Convergence Rate of the Modified Landweber Method for Solving Inverse Potential Problems
In this paper, we present the convergence rate analysis of the modified Landweber method under logarithmic source condition for nonlinear ill-posed problems. The regularization parameter is chosen according to the discrepancy principle. The reconstructions of the shape of an unknown domain for an in...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/4/608 |
| _version_ | 1797570525067739136 |
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| author | Pornsarp Pornsawad Parada Sungcharoen Christine Böckmann |
| author_facet | Pornsarp Pornsawad Parada Sungcharoen Christine Böckmann |
| author_sort | Pornsarp Pornsawad |
| collection | DOAJ |
| description | In this paper, we present the convergence rate analysis of the modified Landweber method under logarithmic source condition for nonlinear ill-posed problems. The regularization parameter is chosen according to the discrepancy principle. The reconstructions of the shape of an unknown domain for an inverse potential problem by using the modified Landweber method are exhibited. |
| first_indexed | 2024-03-10T20:25:45Z |
| format | Article |
| id | doaj.art-05e30569d23a4356b69c9f77b68ce7f8 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T20:25:45Z |
| publishDate | 2020-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-05e30569d23a4356b69c9f77b68ce7f82023-11-19T21:46:01ZengMDPI AGMathematics2227-73902020-04-018460810.3390/math8040608Convergence Rate of the Modified Landweber Method for Solving Inverse Potential ProblemsPornsarp Pornsawad0Parada Sungcharoen1Christine Böckmann2Department of Mathematics, Faculty of Science, Silpakorn University, 6 Rachamakka Nai Rd., Nakhon Pathom 73000, ThailandDepartment of Mathematics, Faculty of Science, Silpakorn University, 6 Rachamakka Nai Rd., Nakhon Pathom 73000, ThailandInstitut für Mathematik, Universität Potsdam, Karl-Liebknecht-Str. 24-25, D-14476 Potsdam OT Golm, GermanyIn this paper, we present the convergence rate analysis of the modified Landweber method under logarithmic source condition for nonlinear ill-posed problems. The regularization parameter is chosen according to the discrepancy principle. The reconstructions of the shape of an unknown domain for an inverse potential problem by using the modified Landweber method are exhibited.https://www.mdpi.com/2227-7390/8/4/608nonlinear operatorregularizationmodified Landweber methoddiscrepancy principlelogarithmic source condition |
| spellingShingle | Pornsarp Pornsawad Parada Sungcharoen Christine Böckmann Convergence Rate of the Modified Landweber Method for Solving Inverse Potential Problems Mathematics nonlinear operator regularization modified Landweber method discrepancy principle logarithmic source condition |
| title | Convergence Rate of the Modified Landweber Method for Solving Inverse Potential Problems |
| title_full | Convergence Rate of the Modified Landweber Method for Solving Inverse Potential Problems |
| title_fullStr | Convergence Rate of the Modified Landweber Method for Solving Inverse Potential Problems |
| title_full_unstemmed | Convergence Rate of the Modified Landweber Method for Solving Inverse Potential Problems |
| title_short | Convergence Rate of the Modified Landweber Method for Solving Inverse Potential Problems |
| title_sort | convergence rate of the modified landweber method for solving inverse potential problems |
| topic | nonlinear operator regularization modified Landweber method discrepancy principle logarithmic source condition |
| url | https://www.mdpi.com/2227-7390/8/4/608 |
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