𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Local convergence of inexact methods under the Hölder condition

✍ Scribed by Chong Li; Weiping Shen

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
816 KB
Volume
222
Category
Article
ISSN
0377-0427

No coin nor oath required. For personal study only.

✦ Synopsis

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 condition, the radius of convergence ball of the inexact Newton-like methods with the new type of residual control is estimated, and a linear and/or superlinear convergence property is proved, which extends the corresponding result of [B. Morini, Convergence behaviour of inexact Newton methods, Math. Comput. 68 (1999Comput. 68 ( ) 1605Comput. 68 ( -1613]]. As an application, we show that the inexact Newton-like method presented in [R.H. Chan, H.L. Chung, S.F. Xu, The inexact Newton-like method for inverse eigenvalue problem, BIT Numer. Math. 43 (2003) 7-20] for solving inverse eigenvalue problems can be regarded equivalently as one of the inexact Newton-like methods considered in this paper. A numerical example is provided to illustrate the convergence performance of the algorithm.

📜 SIMILAR VOLUMES

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

Local convergence of Newton’s method und
Local convergence of Newton’s method under majorant condition
✍ 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

On the semilocal convergence of inexact
On the semilocal convergence of inexact Newton methods in Banach spaces
✍ Ioannis K. Argyros 📂 Article 📅 2009 🏛 Elsevier Science 🌐 English ⚖ 489 KB

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

On the Rate of Convergence of Singular I
On the Rate of Convergence of Singular Integrals for Hölder Continuous Functions
✍ B. N. Mohapatra; R. S. Rodriguez 📂 Article 📅 1990 🏛 John Wiley and Sons 🌐 English ⚖ 236 KB

Math. Nechr. 149 (1990) and (1.7) respectively, where the parameter 5 tends to 0. n W Z , 5 ) = ( 6 Z -l J I(% + 1) exp (-t2/5) d t , -JI Throughout the paper, we shall write (1.8) @A = I(% + 1) -2f(Z)'+ f ( Z -0 . 2.