Inverses of Matern Covariances on Grids

26 Dec 2019Joseph Guinness

We conduct a theoretical and numerical study of the aliased spectral densities and inverse operators of Mat\'ern covariance functions on regular grids. We apply our results to provide clarity on the properties of a popular approximation based on stochastic partial differential equations; we find that it can approximate the aliased spectral density and the covariance operator well as the grid spacing goes to zero, but it does not provide increasingly accurate approximations to the inverse operator as the grid spacing goes to zero... (read more)

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