A shifted nested splitting iterative method with applications to ill-posed problems and image restoration

被引：5

作者：

Zak, Mohammad Khorsand ^{[1
]}

Toutounian, Faezeh ^{[2
,3
]}

机构：

[1] Islamic Azad Univ, Aligoudarz Branch, Dept Appl Math, Aligoudarz, Iran

[2] Ferdowsi Univ Mashhad, Sch Math Sci, Dept Appl Math, Mashhad, Iran

[3] Ferdowsi Univ Mashhad, Ctr Excellence Modelling & Control Syst, Mashhad, Iran

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2016年 / 71卷 / 01期

关键词：

CGNR; Hermitian and skew-Hermitian splitting; Tikhonov regularization; Image restoration; DEFINITE LINEAR-SYSTEMS; REGULARIZATION;

D O I：

10.1016/j.camwa.2015.11.005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present a shifted nested iterative method for solving systems of linear equations with a coefficient matrix that contains a dominant skew-Hermitian part. This new scheme is practically the inner/outer iterations, which employs the CGNR method as inner iteration to approximate each outer iterate, while each outer iteration is induced by a convergent splitting of the coefficient matrix. Convergence properties of the new scheme are studied in depth and possible choices of the shift parameter are discussed. Moreover, an adapted version of the method is used for ill-posed problems and image restoration. At the last, numerical examples are used to further examine the effectiveness and robustness of the new method. (C) 2015 Elsevier Ltd. All rights reserved.

引用

页码：213 / 223

页数：11

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