Fast random field generation with $H$-matrices
This provides a fast, general alternative to circulant embedding for generating random fields, which is limited to regular grids and stationary covariances.
The authors use H-matrix technology to compute approximate square roots of covariance matrices in linear cost, enabling optimal-cost generation of normal and log-normal random fields on general point sets with rigorous error estimates.
We use the $H$-matrix technology to compute the approximate square root of a covariance matrix in linear cost. This allows us to generate normal and log-normal random fields on general point sets with optimal cost. We derive rigorous error estimates which show convergence of the method. Our approach requires only mild assumptions on the covariance function and on the point set. Therefore, it might be also a nice alternative to the circulant embedding approach which applies only to regular grids and stationary covariance functions.