Inverses of Matérn covariances on grids

Summary We conduct a study of the aliased spectral densities Matérn covariance functions on regular grid points, elucidating properties popular approximation based stochastic partial differential equations. While other researchers have shown that this can work well for function, we find it assigns too much power at high frequencies and does not provide increasingly accurate approximations to inverse as spacing goes zero, except in one-dimensional exponential case.