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 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.