A uniparametric LU-SGS method for systems of nonlinear equations

The preconditioned Newton-GMRES method is used in many applications for computing efficiently the solution of large sparse systems of nonlinear equations. In this paper, we present a new LU-SGS preconditioner with an adaptive parameter. In each iteration of Newton method, the optimal parameter can be computed and then the classical LU-SGS preconditioner is improved. Numerical results show that with this new preconditioner, Newton-GMRES method can be more efficient and robust.