Verschelde, Jan; Verlinden, Pierre; Cools, Ronald Homotopies exploiting Newton polytopes for solving sparse polynomial systems. (English) Zbl 0809.65048 SIAM J. Numer. Anal. 31, No. 3, 915-930 (1994). The paper extensively deals with the computation of the Bernstein- Kushnirenko-Khovanskij upper bound for the number of solutions of a polynomial system as the mixed volume of the Newton polytopes induced by the given system. The basic operations needed for the computing are accomplished by three algorithms given in section 2. Section 3 is devoted to the construction of the start system \(G\) involved in any homotopy method while section 4 is concerned with the improvement of the efficiency of the mixed homotopy continuation method. Finally, section 5 presents six examples of polynomial systems arising in various fields: chemistry, economics modelling, mechanics, and neurophysiology. Reviewer: V.Berinde (Baia Mare) Cited in 62 Documents MSC: 65H10 Numerical computation of solutions to systems of equations 65H20 Global methods, including homotopy approaches to the numerical solution of nonlinear equations Keywords:Bernstein-Kushnirenko-Khovanskij upper bound; number of solutions; polynomial system; mixed volume; Newton polytopes; homotopy continuation method PDFBibTeX XMLCite \textit{J. Verschelde} et al., SIAM J. Numer. Anal. 31, No. 3, 915--930 (1994; Zbl 0809.65048) Full Text: DOI