Unisolvence of unsymmetric Kansa collocation is still a substantially open problem. We prove that Kansa matrices with MultiQuadrics and Inverse MultiQuadrics for the Dirichlet problem of the Poisson equation are almost surely nonsingular, when the collocation points are chosen by any continuous random distribution in the domain interior and arbitrarily on its boundary.

翻译：非对称Kansa配置的唯一可解性仍是一个本质上的开放问题。我们证明，当配置点由域内任意连续随机分布选择、并在边界上任意选取时，基于MultiQuadric和Inverse MultiQuadric核函数的Kansa矩阵在处理泊松方程Dirichlet问题时几乎必然非奇异。