Discrete Newton's method with local variations for solving large-scale nonlinear systems

A globally convergent discrete Newton method is proposed for solving large-scale nonlinear systems of equations. Advantage is taken from discretization steps so that the residual norm can be reduced while the Jacobian is approximated, besides the reduction at Newtonian iterations. The Curtis–Powell–Reid (CPR) scheme for discretization is used for dealing with sparse Jacobians. Global convergence is proved and numerical experiments are presented.