We study randomized sketching methods for approximately solving least-squares problem with a general convex constraint. The quality of a least-squares approximation can be assessed in different ways: either in terms of the value of the quadratic objective function (cost approximation), or in terms of some distance measure between the approximate minimizer and the true minimizer (solution approx...

State covariances of linear systems satisfy certain constraints imposed by the underlying dynamics. These constraints dictate a particular structure of state covariances. However, sample covariances almost always fail to have the required structure. The renewed interest in using state covariances for estimating the power spectra of inputs gives rise to the approximation problem. In this note, t...