𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On the semilocal convergence of inexact Newton methods in Banach spaces

✍ Scribed by Ioannis K. Argyros

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
489 KB
Volume
228
Category
Article
ISSN
0377-0427

No coin nor oath required. For personal study only.

✦ Synopsis

We provide two types of semilocal convergence theorems for approximating a solution of an equation in a Banach space setting using an inexact Newton method [I.K. Argyros, Relation between forcing sequences and inexact Newton iterates in Banach spaces, Computing 63 (2) (1999) 134-144; I.K. Argyros, A new convergence theorem for the inexact Newton method based on assumptions involving the second FrΓ©chet-derivative,

πŸ“œ SIMILAR VOLUMES

The cubic semilocal convergence on two v
The cubic semilocal convergence on two variants of Newton's method
✍ Quan Zheng; Rongxia Bai; Zhongli Liu πŸ“‚ Article πŸ“… 2008 πŸ› Elsevier Science 🌐 English βš– 169 KB

In this paper, we discuss two variants of Newton's method without using any second derivative for solving nonlinear equations. By using the majorant function and confirming the majorant sequences, we obtain the cubic semilocal convergence and the error estimation in the Kantorovich-type theorems. Th

On the local convergence of inexact Newt
On the local convergence of inexact Newton-type methods under residual control-type conditions
✍ Hongmin Ren; Ioannis K. Argyros πŸ“‚ Article πŸ“… 2010 πŸ› Elsevier Science 🌐 English βš– 322 KB

A local convergence analysis of inexact Newton-type methods using a new type of residual control was recently presented by C. Li and W. Shen. Here, we introduce the center-HΓΆlder condition on the operator involved, and use it in combination with the HΓΆlder condition to provide a new local convergenc