Local ultrametric approximation of graph distance based Laplacian diffusion
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915084576489472 |
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| author | Bradley, Patrick Erik |
| author_facet | Bradley, Patrick Erik |
| contents | The error estimation for eigenvalues and eigenvectors of a small positive symmetric perturbation on the spectrum of a graph Laplacian is related to Gauß hypergeometric functions. Based on this, a heuristic polynomial-time algorithm for finding an optimal locally ultrametric approximation of a graph-distance power Laplacian matrix via the Vietoris-Rips graph based on the graph distance function is proposed. In the end, the error in the solution to the graph Laplacian heat equation given by extension to a locally p-adic equation is estimated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20591 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Local ultrametric approximation of graph distance based Laplacian diffusion Bradley, Patrick Erik Analysis of PDEs Mathematical Physics 35P15 The error estimation for eigenvalues and eigenvectors of a small positive symmetric perturbation on the spectrum of a graph Laplacian is related to Gauß hypergeometric functions. Based on this, a heuristic polynomial-time algorithm for finding an optimal locally ultrametric approximation of a graph-distance power Laplacian matrix via the Vietoris-Rips graph based on the graph distance function is proposed. In the end, the error in the solution to the graph Laplacian heat equation given by extension to a locally p-adic equation is estimated. |
| title | Local ultrametric approximation of graph distance based Laplacian diffusion |
| topic | Analysis of PDEs Mathematical Physics 35P15 |
| url | https://arxiv.org/abs/2412.20591 |