  Eigensystem Realization Algorithm (ERA) is a data-driven approach for
subspace system identification and is widely used in many areas of engineering.
However, the computational cost of the ERA is dominated by a step that involves
the singular value decomposition (SVD) of a large, dense matrix with block
Hankel structure. This paper develops computationally efficient algorithms for
reducing the computational cost of the SVD step by using randomized subspace
iteration and exploiting the block Hankel structure of the matrix. We provide a
detailed analysis of the error in the identified system matrices and the
computational cost of the proposed algorithms. We demonstrate the accuracy and
computational benefits of our algorithms on two test problems: the first
involves a partial differential equation that models the cooling of steel
rails, and the second is an application from power systems engineering.
