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
On the convergence of an inexact Newton-type method
β Scribed by Guanglu Zhou; Liqun Qi
- Publisher
- Elsevier Science
- Year
- 2006
- Tongue
- English
- Weight
- 168 KB
- Volume
- 34
- Category
- Article
- ISSN
- 0167-6377
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π SIMILAR VOLUMES
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
## a b s t r a c t We introduce two families of Newton-type methods for multiple roots with cubic convergence. A further Newton-type method for multiple roots with cubic convergence is presented that is related to quadrature. We also provide numerical tests that show that these new methods are comp