Tikhonov regularization with MTRSVD method for solving large-scale discrete ill-posed problems
Regularization is possibly the most popular method for solving discrete ill-posed problems, whose solution is less sensitive to the error in the observed vector in the right hand than the original solution. This paper presents a new modified truncated randomized singular value decomposition (TR-MTRS...
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| Veröffentlicht in: | Journal of computational and applied mathematics Jg. 405; S. 113969 |
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| Abstract | Regularization is possibly the most popular method for solving discrete ill-posed problems, whose solution is less sensitive to the error in the observed vector in the right hand than the original solution. This paper presents a new modified truncated randomized singular value decomposition (TR-MTRSVD) method for large Tikhonov regularization in standard form. The proposed TR-MTRSVD algorithm introduces the idea of randomized algorithm into the improved truncated singular value decomposition (MTSVD) method to solve large Tikhonov regularization problems. The approximation matrix Ãℓ produced by randomized SVD is replaced by the closest matrix Ãk̃ in a unitarily invariant matrix norm with the same spectral condition number. The regularization parameters are determined by the discrepancy principle. Numerical examples show the effectiveness and efficiency of the proposed TR-MTRSVD algorithm for large Tikhonov regularization problems. |
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| AbstractList | Regularization is possibly the most popular method for solving discrete ill-posed problems, whose solution is less sensitive to the error in the observed vector in the right hand than the original solution. This paper presents a new modified truncated randomized singular value decomposition (TR-MTRSVD) method for large Tikhonov regularization in standard form. The proposed TR-MTRSVD algorithm introduces the idea of randomized algorithm into the improved truncated singular value decomposition (MTSVD) method to solve large Tikhonov regularization problems. The approximation matrix Ãℓ produced by randomized SVD is replaced by the closest matrix Ãk̃ in a unitarily invariant matrix norm with the same spectral condition number. The regularization parameters are determined by the discrepancy principle. Numerical examples show the effectiveness and efficiency of the proposed TR-MTRSVD algorithm for large Tikhonov regularization problems. |
| ArticleNumber | 113969 |
| Author | Huang, Guangxin Yin, Feng Liu, Yuanyuan |
| Author_xml | – sequence: 1 givenname: Guangxin orcidid: 0000-0003-3220-3083 surname: Huang fullname: Huang, Guangxin email: huangx@cdut.edu.cn organization: Geomathematics Key Laboratory of Sichuan, College of Mathematics and Physics, Chengdu University of Technology, Chengdu, 610059, PR China – sequence: 2 givenname: Yuanyuan surname: Liu fullname: Liu, Yuanyuan email: wuyouxiaoxiaoxin@163.com organization: Geomathematics Key Laboratory of Sichuan, College of Mathematics and Physics, Chengdu University of Technology, Chengdu, 610059, PR China – sequence: 3 givenname: Feng surname: Yin fullname: Yin, Feng email: fyin@suse.edu.cn organization: College of Mathematical and statistics, Sichuan University of Science and Engineering, Zigong, 643000, PR China |
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| Cites_doi | 10.1088/0266-5611/31/8/085008 10.1137/090767911 10.1023/A:1022383005969 10.1137/090771806 10.1016/j.cam.2011.09.039 10.1137/0913066 10.1088/1361-6420/aab92d 10.1137/15M1030200 10.1007/s11075-008-9163-1 10.1088/0266-5611/29/8/085008 10.1002/nla.1938 10.1007/BF01937276 10.1016/j.apnum.2020.08.019 10.1007/s11075-012-9612-8 10.1007/s11075-007-9136-9 |
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| Title | Tikhonov regularization with MTRSVD method for solving large-scale discrete ill-posed problems |
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