(untitled) (Journal of Computational Mathematics, 2007)
Inexact Newton methods are constructed by combining Newton's method with another iterative method that is used to solve the Newton equations inexactly. In this paper, we establish two semilocal convergence theorems for the inexact Newton methods. When these two theorems are specified to Newton's method, we obtain a different Newton-Kantorovich theorem about Newton's method. When the iterative method for solving the Newton equations is specified to be the splitting method, we get two estimates about the iteration steps for the special inexact Newton methods.