We study Newton's method for determining the solution off(x) = 0 whenf(x) is required only to be continuous and piecewise continuously differentiable in some sphere about the initial iterate, x ) is nonsingular, (lc) II J-l(x~m)[J(x) -J(y)][I ~ o~(I x -y f), for all x andy ~ D.
On the convergence of Newton-type methods under mild differentiability conditions
✍ Scribed by Ioannis K. Argyros; Saïd Hilout
- Publisher
- Springer US
- Year
- 2009
- Tongue
- English
- Weight
- 432 KB
- Volume
- 52
- Category
- Article
- ISSN
- 1017-1398
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
In this work, we obtain a semilocal convergence result for the secant method in Banach spaces under mild convergence conditions. We consider a condition for divided differences which generalizes those usual ones, i.e., Lipschitz continuous and Holder continuous conditions. Also, we obtain a result f
We establish a convergence theorem for the Midpoint method using a new system of rectu'rence relations. The purpose of this note is to relax its convergence conditions. We also give an example where our convergence theorem can be applied but other ones cannot.
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-Hölder condition on the operator involved, and use it in combination with the Hölder condition to provide a new local convergenc
Under weak conditions, we present an iteration formula to improve Newton's method for solving nonlinear equations. The method is free from second derivatives, permitting f (x) = 0 in some points and per iteration it requires two evaluations of the given function and one evaluation of its derivative.