Solving systems of nonlinear equations by the parametric approach with an arbitrary initial point

We propose a number of algorithms for solving systems of nonlinear equations, when a good approximation to solution is unknown, and the Newton method is not efficient. These methods are based on the choice of weights for an auxiliary function and on the descent in the space of weights. The convergence depends on relations between the measures of regions of attraction of the solutions. In order to improve the performance, we consider perturbation methods.