Nonsingularity of unsymmetric Kansa matrices: Random collocation by MultiQuadrics and Inverse MultiQuadrics
Roberto Cavoretto, Alessandra De Rossi, Francesco Dell’Accio, Alvise Sommariva, M. Vianello · Mathematics and Computers in Simulation · 2025
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.