LUPOD: Collocation in POD via LU decomposition

A collocation method is developed for the (truncated) POD of a set of snapshots. In other words, POD computations are performed using only a set of collocation points, whose number is comparable to the number of retained modes, in a similar fashion as in collocation spectral methods. Intending to rely on simple ideas which, moreover, are consistent with the essence of POD, collocation points are computed via the LU decomposition with pivoting of the snapshot matrix. The new method is illustrated in simple applications in which POD is used as a data-processing method. The performance of the method is tested in the computationally efficient construction of reduced order models based on POD plus Galerkin projection for the complex Ginzburg-Landau equation in one and two space dimensions.