The local SVD-FMM is a new numerical approximation method for the fast computation of matrix-vector products. The acronym SVD stands for singular value decomposition and FMM stands for fast multipole method. This MATLAB code was written for the numerical experiments in a related publication, which show the application of the method to numerical weather prediction data assimilation. However, the code can be adapted to a wider range of applications, provided that the matrices therein are generated in the way described in the Methods section at the bottom of the README file. More information can be found in the related publication.