𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Remark on the convergence of the midpoint method under mild differentiability conditions

✍ Scribed by J.A. Ezquerro; M.A. Hernández; M.A. Salanova

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
190 KB
Volume
98
Category
Article
ISSN
0377-0427

No coin nor oath required. For personal study only.

✦ Synopsis

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.

📜 SIMILAR VOLUMES

Semilocal convergence of the secant meth
Semilocal convergence of the secant method under mild convergence conditions of differentiability
✍ M.A. Hernández; M.J. Rubio 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 548 KB

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

Local convergence of inexact methods und
Local convergence of inexact methods under the Hölder condition
✍ Chong Li; Weiping Shen 📂 Article 📅 2008 🏛 Elsevier Science 🌐 English ⚖ 816 KB

We study the convergence properties for some inexact Newton-like methods including the inexact Newton methods for solving nonlinear operator equations on Banach spaces. A new type of residual control is presented. Under the assumption that the derivative of the operator satisfies the Hölder conditio

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 📂 Article 📅 2010 🏛 Elsevier Science 🌐 English ⚖ 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-Hölder condition on the operator involved, and use it in combination with the Hölder condition to provide a new local convergenc