Galerkin-Chebyshev approximation of Gaussian random fields on compact Riemannian manifolds
Preprint, 2021

A new numerical approximation method for a class of Gaussian random fields on compact Riemannian manifolds is introduced. This class of random fields is characterized by the Laplace-Beltrami operator on the manifold. A Galerkin approximation is combined with a polynomial approximation using Chebyshev series. This so-called Galerkin-Chebyshev approximation scheme yields efficient and generic sampling algorithms for Gaussian random fields on manifolds. Strong and weak orders of convergence for the Galerkin approximation and strong convergence orders for the Galerkin-Chebyshev approximation are shown and confirmed through numerical experiments.

Strong convergence

Weak convergence

Compact Riemannian manifolds

Laplace-Beltrami operator

Galerkin approximation

Chebyshev polynomials

Whittle-Matérn fields

Gaussian random fields


Annika Lang

University of Gothenburg

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Mike Pereira

University of Gothenburg

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Areas of Advance


Subject Categories

Computational Mathematics

Probability Theory and Statistics

Mathematical Analysis


Basic sciences

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9/9/2022 7