Optimal Stable Approximation for the Cauchy Problem for Laplace Equation
Cauchy problem for Laplace equation in a strip is considered. The optimal error bounds between the exact solution and its regularized approximation are given, which depend on the noise level either in a Hölder continuous way or in a logarithmic continuous way. We also provide two special regularizat...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2016/1468634 |
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| _version_ | 1832567487727665152 |
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| author | Hongfang Li Feng Zhou |
| author_facet | Hongfang Li Feng Zhou |
| author_sort | Hongfang Li |
| collection | DOAJ |
| description | Cauchy problem for Laplace equation in a strip is considered. The optimal error bounds between the exact solution and its regularized approximation are given, which depend on the noise level either in a Hölder continuous way or in a logarithmic continuous way. We also provide two special regularization methods, that is, the generalized Tikhonov regularization and the generalized singular value decomposition, which realize the optimal error bounds. |
| format | Article |
| id | doaj-art-f5a63a2b20cc445c81e8cdc2a676d35a |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-f5a63a2b20cc445c81e8cdc2a676d35a2025-02-03T01:01:26ZengWileyAdvances in Mathematical Physics1687-91201687-91392016-01-01201610.1155/2016/14686341468634Optimal Stable Approximation for the Cauchy Problem for Laplace EquationHongfang Li0Feng Zhou1College of Science, China University of Petroleum (East China), Qingdao 266580, ChinaCollege of Science, China University of Petroleum (East China), Qingdao 266580, ChinaCauchy problem for Laplace equation in a strip is considered. The optimal error bounds between the exact solution and its regularized approximation are given, which depend on the noise level either in a Hölder continuous way or in a logarithmic continuous way. We also provide two special regularization methods, that is, the generalized Tikhonov regularization and the generalized singular value decomposition, which realize the optimal error bounds.http://dx.doi.org/10.1155/2016/1468634 |
| spellingShingle | Hongfang Li Feng Zhou Optimal Stable Approximation for the Cauchy Problem for Laplace Equation Advances in Mathematical Physics |
| title | Optimal Stable Approximation for the Cauchy Problem for Laplace Equation |
| title_full | Optimal Stable Approximation for the Cauchy Problem for Laplace Equation |
| title_fullStr | Optimal Stable Approximation for the Cauchy Problem for Laplace Equation |
| title_full_unstemmed | Optimal Stable Approximation for the Cauchy Problem for Laplace Equation |
| title_short | Optimal Stable Approximation for the Cauchy Problem for Laplace Equation |
| title_sort | optimal stable approximation for the cauchy problem for laplace equation |
| url | http://dx.doi.org/10.1155/2016/1468634 |
| work_keys_str_mv | AT hongfangli optimalstableapproximationforthecauchyproblemforlaplaceequation AT fengzhou optimalstableapproximationforthecauchyproblemforlaplaceequation |