Newton Generalized Hessenberg method for solving nonlinear systems of equations

In this paper, we give and analyze a Finite Difference version of the Generalized Hessenberg (FDGH) method. The obtained results show that applying this method in solving a linear system is equivalent to applying the Generalized Hessenberg method to a perturbed system. The finite difference version of the Generalized Hessenberg method is used in the context of solving nonlinear systems of equations using an inexact Newton method. The local convergence of the finite difference versions of the Newton Generalized Hessenberg method is studied. We obtain theoretical results that generalize those obtained for Newton-Arnoldi and Newton-GMRES methods. Numerical examples are given in order to compare the performances of the finite difference versions of the Newton-GMRES and Newton-CMRH methods. This revised version was published online in June 2006 with corrections to the Cover Date.