A perturbation theorem for sensitivity analysis of SVD based algorithms

A perturbation theorem on perturbations in the singular-value-decomposition (SVD) truncated matrices and SVD truncated pseudoinverses is presented. The theorem can be applied for sensitivity analysis of any SVD-based algorithm that can be formulated in terms of SVD truncated matrices or/and SVD truncated pseudoinverses. The theorem is applied to an SVD-based polynomial method and an SVD-based direct matrix pencil method for estimating parameters of complex exponential signals in noise. With the theorem, it is simple to show that TLS-ESPRIT, Pro-ESPRIT, and the state space method are equivalent to the direct matrix pencil method to the first-order approximation.<>