On Convergence of the Additive Schwarz Preconditioned Inexact Newton Method

The additive Schwarz preconditioned inexact Newton (ASPIN) method was recently introduced [X.-C. Cai and D. E.\ Keyes, {\it SIAM J. Sci.\ Comput.}, 24 (2002), pp. 183--200] to solve the systems of nonlinear equations with nonbalanced nonlinearities. Although the ASPIN method has successfully been used to solve some difficult nonlinear equations, its convergence property has not been studied since it was proposed. In this paper, the convergence property of the ASPIN method is studied, and the obtained result shows that this method is locally convergent. Furthermore, the convergence rate for the ASPIN method is discussed and the obtained result is similar to that of the inexact Newton method.