Unisolvence of unsymmetric random Kansa collocation by Gaussians and other analytic RBF vanishing at infinity
<|reference_start|>Unisolvence of unsymmetric random Kansa collocation by Gaussians and other analytic RBF vanishing at infinity: We give a short proof of almost sure invertibility of unsymmetric random Kansa collocation matrices by a class of analytic RBF vanishing at infinity, for the Poisson equation with Dirichlet boundary conditions. Such a class includes popular Positive Definite instances such as Gaussians, Generalized Inverse MultiQuadrics and Matern RBF. The proof works on general domains in any dimension, with any distribution of boundary collocation points and any continuous random distribution of internal collocation points.<|reference_end|>
@article{sommariva2024unisolvence,
    title={Unisolvence of unsymmetric random Kansa collocation by Gaussians and
  other analytic RBF vanishing at infinity},
    author={Alvise Sommariva and Marco Vianello},
    journal={arXiv preprint arXiv:2405.18550},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.18550},
    primaryClass={math.NA cs.NA math.PR}
}