Conditioning of infinite Hankel matrices of finite rank

Let H be an infinite Hankel matrix with h as its (i,j)-entry, h = Σ rz, k = 0, 1,..., |z| <1, and r,z ∈ ℂ. We derive upper bounds for the 2-condition number of H as functions of n, r and z, which show that the Hankel matrix H becomes well conditioned whenever the z's are close to the unit circle but not extremely close to each other. Numerical results which illustrate the theory are provided.