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非对称配置法唯一可解性的充分条件存在性问题仍是一个公开难题。本文朝该方向迈出第一步，证明在解析边界区域上随机选取离散点时，二维泊松方程的薄板样条非对称配置矩阵几乎必然非奇异。