Positive Semidefinite Hankel Structured Low Rank Approximation using Vandermonde Decomposition

Abstract

In this paper, we propose a decomposition based method for solving the positive semidefinite Hankel structured low rank approximation (PHSLRA) of a given matrix. This problem is formulated as an unconstrained optimization problem using the Vandermonde decomposition of the positive semidefinite Hankel matrix. We use the alternating minimization method to solve this optimization problem. To the best of our knowledge, an alternating minimization method for solving PHSLRA has not been proposed in the literature. We apply the proposed algorithm on various numerical examples to illustrate the superiority of our approach.