Weaker Kantorovich type criteria for inexact Newton methods

Authors:
I. K. Argyros;S. K. Khattri
Affiliations:
-;-
Venue:
Journal of Computational and Applied Mathematics
Year:
2014

Citing 7
Cited 0

Convergence of Newton's method and inverse function theorem in Banach space

Mathematics of Computation
Relations between forcing sequences and inexact Newton iterates in Banach space

Computing
Convergence behaviour of inexact Newton methods

Mathematics of Computation
Kantorovich-type convergence criterion for inexact Newton methods

Applied Numerical Mathematics
New general convergence theory for iterative processes and its applications to Newton-Kantorovich type theorems

Journal of Complexity
Extending the Newton-Kantorovich hypothesis for solving equations

Journal of Computational and Applied Mathematics
Weaker conditions for the convergence of Newton's method

Journal of Complexity

Quantified Score

Hi-index	7.29

Visualization

Abstract

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.