A globally convergent Newton-GMRES subspace method for systems of nonlinear equations

Newton-Krylov methods are variants of inexact: Newton methods where the approximate Newton direction is taken from a subspace of small dimension. Here we introduce a new hybrid Newton-GMRES method where a global strategy restricted to a low-dimensional subspace generated by GMRES is performed. The obtained process is consistent with preconditioning and with matrix-free implementation. Computational results indicate that our proposal enhances the classical backtracking inexact method.