Convergence analysis of a variant of the Newton method for solving nonlinear equations

The paper presents a convergence analysis of a modified Newton method for solving nonlinear systems of equations. The convergence results show that this method converges cubically in the nonsingular case, and linearly with the rate 3=8 under some sufficient conditions when the Jacobian is singular at the root. The convergence theory is used to analyze the convergence behavior when the modified Newton method is applied to a nonsymmetric algebraic Riccati equation arising in transport theory. Numerical experiment confirms the theoretical results.