Iterative regularization methods for ill-posed Hammerstein-type operator equations in Hilbert scales

被引：0

作者：

Argyros, Ioannis K. ^{[1
]}

George, Santhosh ^{[2
]}

Kunhanandan, M. ^{[3
]}

机构：

[1] Cameron Univ, Dept Math Sci, Lawton, OK 73505 USA

[2] Natl Inst Technol, Dept Math & Computat Sci, Karnataka 575025, Surathkal, India

[3] Goa Univ, Dept Math, Taleigao 403206, Goa, India

来源：

STUDIA UNIVERSITATIS BABES-BOLYAI MATHEMATICA | 2014年 / 59卷 / 02期

关键词：

Nonlinear ill-posed Hammerstein type equations; iterative regularization; adaptive choice; Hilbert scales;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we report on a method for regularizing a nonlinear Hammerstein type operator equation in Hilbert scales. The proposed method is a combination of Lavrentieve regularization method and a Modified Newton's method in Hilbert scales. Under the assumptions that the operator F is continuously differentiable with a Lipschitz-continuous first derivative and that the solution of (1.1) fulfills a general source condition, we give an optimal order convergence rate result with respect to the general source function.

引用

页码：247 / 262

页数：16

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