational representation theory for solving a high-dimensional polynomial system, which uses so-called rational representation sets to describe all the zeros of a high-dimensional polynomial system. This paper is devoted to giving an improvement for the rational representation. The idea of this improvement comes from a minimal Dickson basis used for computing a comprehensive Grobner system of a parametric polynomial system to reduce the number of branches. The authors replace the normal Grobner basis G satisfying certain conditions in the original algorithm (Tan-Zhang's algorithm) with a minimal Dickson basis G(m) of a Grobner basis for the ideal, where G(m) is smaller in size than G. Based on this, the authors give an improved algorithm. Moreover, the proposed algorithm has been implemented on the computer algebra system Maple. Experimental data and its performance comparison with the original algorithm show that it generates fewer branches and the improvement is rewarding. |
| 资助项目 | National Natural Science Foundation of China[11801558] ; Chinese Universities Scientific Funds[15059002] ; CAS Key Project[QYZDJ-SSW-SYS022] |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000587281000025 |
| 出版者 | SPRINGER HEIDELBERG |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/52433]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Lu, Dong |
| 作者单位 | 1.China Agr Univ, Coll Sci, Beijing 100083, Peoples R China 2.Beihang Univ, Beijing Adv Innovat Ctr Big Data & Brain Comp, Beijing 100191, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 4.Chinese Acad Sci, KLMM, Acad Math & Syst Sci, Beijing 100190, Peoples R China 5.Beihang Univ, Sch Math Sci, Beijing 100191, Peoples R China |
| 推荐引用方式 GB/T 7714 | Xiao, Fanghui,Lu, Dong,Ma, Xiaodong,et al. An Improvement of the Rational Representation for High-Dimensional Systems[J]. JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY,2020:18. |
| APA | Xiao, Fanghui,Lu, Dong,Ma, Xiaodong,&Wang, Dingkang.(2020).An Improvement of the Rational Representation for High-Dimensional Systems.JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY,18. |
| MLA | Xiao, Fanghui,et al."An Improvement of the Rational Representation for High-Dimensional Systems".JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY (2020):18. |
入库方式： OAI收割
来源：数学与系统科学研究院
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