Homotopies for systems of polynomial equations (Q1384427)

The Nielsen number for maps arising from complex systems of polynomial maps is discussed. It is sugessted that the Nielsen number concept gives a better guide for choosing starting maps in numerical homotopy methods than the starting maps guided by the Bézout number. Recently a yet better approach involving the Newton polytope concept has been given. The latter approach has been extensively surveyed by \textit{T.-Y. Li} [Iserles, A. (ed.), Acta Numerica Vol. 6, 1997. Cambridge University Press. 399-436 (1997; Zbl 0886.65054)].