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Efficient simulation of Gaussian Markov random fields by Chebyshev polynomial approximation

Abstract : This 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.
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Preprints, Working Papers, ...
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https://hal-mines-paristech.archives-ouvertes.fr/hal-02075386
Contributor : Nicolas Desassis <>
Submitted on : Thursday, March 21, 2019 - 1:28:52 PM
Last modification on : Thursday, September 24, 2020 - 4:34:26 PM

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  • HAL Id : hal-02075386, version 1
  • ARXIV : 1805.07423

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Mike Pereira, Nicolas Desassis. Efficient simulation of Gaussian Markov random fields by Chebyshev polynomial approximation. 2019. ⟨hal-02075386⟩

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