The classical Kantorovich theorem on Newton's method assumes that the first 5 w Ž . derivative of the operator involved satisfies a Lipschitz condition ⌫ FЈ x y 0 Ž .x5 5 5 FЈ y F L x y y . In this paper, we weaken this condition, assuming that 5 w Ž . Ž .x5 Ž5 5 . ⌫ FЈ x y FЈ x F x y x for a given
✦ LIBER ✦
Weaker conditions for the convergence of Newton’s method
✍ Scribed by Ioannis K. Argyros; Saïd Hilout
- Book ID
- 113689553
- Publisher
- Elsevier Science
- Year
- 2012
- Tongue
- English
- Weight
- 296 KB
- Volume
- 28
- Category
- Article
- ISSN
- 0885-064X
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
Relaxing Convergence Conditions for Newt
✍
M.A. Hernández
📂
Article
📅
2000
🏛
Elsevier Science
🌐
English
⚖ 100 KB
Relaxing the convergence conditions for
✍
Ioannis K. Argyros
📂
Article
📅
2006
🏛
Springer-Verlag
🌐
English
⚖ 179 KB
Local convergence of Newton’s method und
✍
O.P. Ferreira
📂
Article
📅
2011
🏛
Elsevier Science
🌐
English
⚖ 240 KB
A local convergence analysis of Newton's method for solving nonlinear equations, under a majorant condition, is presented in this paper. Without assuming convexity of the derivative of the majorant function, which relaxes the Lipschitz condition on the operator under consideration, convergence, the
Weak convergence conditions for Inexact
✍
Ioannis K. Argyros; Saïd Hilout
📂
Article
📅
2011
🏛
Elsevier Science
🌐
English
⚖ 236 KB
On the convergence of newton's method
✍
Joel Friedman
📂
Article
📅
1989
🏛
Elsevier Science
🌐
English
⚖ 803 KB
Convergence of Newton’s Method for Secti
✍
J. H. Wang
📂
Article
📅
2010
🏛
Springer
🌐
English
⚖ 502 KB