Unisolvence of random Kansa collocation by Thin-Plate Splines for the Poisson equation
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913285945688064 |
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| author | Dell'Accio, Francesco Sommariva, Alvise Vianello, Marco |
| author_facet | Dell'Accio, Francesco Sommariva, Alvise Vianello, Marco |
| contents | Existence of sufficient conditions for unisolvence of Kansa unsymmetric collocation for PDEs is still an open problem. In this paper we make a first step in this direction, proving that unsymmetric collocation matrices with Thin-Plate Splines for the 2D Poisson equation are almost surely nonsingular, when the discretization points are chosen randomly on domains with analytic boundary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_06646 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Unisolvence of random Kansa collocation by Thin-Plate Splines for the Poisson equation Dell'Accio, Francesco Sommariva, Alvise Vianello, Marco Numerical Analysis Existence of sufficient conditions for unisolvence of Kansa unsymmetric collocation for PDEs is still an open problem. In this paper we make a first step in this direction, proving that unsymmetric collocation matrices with Thin-Plate Splines for the 2D Poisson equation are almost surely nonsingular, when the discretization points are chosen randomly on domains with analytic boundary. |
| title | Unisolvence of random Kansa collocation by Thin-Plate Splines for the Poisson equation |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2403.06646 |