𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Concerning the “terra incognita” between convergence regions of two Newton methods

✍ Scribed by Ioannis K. Argyros

Publisher
Elsevier Science
Year
2005
Tongue
English
Weight
212 KB
Volume
62
Category
Article
ISSN
0362-546X

No coin nor oath required. For personal study only.

✦ Synopsis

The majorizing principle is used to show local and semilocal convergence of Newton methods to a locally unique solution of a nonlinear operator in a Banach space, when the Fréchet derivative of the operator involved satisfies a center-Hölder and a Hölder continuity condition. Then we investigate an unknown area ("terra incognita") between the convergence regions of Newton's method, and the corresponding modified Newton's method. Our approach compares favorably with other corresponding ones in this direction.

📜 SIMILAR VOLUMES

Concerning the convergence of inexact Ne
Concerning the convergence of inexact Newton methods
✍ Ioannis K. Argyros 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 576 KB

In this study, we use inexact Newton methods to find solutions of nonlinear operator equations on Banach spaces with a convergence structure. Our technique involves the introduction of a generalized norm as an operator from a linear space into a partially ordered Banach space. In this way the metric

The cubic semilocal convergence on two v
The cubic semilocal convergence on two variants of Newton's method
✍ Quan Zheng; Rongxia Bai; Zhongli Liu 📂 Article 📅 2008 🏛 Elsevier Science 🌐 English ⚖ 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

The convergence of two Newton-like metho
The convergence of two Newton-like methods for solving block nonlinear equations and a class of r-point (r + 1)st-order A-stable one-block methods
✍ Shuangsuo Zhao; Guofeng Zhang; Changyin Wang 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 775 KB

In this paper, for a Newton-like method for solving block nonlinear equations arising in the numerical solution of stiff ODEs y' = f(y), which involves a smaller quantity of computation, we prove that it is convergent and the convergence is independent of the stiffness of f(y), and give the error es