A modified Tikhonov regularization method based on Hermite expansion for solving the Cauchy problem of the Laplace equation
In this paper, a Cauchy problem for the Laplace equation is considered. We develop a modified Tikhonov regularization method based on Hermite expansion to deal with the ill posed-ness of the problem. The regularization parameter is determined by a discrepancy principle. For various smoothness condit...
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| Format: | Article |
| Language: | English |
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De Gruyter
2020-12-01
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| Series: | Open Mathematics |
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| Online Access: | http://www.degruyter.com/view/j/math.2020.18.issue-1/math-2020-0111/math-2020-0111.xml?format=INT |
| _version_ | 1818854717844881408 |
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| author | Zhao Zhenyu You Lei Meng Zehong |
| author_facet | Zhao Zhenyu You Lei Meng Zehong |
| author_sort | Zhao Zhenyu |
| collection | DOAJ |
| description | In this paper, a Cauchy problem for the Laplace equation is considered. We develop a modified Tikhonov regularization method based on Hermite expansion to deal with the ill posed-ness of the problem. The regularization parameter is determined by a discrepancy principle. For various smoothness conditions, the solution process of the method is uniform and the convergence rate can be obtained self-adaptively. Numerical tests are also carried out to verify the effectiveness of the method. |
| first_indexed | 2024-12-19T07:57:09Z |
| format | Article |
| id | doaj.art-96aa876ca12c466c8477b61ec4194f14 |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-12-19T07:57:09Z |
| publishDate | 2020-12-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-96aa876ca12c466c8477b61ec4194f142022-12-21T20:29:58ZengDe GruyterOpen Mathematics2391-54552020-12-011811685169710.1515/math-2020-0111math-2020-0111A modified Tikhonov regularization method based on Hermite expansion for solving the Cauchy problem of the Laplace equationZhao Zhenyu0You Lei1Meng Zehong2Southern Marine Science and Engineering Guangdong Laboratory (Zhanjiang), Zhanjiang 524000, ChinaCollege of Science, Guangdong Ocean University, Zhanjiang 524088, ChinaSchool of Mathematics and Statistics, Zhejiang University of Finance and Economics, Hangzhou 310018, ChinaIn this paper, a Cauchy problem for the Laplace equation is considered. We develop a modified Tikhonov regularization method based on Hermite expansion to deal with the ill posed-ness of the problem. The regularization parameter is determined by a discrepancy principle. For various smoothness conditions, the solution process of the method is uniform and the convergence rate can be obtained self-adaptively. Numerical tests are also carried out to verify the effectiveness of the method.http://www.degruyter.com/view/j/math.2020.18.issue-1/math-2020-0111/math-2020-0111.xml?format=INTcauchy problem for laplace equationill-posed problemtikhonov regularizationhermite approximationdiscrepancy principle65d1565n2165n35 |
| spellingShingle | Zhao Zhenyu You Lei Meng Zehong A modified Tikhonov regularization method based on Hermite expansion for solving the Cauchy problem of the Laplace equation Open Mathematics cauchy problem for laplace equation ill-posed problem tikhonov regularization hermite approximation discrepancy principle 65d15 65n21 65n35 |
| title | A modified Tikhonov regularization method based on Hermite expansion for solving the Cauchy problem of the Laplace equation |
| title_full | A modified Tikhonov regularization method based on Hermite expansion for solving the Cauchy problem of the Laplace equation |
| title_fullStr | A modified Tikhonov regularization method based on Hermite expansion for solving the Cauchy problem of the Laplace equation |
| title_full_unstemmed | A modified Tikhonov regularization method based on Hermite expansion for solving the Cauchy problem of the Laplace equation |
| title_short | A modified Tikhonov regularization method based on Hermite expansion for solving the Cauchy problem of the Laplace equation |
| title_sort | modified tikhonov regularization method based on hermite expansion for solving the cauchy problem of the laplace equation |
| topic | cauchy problem for laplace equation ill-posed problem tikhonov regularization hermite approximation discrepancy principle 65d15 65n21 65n35 |
| url | http://www.degruyter.com/view/j/math.2020.18.issue-1/math-2020-0111/math-2020-0111.xml?format=INT |
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