Global Algorithm For Incomplete Newton - GMRES Method

The inexact Newton-GMRES method is one of most powerful tools for solving the problems of the system of nonlinear equations.In this paper we introduce one globalization algorithm in connection with inexact Newton-GMRES method for nonlinear equations and prove its global convergence. In Chapter1, we introduce some background knowledge of inexact Newton method. In Chapter2, we analyze the globalization algorithm of inexact Newton-GMRES method. Firstly we describe one variant of inexact Newton-GMRES method. Second-ly we describe one linesearch strategy. Finally we present this globalization algorithm and prove the algorithm’s global convergence theorem. In Chapter3, we give some numerical examples.