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Fast generation of isotropic Gaussian random fields on the sphere

Author

Listed:
  • Creasey Peter E.

    (Department of Physics and Astronomy, University of California, Riverside, CA 92507, USA)

  • Lang Annika

    (Department of Mathematical Sciences, Chalmers University of Technology & University of Gothenburg, 412 96Göteborg, Sweden)

Abstract

The efficient simulation of isotropic Gaussian random fields on the unit sphere is a task encountered frequently in numerical applications. A fast algorithm based on Markov properties and fast Fourier transforms in 1d is presented that generates samples on an n×n{n\times n} grid in O⁡(n2⁢log⁡n){\operatorname{O}(n^{2}\log n)}. Furthermore, an efficient method to set up the necessary conditional covariance matrices is derived and simulations demonstrate the performance of the algorithm. An open source implementation of the code has been made available at https://github.com/pec27/smerfs.

Suggested Citation

  • Creasey Peter E. & Lang Annika, 2018. "Fast generation of isotropic Gaussian random fields on the sphere," Monte Carlo Methods and Applications, De Gruyter, vol. 24(1), pages 1-11, March.
    • Handle: RePEc:bpj:mcmeap:v:24:y:2018:i:1:p:1-11:n:1
    DOI: 10.1515/mcma-2018-0001
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    References listed on IDEAS

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    1. Finn Lindgren & Håvard Rue & Johan Lindström, 2011. "An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(4), pages 423-498, September.
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