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Fast generation of isotropic Gaussian random fields on the sphere

Journal article
Authors P. E. Creasey
Annika Lang
Published in Monte Carlo Methods and Applications
Volume 24
Issue 1
Pages 1-11
ISSN 0929-9629
Publication year 2018
Published at Department of Mathematical Sciences
Pages 1-11
Language en
Keywords Gaussian random fields, isotropic random fields, Gaussian Markov random fields, fast Fourier, markov random-fields, light-scattering, models, Mathematics
Subject categories Mathematics


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 x n grid in 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

Page Manager: Webmaster|Last update: 9/11/2012

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