Complete numerical isolation of real roots in zero-dimensional triangular systems

doi:10.1016/j.jsc.2008.04.017

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	Complete numerical isolation of real roots in zero-dimensional triangular systems
	Cheng, Jin-San 1,2; Gao, Xiao-Shan 1; Yap, Chee-Keng 3,4
	2009-07-01
发表期刊	JOURNAL OF SYMBOLIC COMPUTATION
ISSN	0747-7171
卷号	44 期号:7 页码:768-785
摘要	We present a complete numerical algorithm for isolating all the real zeros of a zero-dimensional triangular polynomial system F-n subset of Z[x(1) ... x(n)]. Our system F-n is general, with no further assumptions. In particular, our algorithm Successfully treats multiple zeros directly in such systems. A key idea is to introduce evaluation hounds and sleeve bounds. We also present a much more efficient algorithm for zero-dimensional triangular systems without multiple roots. We implemented Our algorithms, and promising experimental results are shown. (C) 2008 Elsevier Ltd. All rights reserved.
关键词	Triangular system Real zero isolation Sleeve bound Evaluation bound
DOI	10.1016/j.jsc.2008.04.017
语种	英语
WOS研究方向	Computer Science ; Mathematics
WOS类目	Computer Science, Theory & Methods ; Mathematics, Applied
WOS记录号	WOS:000266058400004
出版者	ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/7004
专题	中国科学院数学与系统科学研究院
通讯作者	Cheng, Jin-San
作者单位	1.Chinese Acad Sci, AMSS, Inst Syst Sci, KLMM, Beijing 100864, Peoples R China 2.LORIA, INRIA Nancy Grand E, Nancy, France 3.NYU, Courant Inst Math Sci, New York, NY 10003 USA 4.Korea Inst Adv Study, Seoul, South Korea
推荐引用方式 GB/T 7714	Cheng, Jin-San,Gao, Xiao-Shan,Yap, Chee-Keng. Complete numerical isolation of real roots in zero-dimensional triangular systems[J]. JOURNAL OF SYMBOLIC COMPUTATION,2009,44(7):768-785.
APA	Cheng, Jin-San,Gao, Xiao-Shan,&Yap, Chee-Keng.(2009).Complete numerical isolation of real roots in zero-dimensional triangular systems.JOURNAL OF SYMBOLIC COMPUTATION,44(7),768-785.
MLA	Cheng, Jin-San,et al."Complete numerical isolation of real roots in zero-dimensional triangular systems".JOURNAL OF SYMBOLIC COMPUTATION 44.7(2009):768-785.