  In recent years there has been a considerable drive towards data-driven
analysis, discovery and control of dynamical systems. To this end, operator
theoretic methods, namely, Koopman operator methods have gained a lot of
interest. In general, the Koopman operator is obtained as a solution to a
least-squares problem, and as such, the Koopman operator can be expressed as a
closed-form solution that involves the computation of Moore-Penrose inverse of
a matrix. For high dimensional systems and also if the size of the obtained
data-set is large, the computation of the Moore-Penrose inverse becomes
computationally challenging. In this paper, we provide an algorithm for
computing the Koopman operator for high dimensional systems in a time-efficient
manner. We further demonstrate the efficacy of the proposed approach on two
different systems, namely a network of coupled oscillators (with state-space
dimension up to 2500) and IEEE 68 bus system (with state-space dimension 204
and up to 24,000 time-points).
