Unisolvence of random Kansa collocation by Thin-Plate Splines for the Poisson equation
Numerical Analysis
2024-03-28 v2 Numerical Analysis
Abstract
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.
Keywords
Cite
@article{arxiv.2403.06646,
title = {Unisolvence of random Kansa collocation by Thin-Plate Splines for the Poisson equation},
author = {Francesco Dell'Accio and Alvise Sommariva and Marco Vianello},
journal= {arXiv preprint arXiv:2403.06646},
year = {2024}
}