In this paper, we investigate the complexity of the numerical construction of the Hankel structured low-rank
approximation (HSLRA) problem, and develop a family of algorithms to solve this problem. Briefly, HSLRA is the problem
of finding the closest (in some pre-defined norm) rank r approximation of a given Hankel matrix, which is also of Hankel
structure. Unlike many other methods described in the literature the family of algorithms we propose has the property of
guaranteed convergence
