An Improvement of the Rational Representation for High-Dimensional Systems
Xiao, Fanghui1,2; Lu, Dong3,4; Ma, Xiaodong5; Wang, Dingkang1,2
AbstractBased 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.
KeywordComprehensive Grobner systems high-dimensional polynomial system rational representation rational univariate representation
Indexed BySCI
Funding ProjectNational Natural Science Foundation of China[11801558] ; Chinese Universities Scientific Funds[15059002] ; CAS Key Project[QYZDJ-SSW-SYS022]
WOS Research AreaMathematics
WOS SubjectMathematics, Interdisciplinary Applications
WOS IDWOS:000587281000025
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Document Type期刊论文
Corresponding AuthorLu, Dong
Affiliation1.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.
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