The Landweber Iterative Regularization Method for Solving the Cauchy Problem of the Modified Helmholtz Equation
In this manuscript, the Cauchy problem of the modified Helmholtz equation is researched. This inverse problem is a serious ill-posed problem. The classical Landweber iterative regularization method is designed to find the regularized solution of this inverse problem. The error estimations between th...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-06-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/6/1209 |
| _version_ | 1797481962088169472 |
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| author | Yong-Gang Chen Fan Yang Qian Ding |
| author_facet | Yong-Gang Chen Fan Yang Qian Ding |
| author_sort | Yong-Gang Chen |
| collection | DOAJ |
| description | In this manuscript, the Cauchy problem of the modified Helmholtz equation is researched. This inverse problem is a serious ill-posed problem. The classical Landweber iterative regularization method is designed to find the regularized solution of this inverse problem. The error estimations between the exact solution and the regularization solution are all obtained under the a priori and the a posteriori regularization parameter selection rule. The Landweber iterative regularization method can also be applied to solve the Cauchy problem of the modified Helmholtz equation on the spherically symmetric and cylindrically symmetric regions. |
| first_indexed | 2024-03-09T22:21:48Z |
| format | Article |
| id | doaj.art-1331a6333b0a4ce5af2b1a4996b3d845 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T22:21:48Z |
| publishDate | 2022-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-1331a6333b0a4ce5af2b1a4996b3d8452023-11-23T19:12:38ZengMDPI AGSymmetry2073-89942022-06-01146120910.3390/sym14061209The Landweber Iterative Regularization Method for Solving the Cauchy Problem of the Modified Helmholtz EquationYong-Gang Chen0Fan Yang1Qian Ding2School of Science, China University of Petroleum, Qindao 266580, ChinaSchool of Science, Lanzhou University of Technology, Lanzhou 730050, ChinaSchool of Science, Lanzhou University of Technology, Lanzhou 730050, ChinaIn this manuscript, the Cauchy problem of the modified Helmholtz equation is researched. This inverse problem is a serious ill-posed problem. The classical Landweber iterative regularization method is designed to find the regularized solution of this inverse problem. The error estimations between the exact solution and the regularization solution are all obtained under the a priori and the a posteriori regularization parameter selection rule. The Landweber iterative regularization method can also be applied to solve the Cauchy problem of the modified Helmholtz equation on the spherically symmetric and cylindrically symmetric regions.https://www.mdpi.com/2073-8994/14/6/1209modified Helmholtz equationill-posed problemerror estimationLandweber iterative method |
| spellingShingle | Yong-Gang Chen Fan Yang Qian Ding The Landweber Iterative Regularization Method for Solving the Cauchy Problem of the Modified Helmholtz Equation Symmetry modified Helmholtz equation ill-posed problem error estimation Landweber iterative method |
| title | The Landweber Iterative Regularization Method for Solving the Cauchy Problem of the Modified Helmholtz Equation |
| title_full | The Landweber Iterative Regularization Method for Solving the Cauchy Problem of the Modified Helmholtz Equation |
| title_fullStr | The Landweber Iterative Regularization Method for Solving the Cauchy Problem of the Modified Helmholtz Equation |
| title_full_unstemmed | The Landweber Iterative Regularization Method for Solving the Cauchy Problem of the Modified Helmholtz Equation |
| title_short | The Landweber Iterative Regularization Method for Solving the Cauchy Problem of the Modified Helmholtz Equation |
| title_sort | landweber iterative regularization method for solving the cauchy problem of the modified helmholtz equation |
| topic | modified Helmholtz equation ill-posed problem error estimation Landweber iterative method |
| url | https://www.mdpi.com/2073-8994/14/6/1209 |
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