Global Behavior of Branin’s Method

Abstract

An analysis of Branin's method for finding all the real zeros of a vector function is carried out. It is based on a global study of this method perceived of as a dynamical system. Since Branin's algorithm is closely related to homotopy methods, this paper sheds some light on the global performance of these methods when employed for locating all the zeros of a vector function. We provide two examples for which the global behavior of Branin's algorithm is carried out using the cell-to-cell mapping computational technique.