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 HOMOTOPY SIMPLEX PIVOT ALGORITHM XU, SL; LIU, SL 1991 Source Publication ACTA MATHEMATICA SCIENTIA ISSN 0252-9602 Volume 11Issue:1Pages:111-120 Abstract In this paper, we study the properties of the zero set of a homotopy H: I(m)x[0, 1]-->R(m) and its piecewise linear approximation phi-sigma-i: I(m)x[0, 1]-->R(m), These properties are very important for the homotopy simplex pivot algorithm. However, we prove that for almost every polynomial mapping the zero set of linear homotopy H(z, t) = tp(z) + (1-t)Q(z) consists of [GRAPHICS] disjoint differential curves, and the zero set of its piecewise linear approximation phi-sigma-i, consists of some broken lines. When delta-i-->0, these broken lines tend to differential curves in the zero set of H. Language 英语 WOS Research Area Mathematics WOS Subject Mathematics WOS ID WOS:A1991FJ76900012 Publisher BALTZER SCI PUBL BV Citation statistics Document Type 期刊论文 Identifier http://ir.amss.ac.cn/handle/2S8OKBNM/27611 Collection 中国科学院数学与系统科学研究院 Affiliation 1.UNIV SCI & TECHNOL CHINA,HEFEI,PEOPLES R CHINA2.CHINESE ACAD SCI,INST SYST SCI,BEIJING,PEOPLES R CHINA Recommended CitationGB/T 7714 XU, SL,LIU, SL. HOMOTOPY SIMPLEX PIVOT ALGORITHM[J]. ACTA MATHEMATICA SCIENTIA,1991,11(1):111-120. APA XU, SL,&LIU, SL.(1991).HOMOTOPY SIMPLEX PIVOT ALGORITHM.ACTA MATHEMATICA SCIENTIA,11(1),111-120. MLA XU, SL,et al."HOMOTOPY SIMPLEX PIVOT ALGORITHM".ACTA MATHEMATICA SCIENTIA 11.1(1991):111-120.
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