Conditioning of infinite Hankel matrices of finite rank

Let H be an infinite Hankel matrix with h(i+j-2) as its (i,j)-entry, h(k) = Sigma (i)(i=1) r(i)z(l)(k), k = 0, 1,...,\z(l)\ < 1, and r(l),z(l) <is an element of> C We derive upper bounds for the 2-condition number of H as fun ctions of n, r(l) and z(l), which show that the Hankel matrix H becomes wel l conditioned whenever the z's are close to the unit circle but not extreme ly close to each other. Numerical results which illustrate the theory are p rovided. (C) 2000 Elsevier Science B.V. All rights reserved.