Expanding the applicability of Lavrentiev regularization methods for ill-posed problems

被引：5

作者：

Argyros, Ioannis K. ^{[1
]}

Cho, Yeol Je ^{[2
,3
]}

George, Santhosh ^{[4
]}

机构：

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

[2] Gyeongsang Natl Univ, Dept Math Educ, Jinju 660701, South Korea

[3] Gyeongsang Natl Univ, RINS, Jinju 660701, South Korea

[4] Natl Inst Technol Karnataka, Dept Math & Computat Sci, Surathkal 757025, Karnataka, India

来源：

BOUNDARY VALUE PROBLEMS | 2013年

基金：

新加坡国家研究基金会;

关键词：

Lavrentiev regularization method; Hilbert space; ill-posed problems; stopping index; Frechet-derivative; source function; boundary value problem; GENERALIZED DISCREPANCY PRINCIPLE; TIKHONOV REGULARIZATION; CONVERGENCE; PARAMETER; EQUATIONS; CHOICE;

D O I：

10.1186/1687-2770-2013-114

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we are concerned with the problem of approximating a solution of an ill-posed problem in a Hilbert space setting using the Lavrentiev regularization method and, in particular, expanding the applicability of this method by weakening the popular Lipschitz-type hypotheses considered in earlier studies such as (Bakushinskii and Smirnova in Numer. Funct. Anal. Optim. 26:35-48, 2005; Bakushinskii and Smirnova in Nonlinear Anal. 64:1255-1261, 2006; Bakushinskii and Smirnova in Numer. Funct. Anal. Optim. 28:13-25, 2007; Jin in Math. Comput. 69:1603-1623, 2000; Mahale and Nair in ANZIAM J. 51:191-217, 2009). Numerical examples are given to show that our convergence criteria are weaker and our error analysis tighter under less computational cost than the corresponding works given in (Bakushinskii and Smirnova in Numer. Funct. Anal. Optim. 26:35-48, 2005; Bakushinskii and Smirnova in Nonlinear Anal. 64:1255-1261, 2006; Bakushinskii and Smirnova in Numer. Funct. Anal. Optim. 28:13-25, 2007; Jin in Math. Comput. 69:1603-1623, 2000; Mahale and Nair in ANZIAM J. 51:191-217, 2009).

引用

页数：15

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