  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.
