Comparison of Brown's and Newton's method in the monotone case (Q1093328)

In many cases when Newton's method, applied to a nonlinear system \(F(x)=0\), produces a monotonically decreasing sequence of iterates, Brown's method converges monotonically, too. We compare the iterates of Brown's and Newton's method in these monotone cases with respect to the natural partial ordering. It turns out that in most of the cases arising in applications Brown's method then produces ``better'' iterates than Newton's method.