Computational experience with globally convergent descent methods for large sparse systems of nonlinear equations

This paper is devoted to globally convergent Armijo-type descent methods for solving large sparse systems of nonlinear equations. These methods include the discrete Newtcin method and a broad class of Newton-like methods based on various approximations of the Jacobian matrix. We propose a general theory of global convergence together with a robust algorithm including a special restarting strategy. This algorithm is based cfn the preconditioned smoothed CGS method for solving nonsymmetric systems of linejtr equations. After reviewing 12 particular Newton-like methods, we propose results of extensive computational experiments. These results demonstrate high efficiency of tip proposed algorithm