Unisolvence of random Kansa collocation by Thin-Plate Splines for the Poisson equation
<|reference_start|>Unisolvence of random Kansa collocation by Thin-Plate Splines for the Poisson equation: 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.<|reference_end|>
@article{dell'accio2024unisolvence,
    title={Unisolvence of random Kansa collocation by Thin-Plate Splines for the
  Poisson equation},
    author={Francesco Dell'Accio, Alvise Sommariva, Marco Vianello},
    journal={arXiv preprint arXiv:2403.06646},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.06646},
    primaryClass={math.NA cs.NA}
}