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 functions of n, r(l) and z(l), 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. (C) 2000 Elsevier Science B.V. All rights reserved.