On constrained covariance extension problems

This paper aims at generalizing the well-known covariance extension problem by considering additional constraints. We first consider degree constraints, i.e., we require the interpolation function to have a given degree. Several results are offered for testing the feasibility via linear matrix inequalities. We then study the spectral zero assignment problem where the the interpolation function is constrained to have the zeros of the spectral factorization of the interpolation function at given locations. A fast iterative algorithm is provided for this problem. Numerical studies support that this algorithm works extremely well, although we are yet to offer a theoretical proof for the convergence of the algorithm.