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Volume 17, Issue 3
A Kind of Implicit Iterative Methods for Ill-Posed Operator Equations

Guo-Qiang He & Lin-Xian Liu

J. Comp. Math., 17 (1999), pp. 275-284.

Published online: 1999-06

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  • Abstract

In this paper we propose a kind of implicit iterative methods for solving ill-posed operator equations and discuss the properties of the methods in the case that the control parameter is fixed. The theoretical results show that the new methods have certain important features and can overcome some disadvantages of Tikhonov-type regularization and explicit iterative methods. Numerical examples are also given in the paper, which coincide well with theoretical results.

  • Keywords

Ill-posed equation, Implicit iterative method, Control parameter, Discrepamcy principle, Optimal convergence rate.

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COPYRIGHT: © Global Science Press

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@Article{JCM-17-275, author = {He , Guo-Qiang and Liu , Lin-Xian}, title = {A Kind of Implicit Iterative Methods for Ill-Posed Operator Equations}, journal = {Journal of Computational Mathematics}, year = {1999}, volume = {17}, number = {3}, pages = {275--284}, abstract = {

In this paper we propose a kind of implicit iterative methods for solving ill-posed operator equations and discuss the properties of the methods in the case that the control parameter is fixed. The theoretical results show that the new methods have certain important features and can overcome some disadvantages of Tikhonov-type regularization and explicit iterative methods. Numerical examples are also given in the paper, which coincide well with theoretical results.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9101.html} }
TY - JOUR T1 - A Kind of Implicit Iterative Methods for Ill-Posed Operator Equations AU - He , Guo-Qiang AU - Liu , Lin-Xian JO - Journal of Computational Mathematics VL - 3 SP - 275 EP - 284 PY - 1999 DA - 1999/06 SN - 17 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9101.html KW - Ill-posed equation, Implicit iterative method, Control parameter, Discrepamcy principle, Optimal convergence rate. AB -

In this paper we propose a kind of implicit iterative methods for solving ill-posed operator equations and discuss the properties of the methods in the case that the control parameter is fixed. The theoretical results show that the new methods have certain important features and can overcome some disadvantages of Tikhonov-type regularization and explicit iterative methods. Numerical examples are also given in the paper, which coincide well with theoretical results.

Guo-Qiang He & Lin-Xian Liu. (1970). A Kind of Implicit Iterative Methods for Ill-Posed Operator Equations. Journal of Computational Mathematics. 17 (3). 275-284. doi:
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