A randomized balanced proper orthogonal decomposition technique

Abstract

In this paper, we consider the model reduction problem of large-scale linear systems, such as systems obtained through the discretization of partial differential equations. We propose a randomized proper orthogonal decomposition (RPOD∗) technique to obtain the reduced order model by perturbing the primal and adjoint system using Gaussian white noise. We show that computations required by RPOD∗ algorithm is orders of magnitude lower while its performance is much better than other state of the art algorithms. We also relate the RPOD∗ algorithm to Krylov subspace methods and show that it constitutes a randomized approach to computational linear algebra problems that utilize Krylov subspace methods.