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

Guo Qiang He & Lin Xian Liu

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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

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@Article{JCM-17-275, author = {}, 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 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 KW - Implicit iterative method KW - Control parameter 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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