A Product-Decomposition Bound for Bezout Numbers
Alexander P. Morgan, Andrew John Sommese, Charles W. Wampler · SIAM Journal on Numerical Analysis · 1995
Most polynomial systems that arise in practice are not completely general but have special structures. A common form is that each equation must be a sum of products, where each factor has an identifiable generic type. 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. To illustrate the practical usefulness of these ideas, we show that a significant design-of-mechanisms problem can be solved with an order of magnitude less work than the published solution.