Weaker Kantorovich type criteria for inexact Newton methods

摘要

We develop a tighter semilocal convergence analysis for the Inexact Newton Method (INM) than in earlier studies such as Shen and Li (2009, 2010), Guo (2007), Smale (1986), Morini (1999), Argyros (1999, 1999, 2007, 2011), Argyros and Hilout (2010, 2012) and Argyros et al. (2012). Our approach is based on the center-Lipschitz condition instead of the Lipschitz condition for computing the inverses of the linear operators involved. Moreover, we expand the applicability of the method by providing weaker sufficient convergence criteria under the same computational cost. Numerical examples where the old convergence criteria are not satisfied but the new convergence criteria hold are also provided in this study. In particular we solve a two-point boundary value problem appearing in magnetohydrodynamics.