caa a22 4500 465774814 CHVBK 20180323111938.0 cr unu---uuuuu 170327e19901201xx s 000 0 eng 10.1007/BF02216827 doi (NATIONALLICENCE)springer-10.1007/BF02216827 Wang Zeke Department of Computer Science, Zhongshan University, Guangzhou, P.R. China aut On the geometry of paths generated by PL homotopy methods [Elektronische Daten] [Zeke Wang] PL homotopy methods are effective numerical methods for highly nonlinear problems. It is widely believed that the feasibility of a PL homotopy method depends on the nondegeneracy condition that the zero set (or the fixed point set in the case of finding fixed points instead of zeroes) of the PL approximation of the homotopy does not intersect the triangulation's skeletons of co-dimensions two and above. This paper shows that, although the sections of the PL approximation's zero set tracked by the PL homotopy method are of dimension one (while other sections may have higher dimensions), the paths generated by the pivoting method are potentially and essentially of dimension two. It makes pathcrossing a safe thing. Thus, this paper first sets up the without exception feasibility of PL homotopy methods geometrically. J.C. Baltzer AG, Scientific Publishing Company, 1990 Annals of Operations Research Baltzer Science Publishers, Baarn/Kluwer Academic Publishers 24/1(1990-12-01), 261-271 0254-5330 24:1<261 1990 24 10479 https://doi.org/10.1007/BF02216827 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02216827 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Wang Zeke Department of Computer Science, Zhongshan University, Guangzhou, P.R. China aut NATIONALLICENCE 773 0- Annals of Operations Research Baltzer Science Publishers, Baarn/Kluwer Academic Publishers 24/1(1990-12-01), 261-271 0254-5330 24:1<261 1990 24 10479 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer