We consider Newton’s algorithm as well as a variant, the Gauss– Newton algorithm, to solve a system of nonlinear equations F (x) = 0, where x ∈ R , F : R → R. We use a line search method to ensure global convergence. The exact form of our algorithm depends on the rank of the Jacobian J(x) of F . Computational results on some standard test problems are presented, which show that the algorithm ma...
