KMS Of Academy of mathematics and systems sciences, CAS
| An Improvement of the Rational Representation for High-Dimensional Systems | |
| Xiao, Fanghui1,2; Lu, Dong3,4; Ma, Xiaodong5; Wang, Dingkang1,2 | |
| 2020-11-07 | |
| Source Publication | JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY
 |
| ISSN | 1009-6124 |
| Pages | 18 |
| Abstract | 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. |
| Keyword | Comprehensive Grobner systems high-dimensional polynomial system rational representation rational univariate representation |
| DOI | 10.1007/s11424-020-9316-4 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | National Natural Science Foundation of China[11801558] ; Chinese Universities Scientific Funds[15059002] ; CAS Key Project[QYZDJ-SSW-SYS022] |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Interdisciplinary Applications |
| WOS ID | WOS:000587281000025 |
| Publisher | SPRINGER HEIDELBERG |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/52434 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Lu, Dong |
| Affiliation | 1.Chinese Acad Sci, KLMM, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Beihang Univ, Beijing Adv Innovat Ctr Big Data & Brain Comp, Beijing 100191, Peoples R China 4.Beihang Univ, Sch Math Sci, Beijing 100191, Peoples R China 5.China Agr Univ, Coll Sci, Beijing 100083, Peoples R China |
| Recommended Citation 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. |
| Files in This Item: | There are no files associated with this item. | |||||
Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.
Edit Comment