FMR: Fast randomized algorithms for covariance matrix computations

International audienceWe present an open-source library implementing fast algorithms for covari-ance matrices computations, e.g., randomized low-rank approximations (LRA) and fast multipole matrix multiplication (FMM). The library can be used to approximate square roots of low-rank covariance matrices in O(N 2) operations in SVD form using randomized LRA, instead of the standard O(N 3) cost. Low-rank covariance matrices given as kernels, e.g., Gaussian decay, evaluated on 3D grids can be decomposed in O(N) operations using the FMM. The performance of the library is illustrated on two examples: • Generation of Gaussian Random Fields (GRF) on large spatial grids • MultiDimensional Scaling (MDS) for the classification of species