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 ;
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 , the second example deals with the hyper-reduction of a partial differential equation modelling a nonlinear diffusion process in the framework of the reduced basis method. For both the examples we compare our method with the one based on \ell^1-norm minimization ;