Nonlinear Analysis 47 (2001), 1961–1971 A NEWTON METHOD FOR SYSTEMS OF m EQUATIONS IN n VARIABLES

Abstract. The classical Newton–Kantorovich method for solving systems of equations f(x) = 0 uses the inverse of the Jacobian of f at each iteration. If the number of equations is different than the number of variables, or if the Jacobian cannot be assumed nonsingular, a generalized inverse of the Jacobian can be used in a Newton method whose limit points are stationary points of ‖f(x)‖2. We study conditions for local convergence of this method, prove quadratic convergence, and implement an adaptive version this iterative method, allowing a controlled increase of the rank