A product-decomposition bound for Bézout numbers. (English) Zbl 0854.65038
The authors are concerned with finding bounds for the number of nonsingular solutions of a polynomial system \(f(z) = 0\) when \(f\) has a “product structure”. A theorem is proven for such systems which offers a method for obtaining a tighter upper bound on the number of nonsingular solutions than is generally available. At the same time this theorem provides an approach for solving such systems via polynomial continuation, which results in less computational work. Also, it is shown how the nine-point problem from the design of mechanisms can be solved efficiently using the present method.
Reviewer: V.A.Kostova (Russe)
MSC:
65H10 | Numerical computation of solutions to systems of equations |
12Y05 | Computational aspects of field theory and polynomials (MSC2010) |
65H20 | Global methods, including homotopy approaches to the numerical solution of nonlinear equations |
26C10 | Real polynomials: location of zeros |
70B10 | Kinematics of a rigid body |