Weaker Kantorovich type criteria for inexact Newton methods

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:261

Article

Argyros, I. K.¹  Khattri, S. K.² 

[1] Cameron Univ, Dept Math Sci, Lawton, OK 73505 USA

[2] Stord Haugesund Univ Coll, Dept Engn, Stord, Norway

关键词: Inexact Newton method;    Banach space;    Kantorovich-theory;    Semilocal convergence;    Frechet derivative;    Center-Lipschitz condition;   

DOI  :  10.1016/j.cam.2013.10.048

来源: Elsevier

【 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. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

Free