Before revision:  Finally  we present two numerical examples to illustrate some practical application: the space-time evaluation of the fundamental solution of  linear 1D Schr\"odinger equation where we compare our method with the one based on \ell^1-norm minimization ; the hyper-reduction of a nonlinear diffusion partial differential equation in the framework of reduced basis method .
After revision:  Finally we present two numerical examples to illustrate some practical application: the space-time evaluation of the fundamental solution of linear 1D Schr\"odinger equation where we compare our method with the one based on \ell^1-norm minimization and the one relaying on the use of the non-negative least square method. Matlab codes related to the numerical examples and the algorithms described are provided .