We make a further step in the unisolvence open problem for unsymmetric Kansa collocation, proving nonsingularity of Kansa matrices with polyharmonic splines and random fictitious centers, for second-order elliptic equations with mixed boundary conditions. We also show some numerical tests, where the fictitious centers are local random perturbations of predetermined collocation points.

翻译：我们在非对称Kansa配点法的解唯一性公开问题上取得了进一步进展，证明了对于具有混合边界条件的二阶椭圆方程，采用多调和样条函数和随机虚拟中心构造的Kansa矩阵是非奇异的。我们还展示了一些数值实验，其中虚拟中心是预设配点位置的局部随机扰动。