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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/2405.00529 |
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| _version_ | 1866917655108124672 |
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| author | Medvedev, Sergey Vaseva, Irina Fedoruk, Mikhail |
| author_facet | Medvedev, Sergey Vaseva, Irina Fedoruk, Mikhail |
| contents | We propose a high precision algorithm for solving the Gelfand-Levitan-Marchenko equation. The algorithm is based on the block version of the Toeplitz Inner-Bordering algorithm of Levinson's type. To approximate integrals, we use the high-precision one-sided and two-sided Gregory quadrature formulas. Also we use the Woodbury formula to construct a computational algorithm. This makes it possible to use the almost Toeplitz structure of the matrices for the fast calculations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_00529 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | High-Order Block Toeplitz Inner-Bordering method for solving the Gelfand-Levitan-Marchenko equation Medvedev, Sergey Vaseva, Irina Fedoruk, Mikhail Numerical Analysis We propose a high precision algorithm for solving the Gelfand-Levitan-Marchenko equation. The algorithm is based on the block version of the Toeplitz Inner-Bordering algorithm of Levinson's type. To approximate integrals, we use the high-precision one-sided and two-sided Gregory quadrature formulas. Also we use the Woodbury formula to construct a computational algorithm. This makes it possible to use the almost Toeplitz structure of the matrices for the fast calculations. |
| title | High-Order Block Toeplitz Inner-Bordering method for solving the Gelfand-Levitan-Marchenko equation |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2405.00529 |