smerfs swMATH ID: 23987 Software Authors: Creasey, Peter E.; Lang, Annika Description: Fast generation of isotropic Gaussian random fields on the sphere. 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 grid in O(n2logn) . 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 url{https://github.com/pec27/smerfs} Homepage: https://github.com/pec27/smerfs Source Code: https://github.com/pec27/smerfs Keywords: Gaussian random fields; isotropic random fields; Gaussian Markov random fields; fast Fourier transform; efficient simulation Related Software: Healpix; TBSIM; AS 312; BETL; Stem; SuperLU; SPGL1; GET; RGeostats; GitHub; GMRFLib; DLMF Cited in: 8 Documents Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year Fast generation of isotropic Gaussian random fields on the sphere. Zbl 1386.60180Creasey, Peter E.; Lang, Annika 2018 all top 5 Cited by 21 Authors 2 Lang, Annika 2 Porcu, Emilio 1 Allard, Denis 1 Creasey, Peter E. 1 Cuevas, Francisco J. 1 Emery, Xavier 1 Freulon, Xavier 1 Furrer, Reinhard 1 Herrmann, Lukas 1 Jansson, Erik 1 Kirchner, Kristin 1 Kolyukhin, Dmitry Romanovich 1 Kovács, Mihály 1 Lantuéjoul, Christian 1 Le Gia, Quoc Thong 1 Minakov, Alexander 1 Renard, Didier 1 Schwab, Christoph 1 Sloan, Ian Hugh 1 Wang, Yuguang 1 Womersley, Robert S. all top 5 Cited in 7 Serials 2 Monte Carlo Methods and Applications 1 Statistics & Probability Letters 1 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 1 SIAM Journal on Scientific Computing 1 Applied and Computational Harmonic Analysis 1 Mathematical Geosciences 1 Statistics and Computing all top 5 Cited in 8 Fields 8 Probability theory and stochastic processes (60-XX) 4 Numerical analysis (65-XX) 3 Partial differential equations (35-XX) 3 Statistics (62-XX) 3 Geophysics (86-XX) 1 Special functions (33-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Astronomy and astrophysics (85-XX) Citations by Year