https://hal-mines-paristech.archives-ouvertes.fr/hal-02075386Pereira, MikeMikePereiraMines Paris - PSL (École nationale supérieure des mines de Paris) - PSL - Université Paris sciences et lettresDesassis, NicolasNicolasDesassisGEOSCIENCES - Centre de Géosciences - Mines Paris - PSL (École nationale supérieure des mines de Paris) - PSL - Université Paris sciences et lettresEfficient simulation of Gaussian Markov random fields by Chebyshev polynomial approximationHAL CCSD2019[MATH.MATH-ST] Mathematics [math]/Statistics [math.ST]Desassis, Nicolas2019-03-21 13:28:522022-10-22 05:15:432019-03-21 13:28:52enPreprints, Working Papers, ...1This paper presents an algorithm to simulate Gaussian random vectors whose precision matrix can be expressed as a polynomial of a sparse matrix. This situation arises in particular when simulating Gaussian Markov random fields obtained by the discretization by finite elements of the solutions of some stochastic partial derivative equations. The proposed algorithm uses a Chebyshev polynomial approximation to compute simulated vectors with a linear complexity. This method is asymptotically exact as the approximation order grows. Criteria based on tests of the statistical properties of the produced vectors are derived to determine minimal orders of approximation.