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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.07303 |
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| _version_ | 1866914831697707008 |
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| author | Qiu, Renjun Xu, Ming Qu, Wei |
| author_facet | Qiu, Renjun Xu, Ming Qu, Wei |
| contents | The Fredholm integral equations of the first kind is a typical ill-posed problem, so that it is usually difficult to obtain its analytical minimal-norm solution. This paper gives a closed-form minimal-norm solution for the degenerate kernel equations based on the H-HK formulation. Furthermore, it has been shown that the structure of solutions to degenerate kernel equations and matrix equations are consistent. Subsequently, the obtained results are extended to non-degenerate integral equations. Finally, the validity and applicability of the proposed method are demonstrated by some examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_07303 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Minimal-norm solution to the Fredholm integral equations of the first kind via the H-HK formulation Qiu, Renjun Xu, Ming Qu, Wei Numerical Analysis The Fredholm integral equations of the first kind is a typical ill-posed problem, so that it is usually difficult to obtain its analytical minimal-norm solution. This paper gives a closed-form minimal-norm solution for the degenerate kernel equations based on the H-HK formulation. Furthermore, it has been shown that the structure of solutions to degenerate kernel equations and matrix equations are consistent. Subsequently, the obtained results are extended to non-degenerate integral equations. Finally, the validity and applicability of the proposed method are demonstrated by some examples. |
| title | Minimal-norm solution to the Fredholm integral equations of the first kind via the H-HK formulation |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2406.07303 |