Perturbation theorem for sensitivity analysis of SVD based algorithms

We present a perturbation theorem on the perturbations in the SVD truncated matrices and the SVD truncated pseudoinverses. The theorem can be easily applied for sensitivity analysis of any SVD based algorithm that can be formulated in terms of the SVD truncated matrices or/and the SVD truncated pseudoinverses. The theorem is applied to a SVD based polynomial method and an SVD based matrix pencil method for estimating parameters of exponential signals in noise.