A Study of an Iteratively-Regularized Simplified Landweber Iteration for Nonlinear Inverse Problems in Hilbert Spaces
Lanweber-type methods are a well-known regularization methods to solve linear and nonlinear ill-posed problems. In this article, we consider a simplified form of Landweber method, say, an iteratively-regularized simplified Landweber iteration for solving nonlinear ill-posed problems. We study a deta...
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| Published in | Numerical functional analysis and optimization Vol. 44; no. 7; pp. 619 - 652 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Abingdon
Taylor & Francis
19.05.2023
Taylor & Francis Ltd |
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| Abstract | Lanweber-type methods are a well-known regularization methods to solve linear and nonlinear ill-posed problems. In this article, we consider a simplified form of Landweber method, say, an iteratively-regularized simplified Landweber iteration for solving nonlinear ill-posed problems. We study a detailed convergence analysis of the method under standard conditions on the nonlinearity and the rate of convergence under a Hölder-type source condition. Finally, numerical simulations are performed to validate the performance of the method. |
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| AbstractList | Lanweber-type methods are a well-known regularization methods to solve linear and nonlinear ill-posed problems. In this article, we consider a simplified form of Landweber method, say, an iteratively-regularized simplified Landweber iteration for solving nonlinear ill-posed problems. We study a detailed convergence analysis of the method under standard conditions on the nonlinearity and the rate of convergence under a Hölder-type source condition. Finally, numerical simulations are performed to validate the performance of the method. |
| Author | Dixit, Sharad Kumar |
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| Cites_doi | 10.1007/978-94-009-1740-8 10.1137/0730091 10.1007/s40819-017-0395-4 10.1515/cmam-2018-0165 10.1007/s002110050158 10.1007/s002459900081 10.1090/S0025-5718-08-02149-2 10.1515/cmam-2017-0045 10.1515/jiip.1996.4.5.381 10.1515/cmam-2016-0044 10.1088/0266-5611/5/4/007 10.1007/s002110050487 10.1515/9783110208276 10.1007/s00211-009-0275-x 10.1080/00036811.2017.1386785 10.1088/0266-5611/16/5/322 |
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| Snippet | Lanweber-type methods are a well-known regularization methods to solve linear and nonlinear ill-posed problems. In this article, we consider a simplified form... |
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| SubjectTerms | Convergence Hilbert space Ill posed problems Inverse problems Iterative methods Iterative regularization methods Morozov-type stopping rule nonlinear ill-posed operator equations nonlinear operators on Hilbert spaces Nonlinearity Primary Mathematics subject index: 47A52 Regularization Secondary Mathematics subject index: 65F22 source conditions |
| Title | A Study of an Iteratively-Regularized Simplified Landweber Iteration for Nonlinear Inverse Problems in Hilbert Spaces |
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