Galerkin-Chebyshev approximation of Gaussian random fields on compact Riemannian manifolds
Journal article, 2023

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.

Whittle-Matérn fields

Compact Riemannian manifolds

Strong convergence

Laplace-Beltrami operator

Chebyshev polynomials

Galerkin approximation

Gaussian random fields

Weak convergence

Author

Annika Lang

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

University of Gothenburg

Mike Pereira

University of Gothenburg

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

BIT Numerical Mathematics

0006-3835 (ISSN) 1572-9125 (eISSN)

Vol. 63 4 51

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Areas of Advance

Transport

Subject Categories

Computational Mathematics

Probability Theory and Statistics

Mathematical Analysis

Roots

Basic sciences

DOI

10.1007/s10543-023-00986-8

More information

Latest update

1/17/2024