Fast QR factorization of Cauchy-like matrices

n this paper we present two fast numerical methods for computing the QR factorization of a Cauchy-like matrix C with data points lying on the real axis or on the unit circle in the complex plane. It is shown that the rows of the Q-factor of C give the eigenvectors of a rank structured matrix partially determined by some prescribed spectral data. This property establishes a basic connection between the computation of Q and the solution of an inverse eigenvalue problem for a rank structured matrix. Exploiting the structure of the associated inverse eigenvalue problem enables us to yield quadratic time algorithms using a linear memory space.