In many practical applications, we must solve a system of polynomial equations. In this lecture I will try to outline some important problems from mechanisms design. Some of these problems motivated the development of the new field "numerical algebraic geometry", proposed by Andrew Sommese and Charles Wampler in a 1996 paper. Recently we developed new numerical homotopy algorithms to deal with positive dimensional solution sets.
Graduate Student Seminar at UIC, 5 September 2003.