An Improvement of the Rational Representation for High-Dimensional Systems

doi:10.1007/s11424-020-9316-4

CSpace

	An Improvement of the Rational Representation for High-Dimensional Systems
	Xiao, Fanghui 1,2; Lu, Dong 3,4; Ma, Xiaodong 5; Wang, Dingkang 1,2
	2020-11-07
发表期刊	JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY
ISSN	1009-6124
页码	18
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.
关键词	Comprehensive Grobner systems high-dimensional polynomial system rational representation rational univariate representation
DOI	10.1007/s11424-020-9316-4
收录类别	SCI
语种	英语
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
WOS类目	Mathematics, Interdisciplinary Applications
WOS记录号	WOS:000587281000025
出版者	SPRINGER HEIDELBERG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/52434
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.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
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.