Unisolvence of Kansa collocation for elliptic equations by polyharmonic splines with random fictitious centers
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914964611006464 |
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| author | Mohammadi, Maryam Sommariva, Alvise Vianello, Marco |
| author_facet | Mohammadi, Maryam Sommariva, Alvise Vianello, Marco |
| contents | We make a further step in the unisolvence open problem for unsymmetric Kansa collocation, proving nonsingularity of Kansa matrices with polyharmonic splines and random fictitious centers, for second-order elliptic equations with mixed boundary conditions. We also show some numerical tests, where the fictitious centers are local random perturbations of predetermined collocation points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_03279 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Unisolvence of Kansa collocation for elliptic equations by polyharmonic splines with random fictitious centers Mohammadi, Maryam Sommariva, Alvise Vianello, Marco Numerical Analysis Analysis of PDEs We make a further step in the unisolvence open problem for unsymmetric Kansa collocation, proving nonsingularity of Kansa matrices with polyharmonic splines and random fictitious centers, for second-order elliptic equations with mixed boundary conditions. We also show some numerical tests, where the fictitious centers are local random perturbations of predetermined collocation points. |
| title | Unisolvence of Kansa collocation for elliptic equations by polyharmonic splines with random fictitious centers |
| topic | Numerical Analysis Analysis of PDEs |
| url | https://arxiv.org/abs/2410.03279 |