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.

Galerkin approximation

Weak convergence

Laplace-Beltrami operator

Whittle-Matérn fields

Chebyshev polynomials

Compact Riemannian manifolds

Strong convergence

Gaussian random fields

Författare

Annika Lang

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Mike Pereira

Chalmers, Elektroteknik, System- och reglerteknik, Reglerteknik

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Chalmers, 2020-02-01 -- 2022-01-31.

Styrkeområden

Transport

Ämneskategorier

Beräkningsmatematik

Sannolikhetsteori och statistik

Matematisk analys

Fundament

Grundläggande vetenskaper

Relaterade dataset

arXiv:2107.02667 [math.NA] [dataset]

URI: https://arxiv.org/abs/2107.02667

Mer information

Skapat

2021-08-11