$\mathcal{H}$-inverses for RBF interpolation
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
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| _version_ | 1866914883811934208 |
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| author | Angleitner, Niklas Faustmann, Markus Melenk, Jens Markus |
| author_facet | Angleitner, Niklas Faustmann, Markus Melenk, Jens Markus |
| contents | We consider the interpolation problem for a class of radial basis functions (RBFs) that includes the classical polyharmonic splines (PHS). We show that the inverse of the system matrix for this interpolation problem can be approximated at an exponential rate in the block rank in the $\mathcal{H}$-matrix format if the block structure of the $\mathcal{H}$-matrix arises from a standard clustering algorithm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_05763 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | $\mathcal{H}$-inverses for RBF interpolation Angleitner, Niklas Faustmann, Markus Melenk, Jens Markus Numerical Analysis We consider the interpolation problem for a class of radial basis functions (RBFs) that includes the classical polyharmonic splines (PHS). We show that the inverse of the system matrix for this interpolation problem can be approximated at an exponential rate in the block rank in the $\mathcal{H}$-matrix format if the block structure of the $\mathcal{H}$-matrix arises from a standard clustering algorithm. |
| title | $\mathcal{H}$-inverses for RBF interpolation |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2109.05763 |