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Volume 26, Issue 1
Multi-Parameter Tikhonov Regularization for Linear Ill-Posed Operator Equations

Zhongying Chen, Yao Lu, Yuesheng Xu & Hongqi Yang

J. Comp. Math., 26 (2008), pp. 37-55.

Published online: 2008-02

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  • Abstract

We consider solving linear ill-posed operator equations. Based on a multi-scale decomposition for the solution space, we propose a multi-parameter regularization for solving the equations. We establish weak and strong convergence theorems for the multi-parameter regularization solution. In particular, based on the eigenfunction decomposition, we develop a posteriori choice strategy for multi-parameters which gives a regularization solution with the optimal error bound. Several practical choices of multi-parameters are proposed. We also present numerical experiments to demonstrate the outperformance of the multi-parameter regularization over the single parameter regularization.

  • Keywords

Ill-posed problems, Tikhonov regularization, Multi-parameter regularization.

  • AMS Subject Headings

47A52.

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{JCM-26-37, author = {Zhongying Chen, Yao Lu, Yuesheng Xu and Hongqi Yang}, title = {Multi-Parameter Tikhonov Regularization for Linear Ill-Posed Operator Equations}, journal = {Journal of Computational Mathematics}, year = {2008}, volume = {26}, number = {1}, pages = {37--55}, abstract = {

We consider solving linear ill-posed operator equations. Based on a multi-scale decomposition for the solution space, we propose a multi-parameter regularization for solving the equations. We establish weak and strong convergence theorems for the multi-parameter regularization solution. In particular, based on the eigenfunction decomposition, we develop a posteriori choice strategy for multi-parameters which gives a regularization solution with the optimal error bound. Several practical choices of multi-parameters are proposed. We also present numerical experiments to demonstrate the outperformance of the multi-parameter regularization over the single parameter regularization.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8609.html} }
TY - JOUR T1 - Multi-Parameter Tikhonov Regularization for Linear Ill-Posed Operator Equations AU - Zhongying Chen, Yao Lu, Yuesheng Xu & Hongqi Yang JO - Journal of Computational Mathematics VL - 1 SP - 37 EP - 55 PY - 2008 DA - 2008/02 SN - 26 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8609.html KW - Ill-posed problems, Tikhonov regularization, Multi-parameter regularization. AB -

We consider solving linear ill-posed operator equations. Based on a multi-scale decomposition for the solution space, we propose a multi-parameter regularization for solving the equations. We establish weak and strong convergence theorems for the multi-parameter regularization solution. In particular, based on the eigenfunction decomposition, we develop a posteriori choice strategy for multi-parameters which gives a regularization solution with the optimal error bound. Several practical choices of multi-parameters are proposed. We also present numerical experiments to demonstrate the outperformance of the multi-parameter regularization over the single parameter regularization.

Zhongying Chen, Yao Lu, Yuesheng Xu and Hongqi Yang. (2008). Multi-Parameter Tikhonov Regularization for Linear Ill-Posed Operator Equations. Journal of Computational Mathematics. 26 (1). 37-55. doi:
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