Inexact methods: forcing terms and conditioning

In this paper, we consider inexact Newton and Newton-like methods and provide new convergence conditions relating the forcing terms to the conditioning of the iteration matrices. These results can be exploited when inexact methods with iterative linear solvers are used. In this framework, preconditioning techniques can be used to improve the performance of iterative linear solvers and to avoid the need of excessively small forcing terms. Numerical experiments validating the theoretical results are discussed.