A study on multivariate interpolation by increasingly flat kernel functions

In this paper, we improve upon some observations made in recent papers on the subject of increasingly flat interpolation. We shall establish that the corresponding Lagrange functions converge both for a finite set of functions (collocation matrix) and also for kernels (Fredholm matrix). In our analysis, we use a finite Maclaurin expansion of a multivariate function with remainder and some additional matrix theoretic facts.