An improved Tikhonov regularization method combined with the exponential filter function.
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| Title: | An improved Tikhonov regularization method combined with the exponential filter function. |
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| Authors: | Zeng, Xiaoniu1 (AUTHOR) xiaoniuzeng@163.com, Liu, Tianyou1 (AUTHOR), Tan, Xiaofeng1 (AUTHOR), Li, Hongru1 (AUTHOR), Luo, Shengjie1 (AUTHOR) |
| Source: | Journal of Computational Methods in Sciences & Engineering (Sage Publications Inc.). Mar2025, Vol. 25 Issue 2, p1114-1122. 9p. |
| Subjects: | Matrix exponential, Exponential functions, Tikhonov regularization |
| Abstract: | Tikhonov regularization is one of the most popular methods for solving linear discrete ill-posed problems. This approach involves transforming the original problem into a penalized least-squares problem, yielding a solution that exhibits greater robustness against data inaccuracies and computational errors that may occur during the solving process. The choice of the regularization matrix significantly influences the accuracy of the resulting solution. In this paper, we propose a novel method for selecting the regularization matrix based on exponential filter functions, which have a unique connection with Tikhonov filter functions. Our proposed Tikhonov-exponential regularization method only requires one parameter, similar to the traditional Tikhonov regularization method. Computational examples demonstrate the advantages of our proposed method. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Computational Methods in Sciences & Engineering (Sage Publications Inc.) is the property of Sage Publications Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Abstract: | Tikhonov regularization is one of the most popular methods for solving linear discrete ill-posed problems. This approach involves transforming the original problem into a penalized least-squares problem, yielding a solution that exhibits greater robustness against data inaccuracies and computational errors that may occur during the solving process. The choice of the regularization matrix significantly influences the accuracy of the resulting solution. In this paper, we propose a novel method for selecting the regularization matrix based on exponential filter functions, which have a unique connection with Tikhonov filter functions. Our proposed Tikhonov-exponential regularization method only requires one parameter, similar to the traditional Tikhonov regularization method. Computational examples demonstrate the advantages of our proposed method. [ABSTRACT FROM AUTHOR] |
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| ISSN: | 14727978 |
| DOI: | 10.1177/14727978241295283 |
