Initialization of the Circulant Embedding method to speed up the generation of Gaussian random fields

The Circulant Embedding Method (CEM) is a well known technique to generate stationary Gaussian Random Fields (GRF). main idea embed the covariance matrix in larger nested block circulant matrix, whose factorization can be rapidly computed thanks fast Fourier transform (FFT) algorithm. CEM requires extended at least positive semidefinite which proven case if enclosing domain sufficiently large, as by Theorem 2.3 [9] for cubic domains. In this paper, we generalize theorem of rectangular parallelepipeds. Then propose new initialization stage algorithm that makes it possible quickly jump size close one needed work. These estimates are based on fitting functions. Examples functions given Matérn family covariances. inspired our numerical simulations and theoretical work from [9]. parameters estimation done numerically. Several tests performed show efficiency proposed algorithms, both isotropic anisotropic