Fast approximation by periodic kernel-based lattice-point interpolation with application in uncertainty quantification

Kaarnioja, Vesa and Kazashi, Yoshihito and Kuo, Frances Y. and Nobile, Fabio and Sloan, Ian H. (2022) Fast approximation by periodic kernel-based lattice-point interpolation with application in uncertainty quantification. Numerische Mathematik, 150. pp. 33-77. ISSN 0029-599X (https://doi.org/10.1007/s00211-021-01242-3)

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Abstract

This paper deals with the kernel-based approximation of a multivariate periodic function by interpolation at the points of an integration lattice—a setting that, as pointed out by Zeng et al. (Monte Carlo and Quasi-Monte Carlo Methods 2004, Springer, New York, 2006) and Zeng et al. (Constr. Approx. 30: 529–555, 2009), allows fast evaluation by fast Fourier transform, so avoiding the need for a linear solver. The main contribution of the paper is the application to the approximation problem for uncertainty quantification of elliptic partial differential equations, with the diffusion coefficient given by a random field that is periodic in the stochastic variables, in the model proposed recently by Kaarnioja et al. (SIAM J Numer Anal 58(2): 1068–1091, 2020). The paper gives a full error analysis, and full details of the construction of lattices needed to ensure a good (but inevitably not optimal) rate of convergence and an error bound independent of dimension. Numerical experiments support the theory.

  • Item type:Article
    ID code:86503
    Dates:
    Date
    Event
    31 January 2022
    Published
    30 November 2021
    Published Online
    2 October 2021
    Accepted
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:16 Aug 2023 14:51
    Last modified:11 Nov 2024 14:01
    URI:https://strathprints.strath.ac.uk/id/eprint/86503
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