Recovering ground truth singular values from randomly perturbed MIMO transfer functions

We show that analytic singular values of randomly perturbed matrices loose intersections and zero crossings compared to the unperturbed ground truth with probability one. As a result, the extracted singular values can significantly vary from the ground truth ones and may require a much high approximation order. To recover a solution closer to the ground truth, we extend a recent approach to extract ground truth analytic eigenvalues from a parahermitian matrix to the specific properties of analytic singular values. This method identifies segments where singular values are well separated, aligns them via partial reconstructions, and then performs an extraction based on the aligned segments. We demonstrate the approach in examples and ensemble simulations, thus highlighting its impact for applications that rely on solutions with low approximation order, and hence low implementation cost and latency.