  Singular value decomposition (SVD) has a crucial role in model order
reduction. It is often utilized in the offline stage to compute basis functions
that project the high-dimensional nonlinear problem into a low-dimensionsl
model which is, then, evaluated cheaply. It constitutes a building block for
many techniques such as e.g. Proper Orthogonal Decomposition and Dynamic Mode
Decomposition. The aim of this work is to provide efficient computation of the
basis functions via randomized matrix decompositions. This is possible due to
the randomized Singular Value Decomposition (rSVD) which is a fast and accurate
alternative of the SVD. Although this is considered as offline stage, this
computation may be extremely expensive and therefore the use of compressed
techniques drastically reduce its cost. Numerical examples show the
effectiveness of the method for both Proper Orthogonal Decomposition (POD) and
Dynamic Mode Decomposition (DMD).
