$\mathcal{H}$-matrix approximability of inverses of discretizations of the fractional Laplacian
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arXiv
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| Format: | Preprint |
| Published: |
2018
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| _version_ | 1866929433412108288 |
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| author | Karkulik, Michael Melenk, Jens Markus |
| author_facet | Karkulik, Michael Melenk, Jens Markus |
| contents | The integral version of the fractional Laplacian on a bounded domain is discretized by a Galerkin approximation based on piecewise linear functions on a quasi-uniform mesh. We show that the inverse of the associated stiffness matrix can be approximated by blockwise low-rank matrices at an exponential rate in the block rank. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1808_04274 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | $\mathcal{H}$-matrix approximability of inverses of discretizations of the fractional Laplacian Karkulik, Michael Melenk, Jens Markus Numerical Analysis The integral version of the fractional Laplacian on a bounded domain is discretized by a Galerkin approximation based on piecewise linear functions on a quasi-uniform mesh. We show that the inverse of the associated stiffness matrix can be approximated by blockwise low-rank matrices at an exponential rate in the block rank. |
| title | $\mathcal{H}$-matrix approximability of inverses of discretizations of the fractional Laplacian |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/1808.04274 |