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

Boundary value problems

Ioannis K Argyros¹  Santhosh George²  Yeol Je Cho³ 

[1] Department of Mathematical Sciences, Cameron University, Lawton, USA;Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Karnataka, India;Department of Mathematics Education and the RINS, Gyeongsang National University, Jinju, Korea

关键词: Lavrentiev regularization method;    Hilbert space;    ill-posed problems;    stopping index;    Fréchet-derivative;    source function;    boundary value problem;   

DOI  :  10.1186/1687-2770-2013-114

学科分类：数学（综合）

来源: SpringerOpen

【 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). MSC:65F22, 65J15, 65J22, 65M30, 47A52.

【 授权许可】

CC BY