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.

翻译：偏微分方程Kansa非对称配点法适定性的充分必要条件仍是一个开放问题。本文在该方向上迈出第一步，证明了当离散点随机选取于解析边界区域时，二维泊松方程中基于薄板样条的非对称配点矩阵几乎必然非奇异。