Efficient Algorithms for Eigensystem Realization Using Randomized SVD

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