Smoothing windows for the synthesis of Gaussian stationary random fields using circulant matrix embedding

When generating Gaussian stationary random fields, a standard method based on circulant matrix embedding usually fails because some of the associated eigenvalues are negative. The eigenvalues can be shown to be nonnegative in the limit of increasing sample size. Computationally feasible large sample sizes, however, rarely lead to nonnegative eigenvalues. Another solution is to extend suitably the covariance Hannes Helgason would like to thank Department of Statistics and Operations Research, UNC, for its hospitality during his visit there when this work was undertaken. AMS Subject classification. Primary: 62M10, 62M40. Secondary: 60G10, 60G15, 60G60